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1
Kropf, Chahan [Verfasser] y Andreas [Akademischer Betreuer] Buchleitner. "Effective dynamics of disordered quantum systems". Freiburg : Universität, 2017. http://d-nb.info/1138922528/34.
2
Mukhopadhyay, Ranjan Goodstein David L. "Quantum phase transitions in disordered Bose systems /". Diss., Pasadena, Calif. : California Institute of Technology, 1998. http://resolver.caltech.edu/CaltechETD:etd-02022007-104407.
3
Schwab, David Jason. "Topics in biophysics and disordered quantum systems". Diss., Restricted to subscribing institutions, 2009. http://proquest.umi.com/pqdweb?did=1971489301&sid=1&Fmt=2&clientId=1564&RQT=309&VName=PQD.
4
Nahm, In Hyun. "Two dimensional disordered electron systems". Thesis, University of Southampton, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.330179.
5
Goswami, Pallab. "Quantum phase transitions in dissipative and disordered systems". Diss., Restricted to subscribing institutions, 2008. http://proquest.umi.com/pqdweb?did=1680035131&sid=4&Fmt=2&clientId=1564&RQT=309&VName=PQD.
6
Ros, Valentina. "Aspects of localization in disordered many-body quantum systems". Doctoral thesis, SISSA, 2016. http://hdl.handle.net/20.500.11767/4906.
Resumen
For a quantum system to be permanently out-of-equilibrium, some non-trivial mechanism must be at play, to counteract the general tendency of entropy increase and flow toward equilibration. Among the possible ways to protect a system against local thermalization, the phenomenon of localization induced by quenched disorder appears to be one of the most promising. Although the problem of localization was introduced almost sixty years ago, its many-body version is still partly unresolved, despite the recent theoretical effort to
tackle it. In this thesis we address a few aspects of the localized phase, mainly focusing on the interacting case. A large part of the thesis is devoted to investigating the underlying “integrable” structure of many-body localized systems, i.e., the existence of non-trivial conservation laws that prevent ergodicity and thermalization. In particular, we show that such conserved operators can be explicitly constructed by dressing perturbatively the non-interacting conserved quantities, in a procedure that converges when scattering processes are weak enough. This is reminiscent of the quasiparticle theory in Fermi liquids, although in the disordered case the construction extends to the full many-body energy spectrum, and it results in operators that are exactly conserved. As an example of how to use the constructive recipe for the conserved quantities, we compute the long-time limit of an order parameter for the MBL phase in antiferromagnetic spin systems. Similar analytical tools as the ones exploited for the construction of the conserved operators are then applied to the problem of the stability of single-particle localization with respect to the coupling to a finite bath. In this context, we identify a quantum-Zeno-type effect, whereby the bath unexpectedly enhances the particle’s localization. In the final part of the thesis, we discuss several mechanisms by which thermal fluctuations may influence the spatial localization of excitations in interacting many-body states.
7
Bapst, Victor. "Quantum disordered systems : from adiabatic computation to localization problems". Paris 6, 2013. http://www.theses.fr/2013PA066351.
Resumen
This thesis is devoted to the study of quantum disordered systems, with applications ranging from Anderson localization to quantum computation. We focus on models defined on tree graphs, or on their finite size regularizations: random graphs. This allows for exact mean-field approaches. The first part deals with the Anderson localization problem. We obtain analytical results on the fast decay of the density of states near its edge (the \textit{Lifshitz tail regime}), as well as a rigorous estimate on the localization threshold in the large connectivity limit. We also study the analogous model for bosons. In a second part, we study the quantum adiabatic algorithm and obtain results on its efficiency in solving a realistic problem, the coloring one, as well as analytical predictions for its performance in solving more generic problems. Finally, we also discuss how this quantum algorithm compares with a classical approximation for itCette thèse est consacrée à l'étude de systèmes désordonnés quantiques, avec des applications allant de la localisation d'Anderson au calcul quantique. Nous nous concentrons sur des modèles définis sur des arbres, ou sur leurs régularisations de taille finie: les graphes aléatoires. Sur ces modèles, les approches de champ moyen sont exactes. La première partie s'intéresse au problème de la localisation d'Anderson. Nous obtenons des résultats analytiques sur la décroissance rapide de la densité d'états près de son bord (le régime de la queue de Lifshitz), ainsi qu'une estimation rigoureuse du seuil de localisation dans la limite de grande connectivité. Nous étudions aussi le problème analogue dans le cas de bosons. Dans une second partie, nous étudions l'algorithme adiabatique quantique et obtenons des résultats sur sa capacité à résoudre un problème réaliste, celui du coloriage, ainsi que des prédictions analytiques sur ses performances pour résoudre des problèmes plus généraux. Enfin, nous discutons également comment cet algorithme quantique se compare à une approximation classique de ce dernier
8
Ludwig, Thomas. "Interaction and phase relaxation in disordered nanowires and quantum hall systems". Karlsruhe : FZKA, 2006. http://bibliothek.fzk.de/zb/berichte/FZKA7204.pdf.
9
Semerjian, Guilhem. "Mean-field disordered systems : glasses and optimization problems, classical and quantum". Habilitation à diriger des recherches, Ecole Normale Supérieure de Paris - ENS Paris, 2013. http://tel.archives-ouvertes.fr/tel-00785924.
Resumen
Ce mémoire présente mes activités de recherche dans le domaine de la mécanique statistique des systèmes désordonnés, en particulier sur les modèles de champ moyen à connectivité finie. Ces modèles présentent de nombreuses transitions de phase dans la limite thermodynamique, avec des applications tant pour la physique des verres que pour leurs liens avec des problèmes d'optimisation de l'informatique théorique. Leur comportement sous l'effet de fluctuations quantiques est aussi discuté, en lien avec des perspectives de calcul quantique.
10
Grabsch, Aurélien. "Random Matrix Theory in Statistical Physics : Quantum Scattering and Disordered Systems". Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLS142/document.
Resumen
La théorie des matrices aléatoires a des applications dans des domaines variés : mathématiques, physique, finance, ... En physique, le concept de matrices aléatoires a été utilisé pour l'étude du transport électronique dans des structures mésoscopiques, de systèmes désordonnés, de l'intrication quantique, de modèles d'interfaces 1D fluctuantes en physique statistique, des atomes froids, ... Dans cette thèse, on s'intéresse au transport AC cohérent dans un point quantique, à des propriétés d'interfaces fluctuantes 1D sur un substrat et aux propriétés topologiques de fils quantiques multicanaux. La première partie commence par une introduction générale a la théorie des matrices aléatoires ainsi qu'a la principale méthode utilisée dans cette thèse : le gaz de Coulomb. Cette technique permet entre autres d'étudier la distribution d'observables qui prennent la forme de statistiques linéaires des valeurs propres, qui représentent beaucoup de quantités physiques pertinentes. Cette méthode est ensuite appliquée à des exemples concrets pour étudier le transport cohérent et les problèmes d'interfaces fluctuantes en physique statistique. La seconde partie se concentre sur un modèle de fil désordonné : l'équation de Dirac multicanale avec masse aléatoire. Nous étendons le puissant formalisme utilisé pour l'étude de systèmes unidimensionnels au cas quasi-1D, et établissons une connexion avec un modèle de matrices aléatoires. Nous utilisons ce résultat pour obtenir la densité d'états et les propriétés de localisation. Nous montrons également que ce système présente une série de transitions de phases topologiques (changement d'un nombre quantique de nature topologique, sans changement de symétrie), contrôlées par le désordreRandom matrix theory has applications in various fields: mathematics, physics, finance, ... In physics, the concept of random matrices has been used to study the electronic transport in mesoscopic structures, disordered systems, quantum entanglement, interface models in statistical physics, cold atoms, ... In this thesis, we study coherent AC transport in a quantum dot, properties of fluctuating 1D interfaces on a substrate and topological properties of multichannel quantum wires. The first part gives a general introduction to random matrices and to the main method used in this thesis: the Coulomb gas. This technique allows to study the distribution of observables which take the form of linear statistics of the eigenvalues. These linear statistics represent many relevant physical observables, in different contexts. This method is then applied to study concrete examples in coherent transport and fluctuating interfaces in statistical physics. The second part focuses on a model of disordered wires: the multichannel Dirac equation with a random mass. We present an extension of the powerful methods used for one dimensional system to this quasi-1D situation, and establish a link with a random matrix model. From this result, we extract the density of states and the localization properties of the system. Finally, we show that this system exhibits a series of topological phase transitions (change of a quantum number of topological nature, without changing the symmetries), driven by the disorder
11
Goldsborough, Andrew M. "Tensor networks and geometry for the modelling of disordered quantum many-body systems". Thesis, University of Warwick, 2015. http://wrap.warwick.ac.uk/70003/.
Resumen
Tensor networks provide a powerful and elegant approach to quantum manybody simulation. The simplest example is the density matrix renormalisation group (DMRG), which is based on the variational update of a matrix product state (MPS). It has proved to be the most accurate approach for the numerical study of strongly correlated one dimensional systems. We use DMRG to study the one dimensional disordered Bose-Hubbard model at fillings N=L = 1=2, 1 and 2 and show that the whole phase diagram for each can be successfully obtained by analysing entanglement properties alone. We �nd that the average entanglement is insufficient to accurately locate all of the phases, however using the standard error on the mean we are able to construct a phase diagram that is consistent with previous studies. It has recently been shown that there is a connection between the geometry of tensor networks and the entanglement and correlation properties that it can encode, which is a generalisation of the so called area law for entanglement entropy. This suggests that whilst gapped quantum systems can be accurately modeled using an MPS, a tensor network with a holographic geometry is natural to capture the logarithmic entanglement scaling and power law decaying correlation functions of critical systems. We create an algorithm for the disordered Heisenberg Hamiltonian that self assembles a tensor network based on the disorder in the couplings. The geometry created is that of a disordered tree tensor network (TTN) that when averaged has the holographic properties characteristic of critical systems. We continue the analysis of holographic tensor network geometry by considering the average length of leaf-to-leaf paths in various tree graphs, which is related to two-point correlation functions in tensor networks. For regular, complete trees we analytically calculate the average path length and all statistical moments, and generalise it for any splitting number. We then turn to the Catalan trees, which is the set of unique binary trees with n vertices, as it has a similar geometry to the disordered TTNs. We calculate the average depth of a leaf and show that it is equal to the average path length. We compare these analytic results with the structures found in the TTN and randomly constructed trees to show that the renormalisation involved in the TTN algorithm is crucial in the selection of the tree structure.
