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1
Wilson, Mark. "Many-body effects in ionic systems". Thesis, University of Oxford, 1994. http://ora.ox.ac.uk/objects/uuid:3c66daa2-5318-40d2-a445-15296d598a57.
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The electron density of an ion is strongly influenced by its environment in a condensed phase. When the environment changes, for example due to thermal motion, non-trivial changes in the electron density, and hence the interionic interactions occur. These interactions give rise to many-body effects in the potential. In order to represent this phenomenon in molecular dynamics (MD) simulations a method has been developed in which the environmentally-induced changes in the ionic properties are represented by extra dynamical variables. These extra variables are handled in an extended Lagrangian formalism by techniques analogous to those used in Car and Parrinello's ab initio MD method. At its simplest level (the polarizable-ion model or PIM) induced dipoles are represented. With the PIM it has proven possible to quantitatively account for numerous properties of divalent metal halides, which had previously been attributed to unspecific "covalent" effects. In the solid-state the prevalence of layered crystal structures is explained. Analogous non-coulombic features in liquid structures, in particular network formation in "strong" liquids like ZnCl2 , have been studied as has network disruption by "modifiers" like RbCl. This work leads to an understanding of the relationship between the microscopic structure and anomalous peaks ("prepeaks") seen in diffraction data of such materials. The PIM was extended to include induced quadrupoles and their effect studied in simulations of AgCl. In the solid-state it is found that the both are crucial in improving the phonon dispersion curves with respect to experiment. In the liquidstate polarization effects lower the melting point markedly. For oxides the short-range energy has been further partitioned into overlap and rearrangement energies and electronic structure calculations are used to parameterize a model in which the radius of the anion is included as an additional degree of freedom. The Bl → B2 phase transition is studied in MgO and CaO and the differences between the new model and a rigid-ion model are analysed.
2
Steiger, Don. "Numerical n-body methods in computational chemistry /". free to MU campus, to others for purchase, 1998. http://wwwlib.umi.com/cr/mo/fullcit?p9924930.
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3
Dinh, Thi Hanh Physics Faculty of Science UNSW. "Application of many-body theory methods to atomic problems". Publisher:University of New South Wales. Physics, 2009. http://handle.unsw.edu.au/1959.4/43734.
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There is strong interest in atomic and nuclear physics to the study of superheavy elements by the search for the island of stability in the region Z=104 to Z=126. There are many experimental efforts and theoretical works devoted to these study in measuring the spectra and chemical properties. In this thesis, calculations of the spectra and the hyperfine structure of some superheavy elements have been performed in an attempt to enrich our knowledge about the elements and even may help in their detection. We perform the high-precision relativistic calculations to determine the spectra of the superheavy element Z=119 (eka-Fr) and the singly-ionized superheavy element Z=120+ (eka-Ra+). Dominating correlation corrections beyond relativistic Hartree-Fock are included to all orders in the residual electron interaction using the Feynman diagram technique and the correlation potential method. The Breit interaction and quantum electrodynamics radiative corrections are considered. Also, the volume isotope shift is determined. We present the relativistic calculations for the energy levels of the superheavy element Z=120. The relativistic Hartree-Fock and configuration interaction techniques are employed. The correlations between core and valence electrons are treated by means of the correlation potential method and many-body perturbation theory. We also try to address the absence of experimental data on the electron structure and energy spectrum of the Uub element (Z=112) by calculating its energy levels. The relativistic Hartree-Fock and configuration interaction methods are combined with the many-body perturbation theory to construct the many-electron wave function for valence electrons and to include core-valence correlations. The hyperfine structure constants of the lowest s and p1/2 states of superheavy elements Z=119 and Z= 120+ are calculated. Core polarization, dominating correlation, Breit and quantum electrodynamic effects are considered. The dependence of the hyperfine structure constants on nuclear radius is discussed. Measurements of the hyperfine structure combined with our calculations will allow one to study nuclear properties and distribution of magnetic moment inside nucleus. Finally, we discuss the possibility of measuring nuclear anapole moments in atomic Zeeman transitions and perform the necessary calculations. Advantages of using Zeeman transitions include variable transition frequencies and the possibility of enhancement of parity nonconservation effects.
4
Gerster, Matthias [Verfasser]. "Tensor network methods for quantum many-body simulations / Matthias Gerster". Ulm : Universität Ulm, 2021. http://d-nb.info/1233737406/34.
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Richard, Ryan. "Increasing the computational efficiency of ab initio methods with generalized many-body expansions". The Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1385570237.
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Molnar, Andras [Verfasser], e Jan von [Akademischer Betreuer] Delft. "Tensor Network methods in many-body physics / Andras Molnar ; Betreuer: Jan von Delft". München : Universitätsbibliothek der Ludwig-Maximilians-Universität, 2019. http://d-nb.info/1185979328/34.
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Blandon, Juan. "DEVELOPMENT OF THEORETICAL AND COMPUTATIONAL METHODS FOR FEW-BODY PROCESSES IN ULTRACOLD QUANTUM GASES". Master's thesis, University of Central Florida, 2006. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/2881.
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We are developing theoretical and computational methods to study two related three-body processes in ultracold quantum gases: three-body resonances and three-body recombination. Three-body recombination causes the ultracold gas to heat up and atoms to leave the trap where they are confined. Therefore, it is an undesirable effect in the process of forming ultracold quantum gases. Metastable three-body states (resonances) are formed in the ultracold gas. When decaying they also give additional kinetic energy to the gas, that leads to the heating too. In addition, a reliable method to obtain three-body resonances would be useful in a number of problems in other fields of physics, for example, in models of metastable nuclei or to study dissociative recombination of H3 +. Our project consists of employing computer modeling to develop a method to obtain three-body resonances. The method uses a novel two-step diagonalization approach to solve the three-body Schrödinger equation. The approach employs the SVD method of Tolstikhin et al. coupled with a complex absorbing potential. We tested this method on a model system of three identical bosons with nucleon mass and compared it to the results of a previous study. This model can be employed to understand the 3He nucleus . We found one three-body bound state and four resonances. We are also studying Efimov resonances using a 4He-based model. In a system of identical spinless bosons, Efimov states are a series of loosely bound three-body states which begin to appear as the energy of the two-body bound state approaches zero . Although they were predicted 35 years ago, recent evidence of Efimov states found by Kraemer et al. in a gas of ultracold Cs atoms has sparked great interest by theorists and experimentalists. Efimov resonances are a kind of pre-dissociated Efimov trimer. To search for Efimov resonances we tune the diatom interaction potential, V(r): V(r) → λV(r) as Esry et al. did . We calculated the first two values of λ for which there is a "condensation" (infinite number) of Efimov states. They are λEfimov1 = 0.9765 and λEfimov2 = 6.834. We performed calculations for λ = 2.4, but found no evidence of Efimov resonances. For future work we plan to work with λ ≈ 4 and λ ≈ λEfimov2 where we might see d-wave and higher l-wave Efimov resonances. There is also a many-body project that forms part of this thesis and consists of a direct diagonalization of the Bogolyubov Hamiltonian, which describes elementary excitations of a gas of bosons interacting through a pairwise interaction. We would like to reproduce the corresponding energy spectrum. So far we have performed several convergence tests, but have not observed the desired energy spectrum. We show preliminary results.M.S.
Department of Physics
Sciences
Physics
8
Motta, M. "DYNAMICAL PROPERTIES OF MANY--BODY SYSTEMS FROM CONFIGURATIONAL AND DETERMINANTAL QUANTUM MONTE CARLO METHODS". Doctoral thesis, Università degli Studi di Milano, 2015. http://hdl.handle.net/2434/345455.
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The numerical simulation of quantum many-body systems is an essential instrument in the research on condensed matter Physics.
Recent years have witnessed remarkable progress in studying dynamical properties of non-relativistic Bose systems with quantum Monte Carlo (QMC) methods.
On the other hand, the numerical study of Fermi systems is a still open problem of great relevance, as fermions constitute a substantial part of ordinary matter and methods for the accurate calculation of their ground-state and dynamical properties would be useful instruments for the interpretation of experimental data.
In this thesis, a number of approximate schemes for studying ground-state and dynamical properties of quantum many-body systems are presented and employed to calculate ground-state and dynamical properties of Bose and Fermi systems.
In particular, the Path Integral Ground State QMC method is used to investigate density fluctuations in one-dimensional systems of Helium atoms and hard rods, and the phaseless Auxiliary field QMC is used to investigate the electronic band
and effective mass of the two-dimensional homogeneous electron gas.
9
Holtz, Susan Lady. "Liouville resolvent methods applied to highly correlated systems". Diss., Virginia Polytechnic Institute and State University, 1986. http://hdl.handle.net/10919/49795.
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Scalesi, Alberto. "On the characterization of nuclear many-body correlations in the ab initio approach". Electronic Thesis or Diss., université Paris-Saclay, 2024. http://www.theses.fr/2024UPASP070.
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La branche 'ab initio' de la théorie de la structure nucléaire s'est traditionnellement concentrée sur l'étude des noyaux de masse légère à moyenne et des systèmes principalement sphériques. Les développements actuels visent à étendre cette approche aux noyaux de masse élevée et aux systèmes à double couche ouverte. L'étude de ces systèmes représente un défi qualitatif et quantitatif.Par conséquent, différentes stratégies doivent être conçues pour capturer efficacement les corrélations dominantes qui ont le plus d'impact sur les observables d'intérêt. Bien qu'il existe en principe des méthodes exactes pour résoudre l'équation de Schrödinger non relativiste pour un hamiltonien nucléaire donné, les limitations pratiques des simulations numériques rendent un tel espoir vain pour la plupart des isotopes. Cela nécessite une hiérarchisation des corrélations mises en jeu dans les différents systèmes nucléaires. La plupart des techniques ab initio reposent sur un calcul initial de type 'champ moyen', généralement effectué via la méthode Hartree-Fock (HF), qui fournit un état de référence contenant la majeure partie des corrélations contribuant aux propriétés nucléaires globales.Lorsqu'on s'attaque à des systèmes à couche ouverte, il s'est avéré particulièrement pratique de briser les symétries du Hamiltonien au niveau du champ moyen pour inclure efficacement les corrélations statiques apparaissant dans les noyaux superfluides (via la théorie HF-Bogoliubov, HFB) ou déformés (via la méthode HF déformée, dHF). Le présent travail contribue à cette ligne de recherche en proposant et en explorant de nouvelles techniques à N-corps applicables à tous les systèmes nucléaires exploitant cette idée de brisure de symétrie. La technique ab initio la plus simple applicable au-delà du champ moyen est la théorie des perturbations à N-corps. Le premier résultat de ce travail est la démonstration qu'une théorie des perturbations incorporant la brisure de la symétrie de rotation (dBMBPT) et employant des interactions nucléaires modernes peut déjà décrire qualitativement les principales observables nucléaires, telles que l'énergie de liaison et le rayon de l'état fondamental.Étant donné que la théorie des perturbations constitue une méthode peu coûteuse permettant d'effectuer des études systématiques sur large partie de la carte des noyaux, une partie du présent travail est consacrée à ouvrir la voie à de tels calculs à grande échelle. Afin de pousser les calculs à N-corps vers une plus grande précision, une nouvelle technique ab initio est ensuite introduite, à savoir la méthode des fonctions de Green-Dyson autoconsistantes déformées (dDSCGF). Cette approche nonperturbative (c'est-à-dire sommant un nombre infini de contributions perturbatives) permet de calculer une grande variété de quantités utiles, à la fois pour l'état fondamental du noyau ciblé et pour les états excités des systèmes voisins. En outre, elle s'étend naturellement en direction des réactions nucléaires afin d'évaluer, par exemple, les potentiels optiques. Étant donné le coût de calcul élevé des méthodes nonperturbatives à N-corps, la dernière section présente des approches possibles pour rendre ces calculs plus efficaces. En particulier, la base des orbitales naturelles est introduite et étudiée dans le contexte des systèmes déformés. Ainsi, il est prouvé que cette technique permet d'utiliser des bases beaucoup plus petites, réduisant ainsi de manière significative le coût final des simulations numériques et étendant leur domaine d'application. En conclusion, les développements présentés dans ce travail ouvrent des voies nouvelles et prometteuses en vue de la description ab initio des noyaux lourds à couches ouvertesThe 'ab initio' branch of nuclear structure theory has traditionally focused on the study of light to mid-mass nuclei and primarily spherical systems. Current developments aim at extending this focus to heavy-mass nuclei and doubly open-shell systems. The study of such systems is qualitatively and quantitatively challenging. Hence, different strategies must be designed to efficiently capture the dominant correlations that most significantly impact the observables of interest. While in principle exact methods exist to solve the non-relativistic Schrödinger equation for a given Nuclear Hamiltonian, practical limitations in numerical simulations make such an approach impossible for most isotopes. This calls for a hierarchical characterization of the main correlations at play in the various nuclear systems. Most ab initio techniques rely on an initial mean-field calculation, typically carried out via the Hartree-Fock (HF) method, which provide a reference state containing the principal part of the correlations contributing to bulk nuclear properties. When tackling open-shell systems, it has been proven particularly convenient to break symmetries at mean-field level to effectively include the static correlations arising in superfluid (via HF-Bogoliubov theory, HFB) or deformed nuclei (via deformed HF, dHF). The present work contributes to this research line by proposing end exploring novel symmetry-breaking many-body techniques applicable to all nuclear systems. The simplest ab initio technique that can be applied on top of the mean-field is many-body perturbation theory. The first result of this work is the demonstration that symmetry-breaking perturbation theory (dBMBPT) based on state-of-the-art nuclear interactions can already qualitatively describe the main nuclear observables, such as ground-state energies and radii. Given that perturbation theory constitutes a cheap and