12
Schneider, Michael Peter. "A theoretical framework for waveguide quantum electrodynamics and its application in disordered systems". Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät, 2016. http://dx.doi.org/10.18452/17415.
Resumen
Wellenleiter Quantenelektrodynamik (Wellenleiter QED) ist ein wichtiger Baustein in vielen zukünftigen, auf Quantenmechanik basierenden Technologien wie z.B. Quantencomputer. Ein typisches Modellsystem besteht aus einem Zwei-Niveau-System (two level system, TLS), das an einen eindimensionalen Wellenleiter gekoppelt wurde. Der Wellenleiter ist dabei durch eine Dispersionsrelation charakterisiert und kann unter anderem Bandkanten enthalten. Wir haben in der Dissertation einen neuartigen Zugang zur Wellenleiter QED präsentiert. Dieser Zugang basiert auf der Quantenfeldtheorie und ermöglicht die Berechnung Greenscher Funktionen im ein- und zwei-Anregungs Unterraum. Diese Greenschen Funktionen wurden benutzt um die Streumatrix und die spektrale Dichte in beiden Unterräumen zu berechnen. Desweiteren konnten wir mit Hilfe von Feynman-Diagrammen die physikalischen Prozesse in der Störungsreihe der Greenschen Funktionen identifizieren. Dies war besonders im zwei-Anregungs-Unterraum von Nutzen. In diesem Fall verhält sich das System nichtlinear, da das TLS nur eine Anregung absorbieren kann. Dadurch werden Effekte induziert wie photon bunching und die effiziente Anregung eines gebundenen Atom-Photon Zustandes. Es war uns möglich diese Effekte in der Störungsreihe der Greenschen Funktion wieder zu finden. Desweiteren haben wir die Greenschen Funktionen im Orts-Zeit-Raum benutzt um ein- und zwei-Photon-Wellenpakete zu propagieren. Es hat sich herausgestellt dass das Verhältnis von Pulsbreite zur spontanten Emissions-zeit sowohl das Streuverhalten als auch die maximale Anregung des TLS bestimmt. Letztendlich haben wir den Einfluss von Unordnung im Wellenleiter auf das Zerfallsverhalten des TLS untersucht. Wir haben entdeckt dass der gebundene Atom-Photon Zustand instabil wird sobald die Unordnung einen kritischen Wert erreicht. Darüberhinaus haben wir eine spezielle Klasse Feynman Diagramme identifiziert, die dem Zerfall eine nichtmarkovsche Dynamik verleihen.Waveguide quantum electrodynamics (waveguide QED) can be considered as a building block for many prospective technologies like quantum computing. A prototypical system consists of a two-level system (TLS) coupled to a one-dimensional waveguide. The waveguide is characterized by its dispersion relation and can also feature a band edge/slow-light regime. In this thesis we have presented a new theoretical framework for waveguide QED, based on quantum field theory. The framework provides the Green''s functions of the system in the single- and two-excitation sectors for an arbitrary dispersion relation. We have calculated the scattering matrix and the spectral density in both sectors. Furthermore, we have also represented the Green''s functions in the form of Feynman diagrams, from which we can identify the underlying physical processes. A special property of the system is that it behaves nonlinear in the case of two or more photons. This is rooted in the structure of the TLS, which can at most absorb one excitation. The nonlinearity leads to two effects: photon bunching and the efficient excitation of an atom-photon bound state. We have found both effects within our framework and we were able to assign them individual terms in the perturbation series of the Green''s function. Furthermore, we have used the Green''s function in space-time domain to propagate Gaussian one- and two-photon wavepackets. Here, we have identified the ratio of the pulsewidth and the spontaneous emission time as the parameter which governs both the scattering behavior of the photons and the maximal TLS excitation. Eventually, we have investigated the effects of disorder in the waveguide on the decay properties of the TLS. We have found here that the atom-photon bound state is stable for small disorder, but breaks down at sufficiently strong disorder. Furthermore, we have identified a special class of diagrams which render the system non-Markovian even for energies far away from the band edge.
13
Yan, Mi. "Quantum Dynamics of Strongly-Interacting Bosons in Optical Lattices with Disorder". Diss., Virginia Tech, 2019. http://hdl.handle.net/10919/87432.
Resumen
Ultracold atoms in optical lattices offer an important tool for studying dynamics in many-body interacting systems in a pristine environment. This thesis focuses on three theoretical works motivated by recent optical lattice experiments. In the first, we theoretically study the center of mass dynamics of states derived from the disordered Bose-Hubbard model in a trapping potential. We find that the edge states in the trap allow center of mass motion even with insulating states in the center. We identify short and long-time mechanisms for edge state transport in insulating phases. We also argue that the center of mass velocity can aid in identifying a Bose-glass phase. Our zero temperature results offer important insights into mechanisms of transport of atoms in trapped optical lattices while putting bounds on center of mass dynamics expected at non-zero temperature.
In the second work, we study the domain wall expansion dynamics of strongly interacting bosons in 2D optical lattices with disorder in a recent experiment {[}J.-y. Choi et al., Science 352, 1547 (2016)]. We show that Gutzwiller mean-field theory (GMFT) captures the main experimental observations, which are a result of the competition between disorder and interactions. Our findings highlight the difficulty in distinguishing glassy dynamics, which can be captured by GMFT, and many-body localization, which cannot be captured by GMFT, and indicate the need for further experimental studies of this system.
The last work features our study of phase diagrams of the 2D Bose-Hubbard model in an optical lattice with synthetic spin-orbit coupling. We investigate the transitions between superfluids with different phase patterns, which may be detected by measuring the spin-dependent momentum distribution.Ph. D.
Ultracold atoms in optical lattices, a periodic potential generated by laser beams, offer an important tool for quantum simulations in a pristine environment. Motivated by recent optical lattice experiments with the implementation of disorder and synthetic spin-orbit coupling, we utilize Gutzwiller mean-field theory (GMFT) to study the dynamics of disordered state in an optical lattice under the sudden shift of the harmonic trap, the domain wall expansion of strongly interacting bosons in 2D lattices with disorder, and spin-orbit-driven transitions in the Bose-Hubbard model. We argue that the center of mass velocity can aid in identifying a Bose-glass phase. Our findings show that evidence for many-body localization claimed in experiments [J.-y. Choi et al., Science 352, 1547 (2016)] must lie in the differences between GMFT and experiments. We also find that strong spin-orbit coupling alone can generate superfluids with finite momentum and staggered phase patterns.
14
Karevski, Dragi. "Ising Quantum Chains". Habilitation à diriger des recherches, Université Henri Poincaré - Nancy I, 2005. http://tel.archives-ouvertes.fr/hal-00113500.
Resumen
The aim of this article is to give a pedagogical introduction to the exact equilibrium and nonequilibrium properties of free fermionic quantum spin chains. In a first part we present in full details the canonical diagonalisation procedure and review quickly the equilibrium dynamical properties. The phase diagram is analysed and possible phase transitions are discussed. The two next chapters are concerned with the effect of aperiodicity and quenched disorder on the critical properties of the quantum chain. The remaining part is devoted to the nonequilibrium dynamical behaviour of such quantum chains relaxing from a nonequilibrium pure initial state. In particular, a special attention is made on the relaxation of transverse magnetization. Two-time linear response functions and correlation functions are also considered, giving insights on the nature of the final nonequilibrium stationnary state. The possibility of aging is also discussed.
15
Dupont, Maxime. "Dynamics and disorder in quantum antiferromagnets". Thesis, Toulouse 3, 2018. http://www.theses.fr/2018TOU30092/document.
Resumen
La physique de la matière condensée, et notamment les systèmes fortement corrélés, amènent à des problèmes parmi les plus stimulants et difficiles de la physique moderne. Dans ces systèmes, les interactions à plusieurs corps et les corrélations entre les particules quantiques ne peuvent être négligées, sinon, les modèles échoueraient simplement à capturer les mécanismes physiques en jeu et les phénomènes qui en découlent. En particulier, le travail présenté dans ce manuscrit traite du magnétisme quantique et aborde plusieurs questions distinctes à l'aide d'approches computationnelles et méthodes numériques à l'état de l'art. Les effets conjoints du désordre (i.e. impuretés) et des interactions sont étudiés concernant un matériau magnétique spécifique : plutôt qu'une phase de la matière dite localisée, attendue à fort champ magnétique, une phase ordonnée induite par le désordre lui-même est mise en lumière, avec une réapparition inattendue de la cohérence quantique dans ledit composé. Par ailleurs, la réponse dynamique d'aimants quantiques à une perturbation externe, comme celle mesurée dans des expériences de résonance magnétique nucléaire ou de diffusion inélastique de neutrons est étudiéeCondensed matter physics, and especially strongly correlated systems provide some of the most challenging problems of modern physics. In these systems, the many-body interactions and correlations between quantum particles cannot be neglected; otherwise, the models would simply fail to capture the relevant physics at play and phenomena ensuing. In particular, the work presented in this manuscript deals with quantum magnetism and addresses several distinct questions through computational approaches and state-of-the-art numerical methods. The interplay between disorder (i.e. impurities) and interactions is studied regarding a specific magnetic compound, where instead of the expected many-body localized phase at high magnetic fields, a novel disorder-induced ordered state of matter is found, with a resurgence of quantum coherence. Furthermore, the dynamical response of quantum magnets to an external perturbation, such as it is accessed and measured in nuclear magnetic resonance and inelastic neutron scattering experiments is investigated
16
Ludwig, Thomas [Verfasser]. "Interaction and phase relaxation in disordered nanowires and quantum hall systems / Forschungszentrum Karlsruhe GmbH, Karlsruhe. Thomas Ludwig". Karlsruhe : FZKA, 2006. http://d-nb.info/980147859/34.
17
Stellin, Filippo. "Anderson localization in interacting quantum systems". Thesis, Université de Paris (2019-....), 2020. http://www.theses.fr/2020UNIP7004.
Resumen
Dans cette thèse nous étudions au niveau théorique le comportement des particules quantiques (électrons, atomes, photons, etc.) se mouvant dans un milieu désordonné et sujets à la localisation d’Anderson. Pour des particules non interagissantes, le spectre de l’énergie peut posséder un ou plus points critiques, où les fonctions d’onde étendues deviennent localisées, en donnant lieu à une transition de phase métal-isolant connue comme Transition d’Anderson.Une question fondamentale est si et comment les transitions d’Anderson survivent dans des systèmesquantiques interagissants. Dans cet ouvrage, nous étudions un modèle simple décrivant le cas de deux particules dans un réseau désordonné et sujettes à des interactions mutuelles à courte portée. En combinant des simulations numériques sur une grande échelle avec des techniques à la fonction de Green, nous montrons que les transitions d’Anderson à deux particules se produisent en trois dimensions et explorons le diagramme de phase dans l’espace de l’énergie, du désordre et de l’interaction.Cette dernière présente une structure riche, caractérisée par un double renfoncement de la limite de phase, engendrée par la compétition entre les états de diffusion et les états liés de la paire. Nous prouvons aussi que les annonces précédentes concernant l’apparition de transitions d’Anderson en deux dimensions étaient essentiellement dues à des effets de taille finie.Un deuxième problème que nous abordons dans cette thèse est celui de l’occurrence de transitions métal-isolant en deux dimensions pour une particule en la présence d’un potentiel spatialement corrélé et sujette à des interactions spin-orbite, modélisées par les couplages Rashba-Dresselhaus. On éclaire que, indépendamment des propriétés du désordre, il y a un régime où l’énergie critique dépend linéairement du paramètre de désordre. La pente et l’intercepte sont étudiées en voisinage du point de symétrie spin-hélice persistant, dans lequel la symétrie SU(2) est restaurée et la transition métal-isolant disparaîtIn this thesis we theoretically investigate the behaviour of quantum particles (electrons, atoms, photons, etc.) moving in a random medium and undergoing Anderson localization. For noninteractingparticles, the energy spectrum can possess one or more critical points, where the nature of the single-particle wavefunctions changes from extended to localized leading to a undergoes a metal-insulator phase transition, also known as Anderson transition.A fundamental question is whether and how Anderson transitions survive in interacting quantum systems. Here we study a minimal model of two particles moving in a disordered lattice and subject to short-range mutual interactions. By combining large-scale numerics with Green’s functions techniques, we show that two-particle Anderson transitions do occur in three dimensions and explore the phase diagram in the space of energy, disorder and interaction strength. The latter presents a rich structure, characterized by a doubly reentrant behavior, caused by the competition between scattering and bound states of the pair. We also show that previous claims of 2D Anderson transitions of the pair are essentially due to finite-size effects.A second problem that we address in this thesis is the occurrence of 2D metal-insulator transitions for a single particle in the presence of a spatially correlated potential and subject to spin-orbit interactions, described by Rashba-Dresselhaus couplings. We illustrate that, irrespective of the properties of the disorder, there is a regime where the critical energy depends linearly on the disorder strength. The slope and the intercept are studied in the vicinity of the spin-helix point, where the SU(2) symmetry is restored and the 2D metal-insulator transition disappears
18
De, Tomasi Giuseppe [Verfasser], Markus [Gutachter] Heyl, Roland [Gutachter] Ketzmerick, Roderich [Gutachter] Moessner y Frank [Gutachter] Pollmann. "Characterization of ergodicity breaking in disordered quantum systems / Giuseppe De Tomasi ; Gutachter: Markus Heyl, Roland Ketzmerick, Roderich Moessner, Frank Pollmann". Dresden : Technische Universität Dresden, 2018. http://d-nb.info/1226813801/34.
19
Schneider, Michael Peter [Verfasser], Kurt [Akademischer Betreuer] Busch, Alejandro [Akademischer Betreuer] Saenz y Alexander [Akademischer Betreuer] Shnirman. "A theoretical framework for waveguide quantum electrodynamics and its application in disordered systems / Michael Peter Schneider. Gutachter: Kurt Busch ; Alejandro Saenz ; Alexander Shnirman". Berlin : Mathematisch-Naturwissenschaftliche Fakultät, 2016. http://d-nb.info/1081715995/34.
20
Meier, Hannes. "Phase transitions in novel superfluids and systems with correlated disorder". Doctoral thesis, KTH, Statistisk fysik, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-160929.
Resumen
Condensed matter systems undergoing phase transitions rarely allow exact solutions. The presence of disorder renders the situation even worse but collective Monte Carlo methods and parallel algorithms allow numerical descriptions. This thesis considers classical phase transitions in disordered spin systems in general and in effective models of superfluids with disorder and novel interactions in particular. Quantum phase transitions are considered via a quantum to classical mapping. Central questions are if the presence of defects changes universal properties and what qualitative implications follow for experiments. Common to the cases considered is that the disorder maps out correlated structures. All results are obtained using large-scale Monte Carlo simulations of effective models capturing the relevant degrees of freedom at the transition. Considering a model system for superflow aided by a defect network, we find that the onset properties are significantly altered compared to the $\lambda$-transition in $^{4}$He. This has qualitative implications on expected experimental signatures in a defect supersolid scenario. For the Bose glass to superfluid quantum phase transition in 2D we determine the quantum correlation time by an anisotropic finite size scaling approach. Without a priori assumptions on critical parameters, we find the critical exponent $z=1.8 \pm 0.05$ contradicting the long standing result $z=d$. Using a 3D effective model for multi-band type-1.5 superconductors we find that these systems possibly feature a strong first order vortex-driven phase transition. Despite its short-range nature details of the interaction are shown to play an important role. Phase transitions in disordered spin models exposed to correlated defect structures obtained via rapid quenches of critical loop and spin models are investigated. On long length scales the correlations are shown to decay algebraically. The decay exponents are expressed through known critical exponents of the disorder generating models. For cases where the disorder correlations imply the existence of a new long-range-disorder fixed point we determine the critical exponents of the disordered systems via finite size scaling methods of Monte Carlo data and find good agreement with theoretical expectations.QC 20150306
21
Bourlet, Nicolas. "Dissipative phase transition and duality of the Josephson junction Absence of a dissipative quantum phase transition in Josephson junctions Microscopic charged fuctuators as a limit to the coherence of disordered superconductor devices". Thesis, université Paris-Saclay, 2020. https://tel.archives-ouvertes.fr/tel-03180143.
Resumen
Plus d'un siècle après sa découverte, la supraconductivité est aujourd'hui utilisée dans de nombreuses applications. Une de ces applications est l'électronique supraconductrice, et un des blocs de base de celle-ci est la jonction Josephson. Cet élément a permis la réalisation de circuits électroniques dans le régime quantique et il a aidé à redéfinir la valeur du Volt dans le Système International d'unité à partir d'effets quantiques. Ces dernières années, beaucoup de temps et d'efforts sont dépensés pour améliorer ce composant et les circuits l'intégrant dans l'objectif de réaliser de meilleurs circuits à bit quantique pour l'informatique quantique. Il est donc normal de se demander si l'existence de ces circuits de pointe contenant des jonctions Josephson et des supraconducteurs conventionnels indique une maîtrise parfaite de ceux-ci. Dans ce travail de thèse, nous montrons que cela n'est pas entièrement le cas via l'exploration de deux circuits quantiques supraconducteurs pour lesquels des études plus approfondies sont nécessaires. Le premier concerne la jonction Josephson elle-même et son comportement lorsqu'elle est mise en présence d'un environnement électromagnétique. En effet, il a été prédit il y a presque 40 ans qu'une jonction Josephson deviendrait isolante lorsqu'elle est connectée à une résistance plus grande que Rq=h/4e²≈6.45 kΩ. Nous ne trouvons aucunes traces de cet état isolant dans nos expériences qui mesurent l'admittance de jonctions Josephson connectées en parallèle de résistance de valeur R>Rq. Le deuxième circuit explore le composant supposé dual de la jonction Josephson, la jonction à sauts de phase quantique, qui consiste en un nanofil de supraconducteur fortement inductif. Dans ces nanofils, des sauts de 2π de la phase supraconductrice sont censés produire les effets duals des paires de Cooper passant par effet tunnel dans la jonction Josephson. La maîtrise de ces effets duals permettrait la réalisation d'une nouvelle classe de circuits supraconducteurs quantiques. Nous avons fabriqué des résonateurs micro-ondes à partir de couches minces de supraconducteur fortement inductif. Nous ne trouvons aucune signature de l'effet des sauts de phase quantiques dans nos dispositifs. Cependant, nous mesurons un fort bruit basse fréquence causé par des systèmes à deux niveaux, et nous explorons ses implications dans ce type de résonateurMore than a century after its discovery, superconductivity is used today in many applications. One of those is in superconducting electronics, of which the Josephson junction is a basic building block. This element has enabled the realisation of electronic circuits in the quantum regime, and it has helped redefining the Volt in the SI system around quantum effects. Nowadays, a lot of time and efforts are spent in order to improve Josephson junction based circuits to realise state of the art Quantum-bits for quantum computing. One may think that those highly sensitive experiments involving Josephson junctions and conventional superconductivity imply an exquisite understanding of the component and its behaviour. We show in this thesis work that this is not entirely the case, and we explore two types of superconducting quantum circuits that are in need of clarification. The first one concerns the Josephson junction itself, and a subtle issue regarding its interaction with its electromagnetic environment. Indeed, it has been predicted nearly 40 years ago that a Josephson junction would become insulating when connected to a resistance larger than Rq=h/4e²≈6.45 kΩ. We find no traces of such insulating state in our experiments which measure the admittance of a Josephson junction connected in parallel to a resistance R>Rq. The second circuit we explore is the supposedly dual circuit to the Josephson junction, the quantum phase slip junction, which consists of a nanowire made of a highly inductive superconductor. In those nanowires 2π phase slips of the superconducting phase should produce the dual effects of the Cooper-pair tunneling in Josephson junctions. The control of such an effect would then permit the realisation of a new class of superconducting quantum devices. We measured microwaves resonators patterned in a thin film of a highly inductive superconductor. We find no clear signal revealing the presence of quantum phase slips in our devices. However, we find a clear signature of two-level system low frequency noise, and we explore its implication in this kind of devices
22
Vieira, Andre de Pinho. "Efeitos de desordem ou aperiodicidade sobre o comportamento de sistemas magnéticos". Universidade de São Paulo, 2002. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-23022012-155648/.