efficient way to perform systematic studies of different nuclei across the nuclear chart, a part of the present work is dedicated to pave the way to such large-scale calculations. In order to push many-body calculations to higher precision, a novel ab initio technique is then introduced, namely the deformed Dyson Self-Consistent Green's function (dDSCGF) method. Such a non-perturbative (i.e., resumming an infinite number of perturbation-theory contributions) approach allows one to compute a wide variety of quantities of interest, both for the ground state of the targeted nucleus and for excited states of neighbouring systems. In addition, it naturally bridges to nuclear reactions giving access to, e.g., the evaluation of optical potentials. Given the high computational cost of non-perturbative many-body methods, the final section introduces possible approaches to make such calculations more efficient. In particular, the Natural Orbital basis is introduced and investigated in the context of deformed systems. Eventually, it is proven that this technique enables the use of much smaller basis sets, thus significantly decreasing the final cost of numerical simulations and enlarging their reach. All together, the developments reported in the present work open up new and promising possibilities for the ab initio description of heavy-mass and open-shell nuclei
11
Rosenbach, Robert [Verfasser]. "Numerical methods for complex quantum dynamics with applications to quantum biology and quantum many-body dynamics / Robert Rosenbach". Ulm : Universität Ulm. Fakultät für Naturwissenschaften, 2016. http://d-nb.info/1093557958/34.
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Xu, Guang-Hui. "Exploratory studies of group theoretic methods in atomic physics". Scholarly Commons, 1989. https://scholarlycommons.pacific.edu/uop_etds/2189.
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The properties of a physical system are determined by its equation of motion, and every such equation admits one-parameter groups which keep the equation invariant. Thus, for a particular system, if one can find the generator of a one-parameter group which keeps the equation and some further function or functional invariant, then one can change this system into others by changing the parameter, while keeping some properties constant. In this way, one can tell why different systems have some common properties. More importantly, one can use this method to find relationships between the physical properties of different systems.
In the next section, we will illustrate the group theoretic approach by applying it to systems of two coupled oscillators and the hydrogen molecular ion. In section III of this thesis, we will investigate the helium atom system, considering both classical and quantum cases. In the quantum case our attention will be concentrated on the Schrodinger equation in matrix form. We will use a finite set of wavefunctions as our basis. Hence the results obtained will be approximate.
13
Dorfner, Florian [Verfasser], e Fabian [Akademischer Betreuer] Heidrich-Meisner. "Numerical methods for strongly correlated many-body systems with bosonic degrees of freedom / Florian Dorfner ; Betreuer: Fabian Heidrich-Meisner". München : Universitätsbibliothek der Ludwig-Maximilians-Universität, 2017. http://d-nb.info/1130587169/34.
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Shi, Bobo. "Implementation and Performance Analysis of Many-body Quantum Chemical Methods on the Intel Xeon Phi Coprocessor and NVIDIA GPU Accelerator". The Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1462793739.
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Abrams, Micah Lowell. "General-Order Single-Reference and Mulit-Reference Methods in Quantum Chemistry". Diss., Georgia Institute of Technology, 2005. http://hdl.handle.net/1853/6852.
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Many-body perturbation theory and coupled-cluster theory, combined with carefully constructed basis sets, can be used to accurately compute the properties of small molecules. We applied a series of methods and basis sets aimed at reaching the ab initio limit to determine the barrier to planarity for ethylene cation. For potential energy surfaces corresponding to bond dissociation, a single Slater determinant is no longer an appropriate reference, and the single-reference hierarchy breaks down. We computed full configuration interaction benchmark data for calibrating new and existing quantum chemical methods for the accurate description of potential energy surfaces. We used the data to calibrate single-reference configuration interaction, perturbation theory, and coupled-cluster theory and multi-reference configuration interaction and perturbation theory, using various types of molecular orbitals, for breaking single and multiple bonds on ground-state and excited-state surfaces. We developed a determinant-based method which generalizes the formulation of many-body wave functions and energy expectation values. We used the method to calibrate single-reference and multi-reference configuration interaction and coupled-cluster theories, using different types of molecular orbitals, for the symmetric dissociation of water. We extended the determinant-based method to work with general configuration lists, enabling us to study, for the first time, arbitrarily truncated coupled-cluster wave functions. We used this new capability to study the importance of configurations in configuration interaction and coupled-cluster wave functions at different regions of a potential energy surface.
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D'Alberto, Jacopo. "Study of a 2D Bose-Fermi mixture with quantum Monte Carlo methods". Master's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/24393/.
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Ultracold gases are an exceptionally versatile platform to test novel physical concepts. Thanks to the development of new experimental techniques, they have greatly advanced our understanding of the physics of many-body systems and allowed precision measurements of fundamental constants. Bose-Fermi mixtures can then be introduced in this context. This novel quantum many-body system is essentially an ultracold gas made up by both bosons and fermions, where tunable attractive or repulsive interactions between the components can be introduced. At T = 0 and for weak interactions the bosons condense while the fermions behave as a Fermi liquid. In particular, a recent system of interest is given by two-dimensional Bose-Fermi mixtures with both Bose-Fermi and Bose-Bose repulsive interactions. In the present work, a Quantum Monte Carlo study is conducted, for a fixed value of boson concentration, at zero-temperature from the weak to the strong Bose-Fermi coupling limit. Variational Monte Carlo and Fixed-Node Diffusion Monte Carlo are applied using an optimized Jastrow-Slater wavefunction, extending previous methodology developed for the three-dimensional case. The results are then compared with perturbative predictions, showing very good agreement in the weak coupling region. Variational Monte Carlo agrees with the analytic predictions only for extremely weak coupling, while Diffusion Monte Carlo proves necessary to recover good agreement over the whole perturbative regime. For stronger couplings, our simulations indicate the tendency of the mixture to form bosonic clusters. This finding would definitively deserve further investigation, which is postponed to future works.
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Li, Ying [Verfasser], Roser [Akademischer Betreuer] [Gutachter] Valenti e Peter [Gutachter] Kopietz. "Electronic and magnetic properties of candidate materials for Kitaev physics using a Combination of density functional theory and many-body methods / Ying Li ; Gutachter: Roser Valentí, Peter Kopietz ; Betreuer: Roser Valentí". Frankfurt am Main : Universitätsbibliothek Johann Christian Senckenberg, 2017. http://d-nb.info/1128229528/34.
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Foyevtsova, Kateryna [Verfasser], Roser [Akademischer Betreuer] Valenti, Peter [Akademischer Betreuer] Kopietz e Peter [Akademischer Betreuer] Hirschfeld. "Investigation of the microscopic behavior of Mott insulators by means of the density functional theory and many-body methods / Kateryna Foyevtsova. Gutachter: Roser Valenti ; Peter Kopietz ; Peter Hirschfeld. Betreuer: Roser Valenti". Frankfurt am Main : Univ.-Bibliothek Frankfurt am Main, 2012. http://d-nb.info/1044275022/34.
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Roux, Antoine. "Emulation of PGCM calculations using the Eigenvector continuation method". Electronic Thesis or Diss., université Paris-Saclay, 2024. http://www.theses.fr/2024UPASP114.
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Le noyau atomique, système quantique de nucléons en interaction, constitue un problème difficle à résoudre exactement. Pour contourner cette difficulté, des méthodes de résolution approchées on été introduites, comme la Projected Generator Coordinate Method (PGCM). La force de la PGCM est de construire un espace de faible dimension, motivé par des considérations physiques, dans lequel trouver un solution approchée est facile. Cependant, le coût numérique du calcul d'un espace PGCM rend cette méthode mal adaptée pour une étude statistique de sensibilité des observables nucléaires vis-à-vis des paramètres du modèle d'interaction, laquelle nécessite un grand nombre de calculs PGCM. Afin de rendre ce type d'études possibles, cette thèse explore la notion d'émulateur PGCM. Dans ce travail, une combinaison de PGCM avec la méthode Eigenvector Continuation (EC) est construite et étudiée. Cette combinaison (l'émulateur PGCM-EC) tire parti des ressemblances formelles entre PGCM et EC, et surtout de la possibilité de décomposer l'hamiltonien comme combinaison linéaire de termes indépendants des paramètres du modèle d'interaction. Cette dernière propriété permet de concentrer la plus grande partie du coût numérique sur le calcul de quantités indépendantes des paramètres de l'interaction (les kernels élémentaires), et ainsi rend possible l'émulation massive de calculs PGCM, au prix d'avoir en amont effectué le calcul très lourd des kernels élémentaires. Les limites de cet émulateur sont aussi étudiées, en introduisant notamment la notion de sur-entraînement, qui provient précisément du fait que la PGCM est une méthode non-exacte de résolution du problème à N-corps nucléaire. Cette thèse démontre au final qu'il est possible d'émuler des millions de calculs PGCM avec une erreur ne dépassant pas 3% sur la spectroscopie collective des noyaux, et avec un faible coût numérique représentant une fraction de 1% du coût des millions de calculs PGCMAn atomic nucleus is a quantum system of interacting nucleons and constitutes a problem difficult to solve exactly. For this reason, a diversity of approximate resolution methods has been designed, and Projected Generator Coordinate Method (PGCM) is one of them. The strong point of PGCM is to construct a physically inspired small dimensional space, in which an approximate solution of the nuclear many-body problem is easily found. However the numerical cost of PGCM space computation make this method inadapted for sensibility analysis of nuclear observables with restect to parametrisation of the interaction model, this analysis requiring an huge number of PGCM computations. In order to make this type of study possible, this thesis explore the concept of PGCM emulator. In this work, a combination of PGCM with Eigenvector Continuation (EC) is constructed and studied. This combination (the PGCM-EC emulator) takes advantage of mathematical similarities between PGCM and EC, and above all of the decomposition of the hamiltonian as a linear combination of parameter-independent terms. The latter property is used to concentrate the heavier numerical cost in the computation of parameter-independent quantities (the elementary kernels), and open the feasability of massive PGCM emulations, the price being having first-handedly computed the costly elementary kernels. Limits of the emulator are also explored, by introducing the concept of over-training, which is exactly a consequence of the aproximativeness of a PGCM computation. Eventually this thesis demonstrates the possibility to emulate millions of PGCM computations with an error on collective spectroscopy less than 3%, and with a low numerical cost fraction of 1% of the million PGCM calculations cost
20
Angelone, Adriano. "Strongly correlated systems of bosons and fermions : a diagrammatic, variational and path integral Monte Carlo study". Thesis, Strasbourg, 2017. http://www.theses.fr/2017STRAF028/document.
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Mon travail de thèse se concentre sur l'étude, à l'aide de techniques numériques, de systèmes de fermions et bosons fortement corrélés. J'étudie Hamiltoniens de bosons sur réseau avec interactions à portée étendue, avant un intérêt pour expériences concernant atomes en états Rydberg-dressed, par moyen de simulations Path Integral Monte Carlo. Mon résultat principal est la démonstration d'un état de superverre en absence de sources de frustration dans le système.J'étudie également la modèle t-J fermionique avec deux trous par moyen de simulationsVariational Monte Carlo avec l’ansatz Entangled Plaquette States (EPS). Mon étude est fondamental en la perspective d'appliquer l'ansatz EPS à autres systèmes fermioniques, d’intérêt pour la supraconductivité à haute temperature, dont le comportement n'a pas encore été déterminé. Finalement, je présente mon travail sur une implémentation de l'algorithme Diagrammatic Monte CarloThe focus of my thesis is the investigation, via numerical approaches, of strongly correlated models of bosons and fermions. I study bosonic lattice Hamiltonians with extended--range interactions, of interest for experiments with cold Rydberg-dressed atoms, via Path Integral MonteCarlo simulations. My main result is the demonstration of a superglass in the absence of frustration sources in the system. I also study the fermionic $t-J$ model in the presence of two holes via Variational Monte Carlo with the Entangled Plaquette States Ansatz. My study is foundational to the extension of this approach to other fermionic systems, of interest for high temperature superconductivity, where the physical picture is still under debate (such as, e.g., the $t-J$ model in the case of finite hole concentration). Finally, I discuss my work on an implementation of the Diagrammatic Monte Carlo algorithm
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Liu, Kuan-Yu. "Generalized Many-Body Expansion: A Fragment-Based Method for modeling Large Systems". The Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu1560442158764827.