Resumen
Consideramos os efeitos de desordem ou aperiodicidade sobre três sistemas magnéticos distintos. Inicialmente, apresentamos um modelo fenomenológico para descrever a dependência térmica da magnetização remanente induzida por diluição numa classe de antiferromagnetos quase-unidimensionais. O modelo trata exatamente as correlações ao longo da direção dominante, levando em conta as demais interações por meio de um campo efetivo. Em seguida, utilizamos uma aproximação autoconsistente de Bethe-Peierls para avaliar os efeitos de um campo cristalino aleatório sobre os diagramas de fases de um modelo de Ising de spins mistos. Mostramos que a desordem é capaz de modificar a natureza dos pontos multicríticos existentes no limite uniforme do modelo. Finalmente, estudamos os efeitos de interações aleatórias ou aperiódicas sobre o comportamento da cadeia XX quântica em baixas temperaturas, através de câlculos numéricos baseados no mapeamento do sistema em um modelo de férmions livres. Apontamos evidências de que, em temperatura zero, existe um único ponto fixo universal, característico de uma fase de singleto aleatório, que governa o comportamento do modelo na presença de interações desordenadas. No caso de interações aperiódicas,obtemos resultados consistentes com previsões de grupo de renormalização, indicando, para uma certa classe de seqüências de substituição, um comportamento semelhante àquele associado à desordem.We consider effects of disorder or aperiodicity on three different magnetic systems. First, we present a phenomenological model to describe the thermal dependence of the dilution-induced remanent magnetization in a class of quasi-one-dimensional antiferromagnets. The model treats correlations along the dominant direction in an exact way, while including the remaining inte-. i ractions via an effective field. Then, we use a self-consistent Bethe-Peierls ~ j .. approximation to gauge the effects of a random crystal field on the phase diagram of a mixed-spin Ising mode!. We show that disorder may have profound effects on the multicritical behavior associated with the uniform limit of the mo de!. Finally, we study effects of random or aperiodic interactions on the behavior of the quantum XX chain at low temperatures, by performing numerical calculations based on a mapping of the system onto a free-fermion mo de!. . We present evidence that, at zero temperature, there exists a single, universal fixed-point, associated with a random-singlet phase, which governs the behavior of the model in the presence of disordered interactions. In the case of aperiodic interactions, our results are consistent with renormalizationgroup predictions, indicating, for a certain class of substitution sequences, a behavior similar to the one induced by disorder.
23
Ossipov, Alexandre. "Open Mesoscopic Systems: beyond the Random Matrix Theory". Doctoral thesis, [S.l.] : [s.n.], 2003. http://deposit.ddb.de/cgi-bin/dokserv?idn=969598173.
24
Weiss, Markus. "Quantum Hall effect in a strongly disordered system". [S.l.] : [s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=97263083X.
25
Voliotis, Dimitrios. "Contribution à l’étude des chaînes de spin quantique avec une perturbation aléatoire ou apériodique". Thesis, Université de Lorraine, 2016. http://www.theses.fr/2016LORR0253/document.
Resumen
Au cours de cette thèse, nous avons étudié le comportement critique de chaînes de spins quantiques en présence de couplages désordonnés ou répartis de manière apériodique. Il est bien établi que le comportement critique des chaînes de spins quantiques d’Ising et de Potts est gouverné par le même point fixe de désordre infini. Nous avons implémenté́ une version numérique de la technique de renormalisation de désordre infini (SDRG) afin de tester cette prédiction. Dans un second temps, nous avons étudié la chaîne quantique d’Ashkin-Teller désordonnée par renormalisation de la matrice densité́ (DMRG). Nous confirmons le diagramme de phase précédemment proposé en déterminant la position des pics du temps d’autocorrélation intégré des corrélations spin-spin et polarisation-polarisation ainsi que ceux des fluctuations de l’aimantation et de la polarisation. Enfin, l’existence d’une double phase de Griffiths est confirmée par une étude détaillée de la décroissance des fonctions d’autocorrélation en dehors des lignes critiques. Comme attendu, l’exposant dynamique diverge à l’approche de ces lignes. Dans le cas apériodique, nous avons étudié les chaînes quantiques d’Ising et de Potts. En utilisant la méthode SDRG, nous avons confirmé les résultats connus pour la chaîne d’Ising et proposé des estimations de la dimension d’échelle magnétique. Dans le cas du modèle de Potts à q états, nous avons estimé l’exposant magnétique et observé qu’il était indépendant du nombre d’états q pour toutes les séquences dont l’exposant de divagation est nul. Toutefois, nous montrons que l’exposant dynamique est fini et augmente avec le nombre d’états q. En revanche, pour la séquence de Rudin-Shapiro, les résultats sont compatibles avec un point fixe de désordre infini et donc un exposant dynamique infiniIn the present thesis, the critical and off-critical behaviors of quantum spin chains in presence of a random or an aperiodic perturbation of the couplings is studied. The critical behavior of the Ising and Potts random quantum chains is known to be governed by the same Infinite-Disorder Fixed Point. We have implemented a numerical version of the Strong-Disorder Renormalization Group (SDRG) to test this prediction. We then studied the quantum random Ashkin-Teller chain by Density Matrix Renormalization Group. The phase diagram, previously obtained by SDRG, is confirmed by estimating the location of the peaks of the integrated autocorrelation times of both the spin-spin and polarization-polarization autocorrelation functions and of the disorder fluctuations of magnetization and polarization. Finally, the existence of a double-Griffiths phase is shown by a detailed study of the decay of the off-critical autocorrelation functions. As expected, a divergence of the dynamical exponent is observed along the two transition lines. In the aperiodic case, we studied both the Ising and Potts quantum chains. Using numerical SDRG, we confirmed the known analytical results for the Ising chains and proposed a new estimate of the magnetic scaling dimension.For the quantum q-state Potts chain, we estimated the magnetic scaling dimension for various aperiodic sequences and showed that it is independent of q for all sequences with a vanishing wandering exponent. However, we observed that the dynamical exponent is finite and increases with the number of states q. In contrast, for the Rudin-Shapiro sequence, the results are compatible with an Infinite-Disorder Fixed Point with a diverging dynamical exponent, equipe de renormalization
26
Denis, Maxime. "Construction d'une expérience de Condensat de Bose-Einstein de 41K pour l'étude du rotateur frappé atomique". Electronic Thesis or Diss., Université de Lille (2022-....), 2022. http://www.theses.fr/2022ULILR064.
Resumen
Ce manuscrit présente la réalisation d'un dispositif expérimental permettant de produire des condensats de Bose-Einstein de potassium 41. Cette expérience a été construite dans le but d'étudier le modèle du rotateur frappé en présence d'interactions. Le choix du potassium 41 pour cette expérience est motivé par deux raisons. La première est que la longueur de diffusion de cet atome est positive (ce qui permet une condensation aisée) et qu'il possède des résonances de Feshbach accessibles. La seconde est que les longueurs d'ondes de ses transitions de refroidissement peuvent être générées par des sources lasers fibrées puissantes du domaine télécom doublées en fréquence. Cela a pour avantage de pouvoir fabriquer des systèmes lasers stables et robustes pour les étapes de refroidissement laser et de piégeage optique du potassium 41. La particularité de notre système réside dans la génération de fréquence qui a lieu en amont des étapes d'amplification à haute puissance et de doublage en fréquence. Le développement de ces bancs lasers agissant sur les deux transitions de refroidissement D1 et D2 a permis de mener à bien les étapes de refroidissement laser. Grâce à ces bancs lasers, un piège magnéto-optique rassemblant 3x10^(9) atomes a été obtenu. La compression et le refroidissement avec une mélasse grise de ce piège magnéto-optique a permis d'atteindre une température de 16 µK et une densité dans l'espace des phases de 10^(-6). Les étapes de refroidissement évaporatif qui suivent sont réalisées successivement avec un piège quadrupolaire, un piège hybride (piège quadrupolaire + piège optique) et pour terminer un piège optique croisé. Des condensats de 500 000 atomes ont été observés dans ce piège optique croisé. Nous avons aussi identifié des résonances de Feshbach qui permettront le contrôle des interactions. Pour l'étude du rotateur frappé, un système laser pulsé original a été conçu en parallèle. La réalisation de ce système a été faite à partir d'un laser pulsé télécom amplifié à haute puissance doublé en fréquence. Ce système produit des pulses laser proches infrarouge avec des impulsions de 10 ns, une fréquence de répétition comprise entre 100 kHz et 500 kHz et une puissance crête optique allant jusqu'à 350W. Ce banc laser pulsé nous a permis de réaliser les premières expériences du rotateur frappé de cette expérience. Un contrôle des interactions avec les résonances de Feshbach identifiées nous permettra d'étudier par la suite le modèle du rotateur frappé en présence d'interactionsThis manuscript presents the realization of an experimental device to produce Bose-Einstein condensates of potassium 41. This experiment was built to study the model of the kicked rotor in the presence of interactions. The choice of potassium 41 for this experiment is motivated by two reasons. The first is that the diffusion length of this atom is positive (allowing easy condensation) and has accessible Feshbach resonances. The second is that the wavelengths of its cooling transitions can be generated by powerful fiber laser sources in the telecom domain doubled in frequency. This has the advantage of being able to manufacture stable and robust laser systems for laser cooling and optical trapping of potassium 41. The particularity of our system lies in the frequency generation that takes place before the high power amplification and frequency doubling stages. The development of these laser benches acting on the two cooling transitions D1 and D2 enabled the laser cooling stages to be completed. Thanks to these laser benches, a magneto-optical trap gathering 3x10^(9) atoms was obtained. Compression and cooling with grey molasses of this magneto-optical trap allowed to reach a temperature of 16 µK and a density in the space of phases of 10^(-6). The following evaporative cooling steps are carried out successively with a quadrupolar trap, a hybrid trap (quadrupolar trap + optical trap) and to finish a crossed optical dipole trap. Condensates of 500,000 atoms were observed in this crossed optical dipole trap. We also identified Feshbach resonances that will allow the control of interactions. For the study of the kicked rotor, an original pulsed laser system was designed in parallel. The realization of this system was made from a high-power amplified telecom pulsed laser doubled in frequency. This system produces near infrared pulses at a repetition frequency between 100 kHz to 500 kHz with peak optical power up to 350W. This pulsed laser bench allowed us to perform the first experiments of the kicked rotor from this experiment. A control of the interactions with the identified Feshbach resonances will allow us to study the model of the kicked rotor in the presence of interactions
27
Jia, Xun. "A study of disorder effects in quantum systems". Diss., Restricted to subscribing institutions, 2009. http://proquest.umi.com/pqdweb?did=1905664041&sid=1&Fmt=2&clientId=1564&RQT=309&VName=PQD.
28
Gawiec, Pierre. "Propriétés statiques et dynamiques des états de basse énergie d'un système de spins bidimensionnel anisotrope désordonné". Université Joseph Fourier (Grenoble), 1994. http://www.theses.fr/1994GRE10206.
Resumen
L'objet de cette these est l'etude des proprietes statiques et dynamiques du modele de spins xxo bimodal sur reseau carre. A partir de simulations numeriques intensives, nous obtenons son diagramme de phase (l,x) classique a temperature nulle ou x est la concentration des defauts magnetiques et l leur force. Nous mettons en evidence, par le calcul de differents parametres d'ordre et des fonctions de correlation spin-spin, une transition qui separe une phase de decroissance algebrique des correlations et un verre de spin isotrope caracterise par une decroissance exponentielle des correlations. Nos resultats suggerent egalement une aimantation nulle pour toute concentration x finie des defauts a la limite thermodynamique. Nous etudions ensuite la dynamique du systeme. Le calcul des quantites hydrodynamiques qui la caracterisent montre l'existence d'ondes de spin de dispersion lineaire dans la limite des basses frequences. L'obtention du facteur de structure dynamique du systeme dans l'approximation harmonique des ondes de spin permet d'acceder aux composantes dans le plan xy et transverse des fluctuations magnetiques. Nous en deduisons differentes quantites qui permettent de discuter du comportement dynamique du systeme. Nous procedons egalement a une modelisation de l'ensemble de ces proprietes dynamiques dans le cadre de l'approximation cpa (coherent potential approximation). Les resultats obtenus par cette approche, qui permet d'alleger notablement la charge numerique et d'acceder a de plus grandes tailles de systemes, sont en tres bon accord avec nos resultats des calculs exacts. Enfin nous etudions l'effet de la frustration sur les fluctuations quantiques du systeme en calculant la premiere correction en 1/s aux grandeurs hydrodynamiques. Nous montrons l'existence, dans le cas ou s=1/2, d'une phase quantique desordonnee a temperature nulle caracterisee par une constante de raideur nulle. Nous proposons egalement une approche originale pour investiguer les proprietes du systeme dans cette phase
29
Bishop, Michael Anthony. "Quantum Systems in Bernoulli Potentials". Diss., The University of Arizona, 2013. http://hdl.handle.net/10150/293431.
Resumen
Quantum mechanics is a theory developed to explain both particle and wave-like properties of small matter such as light and electrons. The consequences of the theory can be counter-intuitive but lead to mathematical and physical theory rich in fascinating phenomena and challenging questions. This dissertation investigates the nature of quantum systems in Bernoulli distributed random potentials for systems on the one dimensional lattice {0, 1, ..., L, L+1} ⊂ Z in the large system limit L → ∞. For single particle systems, the behavior of the low energy states is shown to be approximated by systems where positive potential is replaced by infinite potential. The approximate shape of these states is described, the asymptotics of their eigenvalues are calculated in the large system limit L → ∞, and a Lifschitz tail estimate on the sparsity of low energy states is proven. For interacting multi-particle systems, a Lieb-Liniger model with Bernoulli distributed potential is studied in the Gross-Pitaevskii approximation. First, to investigate localization in these settings, a general inequality is proven to bound from below the support of the mean-field. The bound depends on the per particle energy, number of particles, and interaction strength. Then, the ground state for the one-dimensional lattice with Bernoulli potential is studied in the large system limit. Specifically, the case where the product of interaction strength and particle density is near zero is considered to investigate whether localization can be recovered.
30
Fischer, Andrea M. "Disorder and interactions in graphene and other quantum systems". Thesis, University of Warwick, 2011. http://wrap.warwick.ac.uk/35238/.
Resumen
This thesis examines the topics of disorder and electron-electron interactions in three distinct quantum systems. Firstly, the Anderson transition is studied for the body centred cubic and face centred cubic lattices. We obtain high precision results for the critical disorder at the band centre and the critical exponent using the transfer-matrix method and finite size scaling. Comparing the critical disorder between the simple cubic, body centred cubic and face centred cubic lattices, an increase in the critical disorder is observed as a function of the coordination number of the lattice. The critical exponent is found to be v ≃ 1:5 in agreement with the value for the simple cubic lattice. Energy-disorder phase diagrams are plotted for both lattice types. Next, we consider the Aharonov-Bohm effect for an exciton in a 1D ring geometry. The aim is to determine how the addition of a constant electric field in the plane of the ring effects the Aharonov-Bohm oscillations, which occur as a function of the magnetic ux threading the ring. We develop a self consistent equation for the ground state energy, which is then solved numerically. Oscillations in the ground state energy have an increasing amplitude as a function of electric field strength until a critical electric field value. At this point, oscillations in the oscillator strength become inverted, with the oscillation minimum reaching zero at half a magnetic ux quantum. This suggests a possible process for controlling the formation and recombination of excitons through tuning the applied fields. The final and largest section of the thesis is concerned with collective excitations of graphene in a strong perpendicular magnetic field. The excitations, which are most strongly mixed are identified and used as a basis to diagonalise the Hamiltonian, which includes the Coulomb interaction between electrons and holes. In this way the oscillator strengths and energies of collective excitations are obtained. The good quantum numbers for collective excitations are identified. In particular, we study those arising from the SU(4) symmetry, which is due to two spin and two valley pseudospin projections. This enables us to determine the multiplet structure of the states. In addition to neutral collective excitations or excitons, we investigate the possible formation of charged collective excitations or trions from nearly full or nearly empty Landau levels. The localisation of neutral collective excitations upon a single Coulomb or δ-function impurity is also examined.
31
Izyumov, Arkady Vasilyevich. "Disorder in quantum and classical systems : field theoretic approach". Thesis, University of Cambridge, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.624562.
32
Thomson, Steven. "The effects of disorder in strongly interacting quantum systems". Thesis, University of St Andrews, 2016. http://hdl.handle.net/10023/9441.
Resumen
This thesis contains four studies of the effects of disorder and randomness on strongly correlated quantum phases of matter. Starting with an itinerant ferromagnet, I first use an order-by-disorder approach to show that adding quenched charged disorder to the model generates new quantum fluctuations in the vicinity of the quantum critical point which lead to the formation of a novel magnetic phase known as a helical glass. Switching to bosons, I then employ a momentum-shell renormalisation group analysis of disordered lattice gases of bosons where I show that disorder breaks ergodicity in a non-trivial way, leading to unexpected glassy freezing effects. This work was carried out in the context of ultracold atomic gases, however the same physics can be realised in dimerised quantum antiferromagnets. By mapping the antiferromagnetic model onto a hard-core lattice gas of bosons, I go on to show the importance of the non-ergodic effects to the thermodynamics of the model and find evidence for an unusual glassy phase known as a Mott glass not previously thought to exist in this model. Finally, I use a mean-field numerical approach to simulate current generation quantum gas microscopes and demonstrate the feasibility of a novel measurement scheme designed to measure the Edwards-Anderson order parameter, a quantity which describes the degree of ergodicity breaking and which has never before been experimentally measured in any strongly correlated quantum system. Together, these works show that the addition of disorder into strongly interacting quantum systems can lead to qualitatively new behaviour, triggering the formation of new phases and new physics, rather than simply leading to small quantitative changes to the physics of the clean system. They provide new insights into the underlying physics of the models and make direct connection with experimental systems which can be used to test the results presented here.
33
Sakaida, Masaru. "Disorder-induced quantum phenomena in inhomogeneous optical lattices". 京都大学 (Kyoto University), 2016. http://hdl.handle.net/2433/215289.
34
Paulin, Guillaume. "Transport électronique et Verres de Spins". Phd thesis, Ecole normale supérieure de lyon - ENS LYON, 2010. http://tel.archives-ouvertes.fr/tel-00556836.
Resumen
The results reported in this thesis contribute to the understanding of disordered systems, to mesoscopic physics on the one hand, and to the physics of spin glasses on the other hand. The first part of this thesis studies numerically coherent electronic transport in a non magnetic metal accurately doped with frozen magnetic impurities (a low temperature spin glass). Thanks to a recursive code that calculates the two terminal conductance of the system, we study in detail the metallic regime of conduction (large conductance) as well as the insulating regime (small conductance). In both regimes, we highlight a universal behavior of the system. Moreover, a study of correlations between the conductance of different spin configurations of impurities allows us to link these correlations with correlations between spin configurations. This study opens the route for the first experimental determination of the overlap via transport measurements. A second part of this thesis deals with the study of the mean field Sherrington-Kirkpatrick model, which describes the low temperature phase of an Ising spin glass. We are interested here in the generalization of this model to quantum spins (i.e including the possibility to flip by quantum tunneling) of this classical model that was well studied during the past thirty years. We deduce analytically motion equations at the semi-classical level, for which the influence of quantum tunneling is weak, and we compare them with the classical case. We finally solve numerically these equations using a pseudo-spectral method.
35
Burdin, Sébastien. "Théories de champ moyen pour les systèmes d'électrons à fortes corrélations". Habilitation à diriger des recherches, Université Sciences et Technologies - Bordeaux I, 2012. http://tel.archives-ouvertes.fr/tel-00711167.
Resumen
Ce mémoire d'habilitation à diriger les recherches présente des théories de champ moyen que j'ai appliquées à l'étude de systèmes d'électrons à fortes corrélations. Il s'appuie sur des travaux que j'ai effectués, pour certains dans la continuité de ma thèse, pour d'autres dans des directions nouvelles. L'une des problématiques centrales est celle des transitions de phases quantiques, et les systèmes considérés ont le point commun de décrire des impuretés quantiques, réelles ou artificielles. Les différentes méthodes de champ moyen utilisées sont présentées par des exemples dans le cadre de problèmes physiques particuliers. Après un premier chapitre introductif fortement focalisé sur l'exemple des composés d'électrons f, ce mémoire est structuré en trois chapitres principaux connectés respectivement aux trois thématiques suivantes : les composés Kondo, les liquides de spin, et les systèmes désordonnés.
36
Coquand, Olivier. "Fluctuations dans la phase plate des membranes cristallines". Thesis, Sorbonne université, 2018. http://www.theses.fr/2018SORUS096.