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Crivelli, Dawid Wiesław. "Particle and energy transport in strongly driven one-dimensional quantum systems". Doctoral thesis, Katowice: Uniwersytet Śląski, 2016. http://hdl.handle.net/20.500.12128/5879.
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This Dissertation concerns the transport properties of a strongly–correlated one–dimensional system
of spinless fermions, driven by an external electric field which induces the flow of charges and energy
through the system. Since the system does not exchange information with the environment, the
evolution can be accurately followed to arbitrarily long times by solving numerically the time–dependent
Schrödinger equation, going beyond Kubo’s linear response theory.
The thermoelectric response of the system is here characterized, using the ratio of the induced
energy and particle currents, in the nonequilibrium state under the steady applied electric field. Even
though the equilibrium response can be reached for vanishingly small driving, strong fields produce
quantum–mechanical Bloch oscillations in the currents, which disrupt the proportionality of the currents.
The effects of the driving on the local state of the ring are analyzed via the reduced density matrix of
small subsystems. The local entropy density can be defined and shown to be consistent with the laws of
thermodynamics for quasistationary evolution. Even integrable systems are shown to thermalize under
driving, with heat being produced via the Joule effect by the flow of currents. The spectrum of the
reduced density matrix is shown to be distributed according the Gaussian unitary ensemble predicted by
random–matrix theory, both during driving and a subsequent relaxation.
The first fully–quantum model of a thermoelectric couple is realized by connecting two correlated
quantum wires. The field is shown to produce heating and cooling at the junctions according to the
Peltier effect, by mapping the changes in the local entropy density. In the quasiequilibrium regime, a
local temperature can be defined, at the same time verifying that the subsystems are in a Gibbs thermal
state. The gradient of temperatures, established by the external field, is shown to counterbalance the
flow of energy in the system, terminating the operation of the thermocouple. Strong applied fields lead
to new nonequilibrium phenomena. At the junctions, observable Bloch oscillations of the density of
charge and energy develop at the junctions. Moreover, in a thermocouple built out of Mott insulators, a
sufficiently strong field leads to a dynamical transition reversing the sign of the charge carriers and the
Peltier effect.
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Hickel, Tilmann. "Theory of many body effects in the Kondo lattice model projection operator method /". [S.l.] : [s.n.], 2005. http://deposit.ddb.de/cgi-bin/dokserv?idn=980739764.
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Hickel, Tilmann. "Theory of many-body effects in the Kondo-lattice model". Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät I, 2006. http://dx.doi.org/10.18452/15500.
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Das magnetische Verhalten zahlreicher Materialien lässt sich auf eine indirekte Wechselwirkung lokalisierter magnetischer Momente, vermittelt durch die Elektronen eines Leitungsbandes, zurückführen. Das Kondo-Gitter-Modell hat sich als elegante Möglichkeit bewährt, diesen Prozess quantenmechanisch zu beschreiben. Es reduziert die Physik auf eine intraatomare Wechselwirkung der Spins von lokalisierten und itineranten Elektronen. Die vorliegende Arbeit ist den analytischen Eigenschaften dieses Modells gewidmet. Die besondere Herausforderung des Kondo-Gitter-Modells besteht dabei im Zusammenwirken zweier verschiedener Teilchensorten, beschrieben durch Fermi-Operatoren sowie quantenmechanische Spins. Bisherige Untersuchungen haben sich in der Regel nur auf eine der beiden Teilchensorten konzentriert. Mit der Projektions-Operator-Methode stellen wir eine Möglichkeit vor, beide Teilsysteme in gleicher Qualität zu behandeln. Die Auswertung des Teilsystems der itineranten Elektronen führt auf einen Ausdruck für die Selbstenergie, der lineare und quadratische Effekte in der Wechselwirkung exakt beschreibt. Die resultierenden Zustandsdichten weisen starke Korrelationseffekte auf. Deren Untersuchung dient sowohl der Bestätigung von Ergebnissen weniger systematischer Zugänge als auch dem Aufzeigen neuer Vielteilchen-Phänomene. Die Anwendung der Projektions-Operator-Methode auf das System der lokalisierten Momente führt zu einer Analyse der bereits bekannten RPA (random phase approximation). Zu diesem Zweck werden die Magnonenspektren und die Curie-Temperaturen systematisch untersucht. Dabei treten bisher unbekannte Schwachpunkte der RPA zu Tage, die auch die Kombination mit Theorien für das itinerante Teilsystem verhindern. Verbesserungen und Alternativen zur RPA werden diskutiert.The magnetic behaviour of various materials is due to an indirect interaction of localized magnetic moments, which is based on itinerant electrons in a conduction band. The Kondo-lattice model is an elegant approach for a quantum-mechanical description of this process. It reduces the relevant physics to an intra-atomic exchange interaction of the localized and the itinerant electrons. The aim of the present work is a detailed investigation of analytic properties of this model. Here, the interplay of two distinct types of particles, described by Fermi operators and quantum-mechanical spin operators respectively, is a major challenge of the considered model. Previous studies have focused on one of these subsystems only. Using the projection-operator method, we suggest an efficient way to describe both subsystems on the same level of approximation. An evaluation of the subsystem of itinerant electrons yields an expression for the self-energy, which describes linear and quadratic interaction effects exactly. The densities of states derived with this theory show strong correlation effects. We were able to assess results obtained with less systematic approaches and to predict new many-particle effects. The application of the projection-operator method to the subsystem of localized magnetic moments results in a detailed analysis of the RPA (random phase approximation). The dependence of magnon spectra and Curie temperatures on model parameters are investigated systematically. Previously unknown drawbacks of the RPA are revealed, which prevent the combination of these results with theories for the itinerant subsystem. Improvements beyond RPA and alternative approximations are discussed.
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Nakib, Protik H. "The Multiconfiguration Time Dependent Hartree-Fock Method for Cylindrical Systems". Thèse, Université d'Ottawa / University of Ottawa, 2013. http://hdl.handle.net/10393/26297.
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Many-body quantum dynamics is a challenging problem that has induced the development of many different computational techniques. One powerful technique is the multiconfiguration time-dependent Hartree-Fock (MCTDHF) method. This method allows proper consideration of electronic correlation with much less computational overhead compared to other similar methods. In this work, we present our implementation of the MCTDHF method on a non-uniform cylindrical grid. With the one-body limit of our code, we studied the controversial topic of tunneling delay, and showed that our results agree with one recent experiment while
disagreeing with another. Using the fully correlated version of the code, we demonstrated the ability of MCTDHF to address correlation by calculating the ground state ionization energies of a few strongly correlated systems.