Resumen
Cette thèse porte sur l'étude des propriétés mécaniques des membranes cristallines, matériaux bidimensionnels comportant un réseau périodique d'atomes ou de molécules à l'échelle microscopique qui leur confère des propriétés élastiques. Il s'agit de l'un des rares exemples de systèmes bidimensionnels possédant une phase ordonnée stable à grande distance en présence de fluctuations thermiques. Dans celle-ci, les vecteurs normaux à la surface engendrée par la membrane sont fortement corrélés, d'où son nom de phase plate. Ce manuscrit présente une étude des propriétés de la phase plate à l'aide de méthodes du groupe de renormalisation, inspirées notamment du formalisme de l'action effective moyenne. Tout d'abord, en étudiant la structure de la théorie de perturbations au-delà de l'ordre le plus bas, nous confirmons le bien fondé du schéma d'approximation de l'action effective moyenne utilisé dans la suite et exhibons les pathologies du développement perturbatif. Puis, nous montrons comment le flot de renormalisation non-perturbatif permet de calculer les différentes propriétés thermodynamiques des membranes cristallines, et d'établir leur diagramme des phases complet dans l'espace (volume, contrainte appliquée, température). Nous améliorons ensuite le modèle utilisé pour tenir compte des fluctuations quantiques grâce auxquelles le régime de basse température peut être décrit. Enfin, nous examinons l'effet de la présence d'impuretés dans le matériau. En particulier, nous prédisons l'existence d'une nouvelle transition de phase en présence de désordre qui pourrait expliquer les observations expérimentales dans ces systèmesThis works deals with the mechanical properties of crystalline membranes, which are two-dimensional materials with an underlying periodic lattice at the microscopic scale which provides them with elastic properties. It is one of the scarce examples of two-dimensional systems possessing a stable ordered phase at large distance in the presence of thermal fluctuations. In that phase, the vectors normal to the surface generated by the membrane are strongly correlated; it is thus called the flat phase. This manuscript presents a study of the properties of the flat phase with help of renormalisation group tools, and in particular the effective average action formalism. First, by studying the perturbation theory beyond lowest order, we confirm the stability of our effective average action ansatz used in the following, and unveil some pathologies of the perturbative development. Then we show how the non-perturbative renormalisation group flow can be used to compute various thermodynamic properties of crystalline membranes and draw their complete phase diagram in the space (volume, applied stress, temperature). Afterwards, we improve our model to account for the effect of quantum fluctuations, which allows to describe the low temperature regime. Finally, we examine the consequences of the presence of various defects in the material. In particular, we describe a new disorder driven phase transition which seems to be in good qualitative agreement with experimental observations
37
Schiulaz, Mauro. "Ideal quantum glass transitions: many-body localization without quenched disorder?" Doctoral thesis, SISSA, 2015. http://hdl.handle.net/20.500.11767/4908.
Resumen
In this work the role of disorder, interaction and temperature in the physics of quantum non-ergodic systems is discussed. I first review what is meant by thermalization in closed quantum systems, and how ergodicity is violated in the presence of strong disorder, due to the phenomenon of Anderson localization. I explain why localization can be stable against the addition of weak dephasing interactions, and how this leads to the very rich phenomenology associated with many-body localization. I also briefly compare localized systems with their closest classical analogue, which are glasses, and discuss their similarities and differences, the most striking being that in quantum systems genuine non ergodicity can be proven in some cases, while in classical systems it is a matter of debate whether thermalization eventually takes place at very long times.
Up to now, many-body localization has been studies in the region of strong disorder and weak interaction. I show that strongly interacting systems display phenomena very similar to localization, even in the absence of disorder. In such systems, dynamics starting from a random inhomogeneous initial condition are non-perturbatively slow, and relaxation takes place only in exponentially long times. While in the thermodynamic limit ergodicity is ultimately restored due to rare events, from the practical point of view such systems look as localized on their initial condition, and this behavior can be studied experimentally. Since their behavior shares similarities with both many-body localized and classical glassy systems, these models are termed “quantum glasses”.
Apart from the interplay between disorder and interaction, another important issue concerns the role of temperature for the physics of localization. In non-interacting systems, an energy threshold separating delocalized and localized states exist, termed “mobility edge”. It is commonly believed that a mobility edge should exist in interacting systems, too. I argue that this scenario is inconsistent because inclusions of the ergodic phase in the supposedly localized phase can serve as mobile baths that induce global delocalization. I conclude that true non-ergodicity can be present only if the whole spectrum is localized. Therefore, the putative transition as a function of temperature is reduced to a sharp crossover. I numerically show that the previously reported mobility edges can not be distinguished from finite size effects. Finally, the relevance of my results for realistic experimental situations is discussed.
38
Herazo, Warnes Jesus Maria 1982. "Transições de fases quânticas em sistemas bosônicos fortemente correlacionados". [s.n.], 2011. http://repositorio.unicamp.br/jspui/handle/REPOSIP/277709.
Resumen
Orientador: Eduardo MirandaTese (doutorado) - Universidade Estadual de Campinas, Instituto de Física "Gleb Wataghin"
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Resumo: A questão da natureza das transições de fases de sistemas de redes de bósons tem se tornado cada vez mais urgente à vista da capacidade de carregamento de átomos ultrafrios em redes ópticas. Nesta tese, tentamos avançar este conhecimento através do estudo de 3 modelos básicos de redes de bósons interagentes. Inicialmente, determinamos o diagrama de fases c as propriedades físicas do modelo bosônico de impureza única de Anderson. Este modelo é interessante tanto em si mesmo quanto por causa de sua relação com outras abordagens teóricas tais como a teoria dinâmica de campo médio bosônica. Usamos como estratégia a inclusão de um pequeno campo externo acoplado ao parâmetro de ordem superfluido, que quebra a simetria global de calibre do modelo. Desta forma, foi possível estudar a transição de condensação de Base-Einstein através do critério de quebra espontânea de simetria global de calibre. Outras quantidades como a ocupação da impureza, o desvio padrão da ocupação e a susceptibilidade com respeito ao campo externo também foram calculadas, caracterizando a transição de fase do modelo. Alguns desses resultados foram comparados com aqueles já obtidos na literatura através do grupo de renormalização numérico. Encontramos bom acordo entre os dois métodos. O segundo estudo realizado nesta tese refere-se ao comportamento crítico do modelo de Bose-Hubbard desordenado através da chamada teoria de campo médio estocástica. O objeto central dessa teoria de campo médio é a distribuição de parâmetros de ordem P(?). Estudos numéricos estabelecem que perto da linha crítica que separa as fases superfluida e vidro de Base do modelo, essa distribuição exibe uma grande região com comportamento de lei de potência P(?) ~ ? ^-(1+ß_c), onde ß_c < 1. Usando esse comportamento como tentativa, obtivemos analiticamente tanto a fronteira de fases quanto o valor do expoente crítico da lei de potência ß_c , encontrando um razoável acordo com os resultados numéricos e avançando o entendimento da natureza da transição de fase específica ao modelo desordenado. Finalmente, o modelo de Bose-Hubbard desordenado para partículas de spin-1 foi estudado dentro da teoria de campo médio estocástica. As distribuições de probabilidade de várias quantidades físicas como o parâmetro de ordem superfluido, o desvio padrão da ocupação por sítio, a fração do condensado, o quadrado do operador de spin, bem como seus valores médios, foram determinados para as três fases do modelo, a saber, o superfluido polar, o isolante de Mott e o vidro de Bose. Uma completa caracterização das propriedades físicas dessas fases e das transições de fase entre elas foi estabelecida
Abstract: The question of the nature of phase transitions of systems of lattice bosons has become increasingly more pressing in view of the capability of loading ultracold atoms in opticallattices. In this thesis we try to advance this understanding through the study of 3 basic models of interacting lattice bosons. Initially, we determined the phase diagram and physical properties of the bosonic singleimpurity Anderson model. This model is interesting both in its own right and because of its relation to other theoretical approaches such as the bosonic dynamical field theory method. We used as strategy the inclusion of a small external field coupled to the superfluid order parameter, which breaks the global gauge symmetry of the model. Thus, it was possible to study the Base-Einstein condensation transition through the criterion of the onset of spontaneous broken global gauge symmetry. Other quantities such as the occupation of the impurity, the standard deviation of the occupation and the susceptibility with respect to the external! Field were calculated characterizing the phase transition in the model. Some of the results were compared with those already reported in the literature, obtained with tic numerical renormalization group. We found good agreement between the two methods. The second study carried out in this thesis concerned the critical behavior of the disordered Bose-Hubbard model within the so-called stochastic mean-field theory. The central object of this mean-field theory is the distribution of order parameters P(?). Numerical studies establish that near the critical line separating the superfluid and Bose glass phases of this model, this distribution shows a wide region of power-law behavior P(?) ~ ? ^-(1+ß_c), where ß_c < 1. Using this behavior as an Ansatz, we obtained analytically both the phase boundary and the value of the critical power-law exponent ß_c, finding a reasonably good agreement with the numerical results and thus shedding new light on the nature of this phase transition specific to disordered model. Finally, the disordered Bose-Hubbard model for spin-1 particles was studied within the stochastic mean-field theory. The probability distributions of various physical quantities, such as the superfluid order parameter, the standard deviation of the occupation per site, the condensate fraction, the square of the spin operator, as well as their average values, were determined for the three phases of the model, namely, the polar superfluid, the Mott insulating and the Bose glass phases. A complete characterization of the physical properties of these phases and the phase transitions between them was then established
Doutorado
Física da Matéria Condensada
Doutor em Ciências
39
Kainaris, Nikolaos [Verfasser] y A. D. [Akademischer Betreuer] Mirlin. "Topology, interactions, and disorder in one-dimensional quantum systems / Nikolaos Kainaris ; Betreuer: A. D. Mirlin". Karlsruhe : KIT-Bibliothek, 2016. http://d-nb.info/1124068864/34.
40
Wang, Ruizhe. "Magnetic fluctuations and clusters in the itinerant ferromagnet Ni-V close to a disordered quantum critical point". Kent State University / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=kent1555936445433091.
41
Sciolla, Bruno. "Dynamique quantique hors-équilibre et systèmes désordonnés pour des atomes ultrafroids bosoniques". Phd thesis, Université Paris Sud - Paris XI, 2012. http://tel.archives-ouvertes.fr/tel-00734641.
Resumen
Durant cette thèse, je me suis intéressé à deux thématiques générales qui peuvent être explorées dans des systèmes d'atomes froids : d'une part, la dynamique hors-équilibre d'un système quantique isolé, et d'autre part l'influence du désordre sur un système fortement corrélé à basse température. Dans un premier temps, nous avons développé une méthode de champ moyen, qui permet de résoudre la dynamique unitaire dans un modèle à géométrie particulière, le réseau complètement connecté. Cette approche permet d'établir une correspondance entre la dynamique unitaire du système quantique et des équations du mouvement classique. Nous avons mis à profit cette méthode pour étudier le phénomène de transition dynamique qui se signale, dans des modèles de champ moyen, par une singularité des observables aux temps longs, en fonction des paramètres initiaux ou finaux de la trempe. Nous avons montré l'existence d'une transition dynamique quantique dans les modèle de Bose-Hubbard, d'Ising en champ transverse et le modèle de Jaynes-Cummings. Ces résultats confirment l'existence d'un lien fort entre la présence d'une transition de phase quantique et d'une transition dynamique.Dans un second temps, nous avons étudié un modèle de théorie des champs relativiste avec symétrie O(N) afin de comprendre l'influence des fluctuations sur ces singularités. À l'ordre dominant en grand N, nous avons montré que la transition dynamique s'apparente à un phénomène critique. En effet, à la transition dynamique, les fonctions de corrélations suivent une loi d'échelle à temps égaux et à temps arbitraires. Il existe également une longueur caractéristique qui diverge à l'approche du point de transition. D'autre part, il apparaît que le point fixe admet une interprétation en terme de particules sans masse se propageant librement. Enfin, nous avons montré que la dynamique asymptotique au niveau du point fixe s'apparente à celle d'une trempe d'un état symétrique dans la phase de symétrie brisée. Le troisième volet de cette thèse apporte des éléments nouveaux pour la compréhension du diagramme des phases du modèle de Bose-Hubbard en présence de désordre. Pour ce faire,nous avons utilisé et étendu la méthode de la cavité quantique en champ moyen de Ioffe et Mézard, qui doit être utilisée avec la méthode des répliques. De cette manière, il est possible d'obtenir des résultats analytiques pour les exposants des lois de probabilité de la susceptibilité.Nos résultats indiquent que dans les différents régimes de la transition de phase de superfluide vers isolant, les lois d'échelle conventionnelles sont tantôt applicables, tantôt remplacées par une loi d'activation. Enfin, les exposants critiques varient continûment à la transition conventionnelle.
42
Capron, Thibaut. "Transport quantique dans les verres de spin". Phd thesis, Université de Grenoble, 2011. http://tel.archives-ouvertes.fr/tel-00686330.
Resumen
Le verre de spin est une phase de la matière dans laquelle le désordre magnétique est gelé. Étant considéré comme un système modèle des verres en général, il a fait l'objet de nombreux travaux théoriques et expérimentaux. Les recherches ont convergé vers deux principales descriptions de l'état fondamental du système diamétralement opposées. D'une part, la solution " champ-moyen " nécessite une brisure de symétrie non triviale, et l'état fondamental est composé de multiples états organisés en une structure hiérarchique. D'autre part, une approche de " gouttelettes ", fondée sur la dynamique hors-équilibre d'un état fondamental unique. La validation expérimentale d'une de ces deux théories nécessite une observation détaillée de l'échantillon au niveau microscopique. La physique mésoscopique, basée sur les effets d'interférences électroniques, propose un outil unique pour accéder à cette configuration microscopique des impuretés: les fluctuations universelles de conductance. En effet, ces fluctuations représentent une empreinte unique du désordre dans l'échantillon. Ce travail présente la mise en œuvre de mesures de fluctuations de conductance universelles dans les verres de spin. Les effets d'interférences électroniques étant sensibles aux processus de décohérence du verre de spin, ils donnent accès expérimentalement à de nouvelles quantités concernant les excitations du système. La mesure des corrélations entre les empreintes du désordre permet quant à elle d'explorer sous un angle nouveau l'ordre non conventionnel de cet état vitreux.
43
Ruess, Frank Joachim Physics Faculty of Science UNSW. "Atomically controlled device fabrication using STM". Awarded by:University of New South Wales. Physics, 2006. http://handle.unsw.edu.au/1959.4/24855.
Resumen
We present the development of a novel, UHV-compatible device fabrication strategy for the realisation of nano- and atomic-scale devices in silicon by harnessing the atomic-resolution capability of a scanning tunnelling microscope (STM). We develop etched registration markers in the silicon substrate in combination with a custom-designed STM/ molecular beam epitaxy system (MBE) to solve one of the key problems in STM device fabrication ??? connecting devices, fabricated in UHV, to the outside world. Using hydrogen-based STM lithography in combination with phosphine, as a dopant source, and silicon MBE, we then go on to fabricate several planar Si:P devices on one chip, including control devices that demonstrate the efficiency of each stage of the fabrication process. We demonstrate that we can perform four terminal magnetoconductance measurements at cryogenic temperatures after ex-situ alignment of metal contacts to the buried device. Using this process, we demonstrate the lateral confinement of P dopants in a delta-doped plane to a line of width 90nm; and observe the cross-over from 2D to 1D magnetotransport. These measurements enable us to extract the wire width which is in excellent agreement with STM images of the patterned wire. We then create STM-patterned Si:P wires with widths from 90nm to 8nm that show ohmic conduction and low resistivities of 1 to 20 micro Ohm-cm respectively ??? some of the highest conductivity wires reported in silicon. We study the dominant scattering mechanisms in the wires and find that temperature-dependent magnetoconductance can be described by a combination of both 1D weak localisation and 1D electron-electron interaction theories with a potential crossover to strong localisation at lower temperatures. We present results from STM-patterned tunnel junctions with gap sizes of 50nm and 17nm exhibiting clean, non-linear characteristics. We also present preliminary conductance results from a 70nm long and 90nm wide dot between source-drain leads which show evidence of Coulomb blockade behaviour. The thesis demonstrates the viability of using STM lithography to make devices in silicon down to atomic-scale dimensions. In particular, we show the enormous potential of this technology to directly correlate images of the doped regions with ex-situ electrical device characteristics.
44
Vermersch, Benoît. "Dynamique d'un gaz de bosons ultra-froids dans un milieu désordonné : Effets des interactions sur la localisation et sur la transition d'Anderson". Phd thesis, Université des Sciences et Technologie de Lille - Lille I, 2013. http://tel.archives-ouvertes.fr/tel-00910405.
Resumen
En présence de désordre, la diffusion des particules peut être complètement annihilée, don- nant lieu à la fameuse localisation d'Anderson. En dimension trois, une transition de phase sépare une telle phase isolante du régime diffusif. À partir de différentes approches théo- riques et numériques, cette thèse a pour objectif de déterminer l'effet des interactions entre particules sur la localisation d'Anderson et sur la transition d'Anderson, dans le contexte expérimental des condensats de Bose-Einstein. Dans le cas unidimensionnel, la compétition entre désordre et interaction induit l'existence de trois régimes dynamiques dont les caracté- ristiques sont étudiées grâce à une approche spectrale. En nous appuyant sur le modèle du rotateur frappé quasi-périodique, nous caractérisons l'émergence du régime sub-diffusif qui tend à remplacer le régime localisé dans le cas tridimensionnel. Nous étudions également la dynamique des excitations du système et démontrons l'universalité de la transition d'An- derson vis-à-vis des quasi-particules de Bogoliubov. Dans l'objectif d'étudier la validité de l'équation de Gross-Pitaevskii, nous nous sommes enfin intéressés à une nouvelle approche, la méthode de la troncature d'Husimi. Celle-ci nous permet d'envisager une étude de la compétition entre désordre et interaction enrichie par la prise en compte du bruit quantique.
45
Percebois, Gaëtan. "Quantum transport in two-dimensional systems : artificial intelligence applied to material science". Electronic Thesis or Diss., Strasbourg, 2023. http://www.theses.fr/2023STRAE033.
Resumen
Les hétérostructures représentent l'un des dispositifs les plus largement utilisés pour générer un gaz d'électrons bidimensionnel (2DEG). Cependant, les propriétés exactes de transport des électrons au sein de tels dispositifs ne sont pas complètement contrôlables et prévisibles. Cela est principalement dû à la présence de dopants ionisés, nécessaires à la création du gaz d’électrons, qui impactent le mouvement des électrons par le biais d'interactions coulombiennes, entraînant ainsi un potentiel de désordre. Dans cette étude, nous introduisons une méthode pour déterminer ce désordre en utilisant des données de transport locales obtenues à partir d'expériences de microscopie à grille locale (SGM). La correspondance entre les données capturées dans une image SGM et le potentiel de désordre est réalisée grâce à l'utilisation d'un algorithme de deep learning. Nous avons démontré que ce problème inverse peut être résolu, et avons déterminé le potentiel de désordre au sein d'une véritable hétérostructure expérimentale. Dans ce manuscrit, nous présentons en détail la méthodologie employée, la rendant ainsi reproductible pour d'autres dispositifsHeterostructures represent one of the most widely employed devices for generating a two-dimensional electron gas (2DEG). However, the precise transport properties of electrons within such devices remain neither completely controllable nor predictable. This is mainly due to the presence of randomly located ionized dopants, that are necessary for creating the electron gas. However, due to the Coulombic interactions, the electron motion is impacted, which results in a disorder potential. In this study, we introduce a method to determine this disorder potential using local transport information obtained from scanning gate microscopy (SGM) experiments. The mapping between the data captured in an SGM image and the disorder potential is achieved through the utilization of a deep learning algorithm. We have demonstrated that this inverse problem can be solved, and we have been able to determine the disorder potential within a real experimental heterostructure. In this manuscript, we detail the employed methodology, making it replicable for other devices
46
Petersen, Greg M. "Anderson Localization in Low-Dimensional Systems with Long-Range Correlated Disorder". Ohio University / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1365762218.
47
Adroguer, Pierre. "Propriétés de transport électronique des isolants topologiques". Phd thesis, Ecole normale supérieure de lyon - ENS LYON, 2013. http://tel.archives-ouvertes.fr/tel-00832048.
Resumen
Les travaux présentés dans cette thèse ont pour objectif d'apporter à la physique mésoscopique un éclairage concernant la compréhension des propriétés de transport électroniques d'une classe de matériaux récemment découverts : les isolants topologiques.La première partie de ce manuscrit est une introduction aux isolants topologiques, mettant en partie l'accent sur leurs spécificités par rapport aux isolants "triviaux" : des états de bords hélicaux (dans le cas de l'effet Hall quantique de spin en 2 dimensions) ou de surface relativistes (pour les isolants topologiques tridimensionnels) robustes vis-à-vis du désordre.La deuxième partie propose une sonde de l'hélicité des états de bords de l'effet Hall quantique de spin en étudiant les propriétés remarquables de l'injection de paires de Cooper dans cette phase topologique.La troisième partie étudie la diffusion des états de surface des isolants topologiques tridimensionnels dans le régime cohérent de phase. L'étude de la diffusion, de la correction quantique à la conductance (antilocalisation faible) et de l'amplitude des fluctuations universelles de conductance de fermions de Dirac sans masse est présentée. Cette étude est aussi menée dans la cas d'états de surface dont la surface de Fermi présente la déformation hexagonale observée expérimentalement.
48
Anfray, Valentin. "Étude numérique du point critique de systèmes quantiques de spin désordonnés en dimensions élevées". Electronic Thesis or Diss., Université de Lorraine, 2022. http://www.theses.fr/2022LORR0127.