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Malpetti, Daniele. "Thermodynamics of strongly interacting bosons on a lattice : new insights and numerical approaches". Thesis, Lyon, 2016. http://www.theses.fr/2016LYSEN065/document.
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Les atomes froids dans les réseaux optiques permettent d'avoir un contrôle sans précédent des états a N-corps fortement corrélés. Pour cette raison, ils représentent un excellent outil pour l'implémentation d'un « simulateur quantique », utile pour réaliser de manière expérimentale de nombreux hamiltoniens de systèmes d'intérêt physique. En particulier, ils rendent possible la création de champs de jauge artificiels; ces derniers permettant d'accéder à la physique du magnétisme frustré. Dans ce travail, il s'agit de s'intéresser à la thermodynamique des atomes froids, en abordant ce sujet de manière théorique et numérique. A ce jour, le Monte Carlo quantique est la méthode la plus efficace dans ce domaine. Néanmoins, en raison de ce qu'on appelle le « problème du signe », elle ne peut s'appliquer qu'à une classe restreinte de systèmes, et dont par exemple les systèmes frustrés ne font pas partie. L'intérêt de cette thèse est de développer une nouvelle méthode approximée fondée sur une approche Monte Carlo. La première partie de cette thèse est consacrée à des considérations de nature théorique sur la structure spatiale des corrélations classiques et quantiques. Ces résultats nous permettent de développer, dans une deuxième partie, une approximation nommée « champ moyen quantique ». Celle-ci permet de proposer, dans une troisième partie, une méthode numérique qu'on appelle « Monte Carlo du champ auxiliaire » et qu'on applique à des cas d'intérêt physique, notamment au réseau triangulaire frustréCold atoms in optical lattices offer unprecedented control over strongly correlatedmany-body states. For this reason they represent an excellent tool for the implementation ofa “quantum simulator”, which can be used to realize experimentally several Hamiltonians ofsystems of physical interest. In particular, they enable the engineering of artificial gaugefields, which gives access to the physics of frustrated magnetism. In this work, we study thethermodynamics of cold atoms both from a theoretical and a numerical point of view. Atpresent days, the most effective method used in this field is the quantum Monte Carlo. Butbecause of the so-called “sign problem” it can only be applied to a limited class of systems,which for example do not include frustrated systems. The interest of this thesis is to developof a new approximated method based on a Monte Carlo approach. The first part of this workis dedicated to theoretical considerations concerning the spatial structure of quantum andclassical correlations. These results permit to develop, in the second part, an approximationcalled quantum mean-field. This latter allows to propose, in the third part, a numericalmethod that we call “auxiliary-field Monte Carlo” and that we apply to some systems ofphysical interest, among which the frustrated triangular lattice
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Comparin, Tommaso. "From few-body atomic physics to many-body statistical physics : the unitary Bose gas and the three-body hard-core model". Thesis, Paris Sciences et Lettres (ComUE), 2016. http://www.theses.fr/2016PSLEE042/document.
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Les gaz d'atomes ultrafroids offrent des possibilités sans précédent pour la réalisation et la manipulation des systèmes quantiques. Le contrôle exercé sur les interactions entre particules permet d'atteindre le régime de fortes interactions, pour des espèces d'atomes à la fois fermioniques et bosoniques. Dans la limite unitaire, où la force d'interaction est à son maximum, des propriétés universelles émergent. Pour les atomes bosoniques, celles-ci comprennent l'effet Efimov, l'existance surprenante d'une séquence infinie d'états liés à trois corps. Dans cette thèse, nous avons étudiés un système de bosons unitaires. Partant des cas à deux et à trois corps, nous avons montrés que le modèle choisi capturait correctement les caractéristiques universelles de l'effet Efimov. Pour le modèle à N-corps, nous avons développé un algorithme de Monte Carlo quantique capable de réaliser les différentes phases thermodynamiques du système : gaz normal à haute-température, condensat de Bose-Einstein, et liquide d'Efimov. Un unique composant de notre modèle resterait pertinent à la limite de température infinie, à savoir la répulsion corps dur à trois corps, qui constitue une généralisation du potentiel classique entre sphères dures. Pour ce modèle, nous avons proposé une solution au problème d'empilement compact en deux et trois dimensions, fondée sur une Ansatz analytique et sur la technique de recuit simulé. En étendant ces résultats à une situation de pression finie, nous avons montré que le système présente une transition de fusion discontinue, que nous avons identifié à travers la méthode de Monte CarloUltracold atomic gases offer unprecedented possibilities to realize and manipulate quantum systems. The control on interparticle interactions allows to reach the strongly-interacting regime, with both fermionic and bosonic atomic species. In the unitary limit, where the interaction strength is at its maximum, universal properties emerge. For bosonic atoms, these include the Efimov effect, the surprising existence of an infinite sequence of three-body bound states. In this thesis, we have studied a system of unitary bosons. Starting from the two- and three-body cases, we have shown that the chosen model correctly captures the universal features of the Efimov effect. For the corresponding many-body problem, we have developed a quantum Monte Carlo algorithm capable of realizing the different thermodynamic phases in which the system may exist: The high-temperature normal gas, Bose-Einstein condensate, and Efimov liquid. A single ingredient of our model would remain relevant in the infinite-temperature limit, namely the three-body hard-core repulsion, which constitutes a generalization of the classical hard-sphere potential. For this model, we have proposed a solution to the two- and three-dimensional packing problem, based on an analytical ansatz and on the simulated-annealing technique. Extending these results to finite pressure showed that the system has a discontinuous melting transition, which we identified through the Monte Carlo method
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Stevenson, Paul. "Nuclear structure calculations using many-body perturbation theory with a separable interaction". Thesis, University of Oxford, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.312333.
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Botzung, Thomas. "Study of strongly correlated one-dimensional systems with long-range interactions". Thesis, Strasbourg, 2019. http://www.theses.fr/2019STRAF062.
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Durant cette thèse, nous étudions des systèmes unidimensionnels avec des couplages longue-portée. Dans la première partie, nous démontrons que ces couplages entraînent une décroissance algébrique des corrélations dans des fils quantiques désordonnés. Deuxièmement, nous analysons un modèle étendu de Hubbard où les particules interagissent via un potentiel « soft-core » générant de nouvelles phases exotiques. Dans le troisième chapitre, nous démontrons que restaurer l’extensivité a une influence sur les propriétés de basse énergie de modèle quantique dans la limite thermodynamique. Finalement, nous présentons des résultats préliminaires sur la modification de la localisation d’Anderson en présence d’un couplage avec une cavitéDuring this Ph.D., we studied one-dimensional systems with long-range couplings. In the first part, we demonstrate that power-law couplings lead to an algebraic decay of correlations at long distances in disordered quantum wires. In the second chapter, we analysed an extended Hubbard model where particles interact via a finite-range potential that induces frustration and new exotic phases. In the third chapter, we demonstrated that restoring energy extensivity has an influence on the low-energy properties of quantum model in the thermodynamic limit. Finally, we provide preliminary results on the modification of Anderson localization due to the coupling to a cavity mode
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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.