Resumen
Nous avons étudié numériquement plusieurs modèles de spins quantiques désordonnés en dimensions D>1 par le groupe de renormalisation en désordre fort (SDRG). Pour cela, nous avons implémenté un algorithme permettant de considérer des systèmes contenant de l'ordre d'un million de spins indépendamment de la dimension du réseau. Nous avons montré que les propriétés critiques du modèle de Potts quantique désordonné à q=2,3,5,10,20 et 50 états en dimensions D=2 et D=3 sont gouvernées par un point fixe de désordre infini. Nous avons estimé les exposants critiques de la longueur de corrélation u, de l'aimantation d_f et du gap d'énergie psi. En exploitant les effets de taille finie et en prenant en compte les corrections, nous avons conclut que les propriétés critiques du modèle de Potts sont indépendantes du nombre d'états q. Nous avons également étudié le modèle d'horloge quantique désordonné à q=2,3,5,8 et 10 états en dimensions D=2 et D=3. L'importance du désordre initial a été mis en évidence pour pouvoir atteindre un point critique de désordre infini. Bien que les incertitudes sur psi soient grandes, nos estimations des exposants u et psi sont compatibles pour tout q avec ceux du modèle d'Ising quantique désordonné. Les estimations de l'exposant d_f sont incompatibles dans les barres d'erreur mais néanmoins très proches. Enfin, nous avons étudié le point tricritique du modèle d'Ashkin-Teller quantique désordonné en dimensions D=2 et D=3. Nous avons montré que l'exposant de la longueur de corrélation dans une des directions instables n'appartient pas à la classe d'universalité du modèle d'Ising quantique désordonnéSeveral random quantum spin models have been numerically studied in dimension D>1 by Strong Disorder Renormalisation Group (SDRG). We have implemented an efficient algorithm to be able to consider a system with up to a billion spins independently of its spatial dimension. Critical properties of the 2D and 3D random quantum Potts model with q=2,3,5,10,20 and 50 states are shown to be governed by an infinite disorder fixed point. We have computed the correlation-length exponent u, the magnetization exponent d_f and the energy gap exponent psi. Using finite-size scaling and taking into account finite-size corrections, critical properties of the Potts model are shown to be q-independent. Random quantum Clock models with q=2,3,5,8 and 10 states have been also studied in 2D and 3D. A minimum amount of initial disorder strength is required to flow to an infinite disorder fixed point. Despite large error bars on psi exponent, our estimates for the critical exponents u and psi for all q are compatible with those of the random transverse-field Ising model. Our estimates for the critical exponent d_f are incompatible within error bar but very close. Lastly, the tricritical point of the random quantum Ashkin-Teller model has been studied in dimension two and three. We have shown that the correlation-length exponent associated with one of the two unstable directions does not belong to the university class of the random transverse-field Ising model
49
Pereira, Ana Luiza Cardoso 1976. "Destino dos estados estendidos e origem dos estados localizados no regime Hall quântico". [s.n.], 2005. http://repositorio.unicamp.br/jspui/handle/REPOSIP/277032.
Resumen
Orientadores: Peter A. B. Schulz, John T. ChalkerTese (doutorado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin
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Resumo: Esse trabalho é dedicado ao estudo de dois problemas de interesse atual em sistemas quânticos de baixa dimensionalidade. Ambos são relacionados ao processo de localização eletrônica no regime Hall quântico. O primeiro problema diz respeito ao destino dos estados estendidos no limite de baixos campos magnéticos ou forte desordem, onde ocorre a transição de líquido de Hall para o isolante de Hall. O problema é abordado através de simulações numéricas, com um modelo de rede bidimensional tratado por um Hamiltoniano tight-binding, considerando-se tanto desordem tipo ruído branco quanto desordem correlacionada com perfil Gaussiano. Nós observamos que à medida que o campo magnético tende a zero ou a desordem é suficientemente aumentada no sistema, os estados estendidos sofrem um deslocamento em relação ao centro das bandas de Landau, indo em direção às mais altas energias e, eventualmente, ultrapassando a energia de Fermi. Esse mecanismo é chamado na literatura de levitação de estados estendidos. Nossos resultados permitem uma análise quantitativa. Identificamos os seguintes parâmetros como sendo os relevantes para mapear a levitação: (i) a razão entre escalas de energia ¿ entre a energia de separação dos níveis de Landau e o alargamento do nível devido à desordem; e (ii) a razão entre escalas de comprimento ¿ entre o comprimento magnético e o comprimento de correlação da desordem. Analisando uma vasta gama de parâmetros, uma expressão de escala descrevendo a levitação de estados estendidos é estabelecida neste trabalho. O segundo problema abordado nesta tese é relacionado ao processo de blindagem do potencial de desordem e ao mecanismo de formação dos estados localizados em sistemas Hall quânticos. O trabalho analítico apresentado aqui é motivado por recentes resultados experimentais, que mostram imagens de microscopia com medidas locais do potencial eletrostático e da compressibilidade desses sistemas, evidenciando como se dá o processo de carga de estados localizados por cargas inteiras ou fracionárias (quase-partículas). Em um regime onde o comportamento é dominado por interações Coulombianas, estabelecemos um modelo eletrostático que descreve o estado localizado como sendo uma região compressível (quantum dot ou antidot) envolta por um plano incompressível, usando a aproximação de Thomas-Fermi para tratar as interações. O potencial eletrostático nas vizinhanças da região compressível é calculado, fornecendo o tamanho dos saltos que ocorrem no potencial à medida que cada carga é adicionada ou removida do estado localizado. Além de mostrar como estes saltos se tornam menores com o aumento do índice de Landau, nossos resultados mostram a dependência deles com a altura de observação do potencial (ou seja, a altura da ponta de prova em relação ao gás de elétrons). O modelo apresentado pode ser usado para tratar estados localizados observados nos platôs do efeito Hall quântico inteiro ou fracionário
Abstract: This work is devoted to the study of two problems of current interest in low dimensional quantum systems. Both are related to the process of electron localization in the quantum Hall regime. The first problem refers to the fate of extended states in the limit of low magnetic fields or strong disorder, where the transition from quantum Hall liquid to Hall insulator takes place. A numerical approach to the problem is used, with a 2D lattice model treated in a tight-binding framework, considering both white-noise and Gaussian correlated disorder. We observe that as the magnetic field vanishes or the disorder is sufficiently increased in the system, the extended states are shifted from the Landau band centers, going to higher energies and, eventually, rising above the Fermi energy. This mechanism is referred in the literature as levitation of extended states. Our results allow a quantitative analysis. We identify the following parameters as the relevant ones to map the levitation: (i) the energy scales ratio - between the energy separation of consecutive Landau levels and the level broadening due to disorder; and (ii) the length scales ratio - between the magnetic length and the disorder correlation length. Analyzing a wide range of parameters, a scaling expression describing the levitation of extended states is established. The second problem considered in this thesis is related to the screening of the disorder potential and to the mechanism of formation of localized states in quantum Hall systems. The analytical work we present here is motivated by recent imaging experiments, which probe locally the electrostatic potential and the compressibility of these systems, showing the charging of individual localized states by integer or fractional charges (quasiparticles). For a regime where the behavior is dominated by Coulomb interactions, we set out an electrostatic model describing the localized state as a compressible region (quantum dot or antidot) embebed in an incompressible background, using the Thomas-Fermi approximation to treat the interactions. The electrostatic potential in the vicinity of the compressible region is calculated, providing the size of potential steps as each charge is added or removed from the localized state. Besides from showing how the potential steps get smaller for higher Landau levels, our results show the dependence of these steps with the height of observation (i.e., the distance from the scanning probe to the electron gas). The proposed model can be used to treat localized states observed on integer or fractional quantum Hall plateaus
Doutorado
Física da Matéria Condensada
Doutor em Ciências
50
Mukhopadhyay, Ranjan. "Quantum phase transitions in disordered Bose systems". Thesis, 1998. https://thesis.library.caltech.edu/463/1/Mukhopadhyay_r_1998.pdf.
Resumen
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
We study the nature of various quantum phase transitions corresponding to the onset of superfluidity, at zero temperature, of bosons in a quenched medium. Particle-hole symmetry plays an essential role in determining the universality class of the transitions. To obtain a model with an exact particle-hole symmetry it is necessary to use the Josephson junction array Hamiltonian, which may include disorder in the Josephson couplings between phases at different sates. The functional integral formulation of this problem in d spatial dimensions yields a (d + 1)-dimensional classical XY-model with extended disorder, constant along the extra imaginary time dimension -- the so-called random rod problem. Particle-hole symmetry may then be broken by adding nonzero chemical potentials or site energies, which may also be site dependent and random. We may then distinguish three cases: (i) exact particle-hole symmetry, in which the site energies all vanish, (ii) statistical particle-hole symmetry in which the site energy distribution is symmetric about zero and hence vanishes on average, and (iii) complete absence of particle-hole symmetry in which the distribution is generic. We explore in each case the nature of the excitations in the nonsuperfluid Pose glass phase. We find, for example, that the compressibility, which has the interpretation of a temporal spin stiffness or superfluid density, is positive in cases (ii) and (iii), but that it vanishes with an essential singularity as full particle-hole symmetry is restored. We then focus on the critical point and discuss the validity of various scaling arguments. In particular, we argue that the dynamical exponent z could be different from d, and the arguments leading to their equality are incorrect. We then discuss the relevance of a type (ii) particle-hole symmetry breaking perturbation to the random rod critical behavior, identifying a nontrivial crossover exponent. This exponent cannot be calculated exactly but is argued to be positive and the symmetry breaking perturbation therefore relevant. We argue next that a perturbation of type (iii) is irrelevant to the resulting type (ii) critical behavior: the statistical symmetry is restored on large scales close to the critical point, and case (ii) therefore describes the dirty boson fixed point. Using various duality transformations we verify all of these ideas in one dimension. To study higher dimensions we attempt, with partial success, to generalize the Dorogovtsev-Cardy-Boyonovsky double epsilon expansion technique to this problem. We find that when the dimension of time [...] is sufficiently small the symmetry breaking perturbation of type (ii) is irrelevant, but that for sufficiently large [...] this is a relevant perturbation and a new stable commensurate fixed point appears. We speculate that this new fixed point becomes the dirty boson fixed point when [...] = 1. We also show that for [...], there exists a particle-hole asymmetric fixed point of type (iii), but we provide evidence that it merges with the commensurate fixed point for some finite [...]. This tends to confirm symmetry restoration at the physical [...] = 1.