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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
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Masella, Guido. "Exotic quantum phenomena in cold atomic gases : numerical approaches". Thesis, Strasbourg, 2019. http://www.theses.fr/2019STRAF061.
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L'objectif principal de cette thèse est l'étude des propriétés à basse énergie et température de systèmes fortement corrélés de bosons interagissant via des potentiels à portée longue et étendue, et pertinentes pour la réalisation expérimentale avec des gaz atomiques froids. Cette étude est réalisée à l'aide d'une combinaison de techniques numériques, comme le Path Integral Montecarlo et de techniques analytiques. Le principal résultat de mon travail est la démonstration de l’existence d’une phase supersolide à bandes et d’une rare transition entre différents supersolides dans un modèle à interaction finie de bosons de coer dur sur un réseau carré. J'étudie également les scénarios hors d'équilibre de tels modèles via des quenches de température simulées. Enfin, j'étudie comment la restauration de l'extensibilité énergétique dans des systèmes en interaction à longue portée peut avoir une incidence profonde sur les propriétés de basse énergie dans la limite thermodynamiqueThe central aim of this thesis is the study of the low-energy and low-temperature properties of strongly correlated systems of bosonic particles interacting via finite- and long-range potentials, and relevant to experimental realization with cold atomic gases. This study is carried out with a combination of state-of-the-art numerical techniques such as Path Integral Monte Carlo and analytical techniques. The main result of my work is the demonstration of the existence of a stripe supersolid phase and of a rare transition between isotropic and anisotropic supersolids in a finite-range interacting model of hard-bosons on a square lattice. I also investigate the out-of-equilibrium scenarios of such models via simulated temperature quenches. Finally, I investigate how restoring energy extensivity in long-range interacting systems can have a profound incidence on the low-energy properties in the thermodynamic limit
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Neff, Thomas. "Short ranged central and tensor correlations in nuclear many-body systems towards ab initio calculations using realistic interactions within the unitary correlation operator method /". Phd thesis, [S.l.] : [s.n.], 2002. https://tuprints.ulb.tu-darmstadt.de/223/1/diss.pdf.
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In this work a unitary correlation operator is presented that explicitly describes the short-ranged central and tensor correlations in the nuclear many-body system. These short-ranged correlations are induced by the repulsive core and the pronounced tensor force of realistic nucleon-nucleon interactions and cannot be described by the simple many-body states of a mean-field or shell model approach. The unitary correlation operator is discussed for the Argonne V18 and the Bonn-A interactions. Applying the correlation operator onto the Hamiltonian a common effective interaction for low momenta is obtained. Calculations for 4He using the one- and two-body part of the correlated Hamiltonian compare favorably with exact many-body methods. Calculations for 16O and 40Ca which are not possible with exact methods are performed using harmonic oscillator shell model states. The observed deviation from the experimental binding energies and radii is attributed to the missing three-body forces. The correlated interaction in a basis-free representation is used in the Fermionic Molecular Dynamics model to calculate the nuclei of the p- and the sd-shell. In this model the uncorrelated many-particle state is given as a Slaterdeterminant of Gaussian wave-packets with spin and isospin degrees of freedom which allows a consistent description of spherically symmetric, intrinsically deformed and clustered nuclei.
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Lambert, Henry A. R. "Electronic excitations in semiconductors and insulators using the Sternheimer-GW method". Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:eb6210c9-e0cc-45e8-93eb-719bdcc83857.
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In this thesis we describe the extension and implementation of the Sternheimer- GW method to a first-principles pseudopotential framework based on a planewaves basis. The Sternheimer-GW method consists of calculating the GW self-energy operator without resorting to the standard expansion over unoccupied Kohn- Sham electronic states. The Green's function is calculated by solving linear systems for frequencies along the real axis. The screened Coulomb interaction is calculated for frequencies along the imaginary axis using the Sternheimer equa- tion, and analytically continued to the real axis. We exploit novel techniques for generating the frequency dependence of these operators, and discuss the imple- mentation and efficiency of the methodology. We benchmark our implementation by performing quasiparticle calculations on common insulators and semiconductors, including Si, diamond, LiCl, and SiC. Our calculated quasiparticle energies are in good agreement with the results of fully-converged calculations based on the standard sum-over-states approach and experimental data. We exploit the methodology to calculate the spectral func- tions for silicon and diamond and discuss quasiparticle lifetimes and plasmaronic features in these materials. We also exploit the methodology to perform quasiparticle calculations on the 2-dimensional transition metal dichalcogenide system molybdenum disulfide (MoS2). We compare the quasiparticle properties for bulk and monolayer MoS2 , and identify significant corrections at the GW level to the LDA bandstructure of these materials. We also discuss changes in the frequency dependence of the electronic screening in the bulk and monolayer systems and relate these changes to the quasiparticle lifetimes and spectral functions in the two limits.
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Salas-Illanes, Nora. "Electronic Structure of Selected Materials by Means of the QSGW Method within the LAPW+LO Framework". Doctoral thesis, Humboldt-Universität zu Berlin, 2019. http://dx.doi.org/10.18452/19804.
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Materialien formen die moderne Welt: Sie umgeben uns in unserem alltäglichen Leben.
Unser Ziel ist die Materialeigenschaften nach unseren Bedürfnissen maßzuschneidern. Viele Materialeigenschaften wie Bandücken und Elektronendichteverteilung werden durch elektronische Zustände bestimmt.
Die meisten Vorhersagen in Bezug auf Materialien entstammen der Dichtefunktionaltheorie (DFT). Diese Theorie ermittelt Grundzustandseigenschaften und kann jedoch keine Energien von angeregten Zuständen liefern. Um angeregte Zusände zu beschreiben, bedarf es daher einer höherstufigen Theorie: die Vielteilchen-Störungstheorie (MBPT) . Im Rahmen von MBPT ist das üblichste Verfahren die GW-Näherung (GWA), worin Elektronen als Quasiteilchen (QP) beschrieben werden. Der Energieunterschied zwischen einem nicht-wechselwirkenden Teilchen und einem QP ist die Selbstenergie. In GWA ergibt sich die Selbsenergie als Produkt aus die Einteilchen-Greenfunktion, G, und die abgeschirmte Coulomb-Wechselwirkung, W, und führt zu der wahren Anregungsenergie von QP.
Diese Doktorarbeit beinhaltet die Implementierung von selbstkonsistentem Quasiteilchen-GW (QSGW) im exciting Code. Dieses Software-Paket benutzt die Linearized-Augmented-Plane-Wave-Methode (LAPW), welche alle Elektronen gleichberechtigt behandelt. Beginnend mit DFT optimiert die QSGW-Methode den Einteilchen-Hamiltonoperator durch eine selbstkonsistente Suche eines optimierten Austausch-Korrelationspotentials. Am Ende des iterativen Prozesses liefert die QSGW-Methode Eigenfunktionen und Eigenwerte der QP. Wir präsentieren mit QSGW ermittelte elektronische Strukturen von neun kristallinen Festkörpern. Wir präsentieren die zugehörigen Bandstrukturen und Zustandsdichtediagramme und vergleichen anhand dieser die QSGW-Ergebnisse mit Ergebnissen von DFT und G0W0. Zusätzlich untersuchen wir die elektronische Ladungsdichte und Wellenfunktion in ausgewählten Materialien.Materials shape the modern world: they appear everywhere in our daily life. We investigate what governs the material's properties, in order to tailor them to meet our needs. Properties, e.g., bandgaps, and electronic density distribution are determined by the electronic structure. Most predictions on materials follow from computational physics, in particular density-functional theory (DFT). This scheme returns ground-state properties, but it fails to provide excited-state energies. To find the latter, we have to recourse to a higher degree of theory, namely many-body perturbation theory (MBPT). Within MBPT, the most popular framework is the GW approximation (GWA) which describes electrons as quasiparticles (QP). The difference in energy between a non-interacting particle and a QP is called the self-energy. In GWA, the product of the Green function G and W, the screened Coulomb interaction, returns the self-energy. GWA is in principle self-consistent, but is mostly implemented as a perturbative correction to DFT results, known as G0W0. Unfortunately, the electronic structure given by G0W0 depends on the initial DFT results. This PhD project consists in the implementation of the self-consistent quasiparticle GW (QSGW) in the exciting code. This software package uses the all-electron linearized augmented planewave (LAPW) method, treating every electron on equal footing. Starting from DFT, the QSGW method (based in the GWA) optimizes the one-particle Hamiltonian through a self-consistent search for an optimized exchange-correlation potential. At the end of the iterative process, the QSGW method provides eigenfunctions and eigenvalues of the QPs. Considering nine crystalline solids, we present their electronic structure by means of QSGW. We present the bandstructures and density of state diagrams, comparing QSGW results to DFT and G0W0 results. In addition, we study the electronic charge density and wavefunction in selected materials.
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Robin, Caroline. "Fully self-consistent multiparticle-multihole configuration mixing method : applications to a few light nuclei". Thesis, Paris 11, 2014. http://www.theses.fr/2014PA112193/document.
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Ce travail de thèse s'inscrit dans le cadre du développement de la méthode de mélange de configurations multiparticules-multitrous visant à décrire les propriétés de structure des noyaux atomiques. Basée sur un double principe variationnel, cette approche permet de déterminer simultanément les coefficients d'expansion de la fonction d'onde et les orbitales individuelles.Dans ce manuscrit, le formalisme complet méthode de mélange de configurations multiparticules-multitrous auto-cohérente est pour la première fois appliqué à la description de quelques noyaux des couches p et sd, avec l'interaction de Gogny D1S.Un première étude du 12C est effectuée afin de tester et comparer le double processus de convergence lorsque différents types de critères sont appliqués pour sélectionner les configurations à N-corps inclues dans la fonction d'onde du noyau. Une analyse détaillée de l'effet induit par l'optimisation des orbitales est conduite. En particulier, son impact sur la densité à un corps et sur la fragmentation de la fonction d'onde de l'état fondamental, est analysé.Une étude systématique de noyaux de la couche sd est ensuite conduite. Une analyse précise du contenu en corrélation de l'état fondamental est effectuée, et quelques quantités observables telles que les énergies de liaison et de séparation, ainsi que les rayons de charge, sont calculées et comparées à l'expérience. Les résultats obtenus sont satisfaisants. La spectroscopie de basse énergie est ensuite étudiée. Les énergies d'excitation théoriques sont en très bon accord avec les données expérimentales, et les caractéristiques dipolaires magnétiques sont également satisfaisantes. Les propriétés quadripolaires électriques, et en particulier les probabilités de transition B(E2), sont par contre largement sous-estimée par rapport aux valeurs expérimentales, et révèle un manque important de collectivité dans la fonction d'onde, dû à l'espace de valence restreint considéré. Si la renormalisation des orbitales induit une importante fragmentation de la fonction d'onde de l'état fondamental, seul un effet très faible est obtenu sur les probabilités de transition B(E2). Une tentative d'explication est donnée.Enfin, les informations de structure fournies par la méthode de mélange de configurations multiparticules-multitrous sont utilisées comme ingrédient de base pour des calculs de réactions telles que la diffusion inélastique de protons et d'électrons sur noyaux de la couche sd. Si les résultats révèlent aussi un manque de collectivité, les tendances expérimentales sont bien reproduites et sont améliorées par l'optimisation des orbitalesThis thesis project takes part in the development of the multiparticle-multihole configuration mixing method aiming to describe the structure of atomic nuclei. Based on a double variational principle, this approach allows to determine the expansion coefficients of the wave function and the single-particle states at the same time. In this work we apply for the first time the fully self-consistent formalism of the mp-mh method to the description of a few p- and sd-shell nuclei, using the D1S Gogny interaction.A first study of the 12C nucleus is performed in order to test the doubly iterative convergence procedure when different types of truncation criteria are applied to select the many-body configurations included in the wave-function. A detailed analysis of the effect caused by the orbital optimization is conducted. In particular, its impact on the one-body density and on the fragmentation of the ground state wave function is analyzed.A systematic study of sd-shell nuclei is then performed. A careful analysis of the correlation content of the ground state is first conducted and observables quantities such as binding and separation energies, as well as charge radii are calculated and compared to experimental data. Satisfactory results are found. Spectroscopic properties are also studied. Excitation energies of low-lying states are found in very good agreement with experiment, and the study of magnetic dipole features are also satisfactory. Calculation of electric quadrupole properties, and in particular transition probabilities B(E2), however reveal a clear lack of collectivity of the wave function, due to the reduced valence space used to select the many-body configurations. Although the renormalization of orbitals leads to an important fragmentation of the ground state wave function, only little effect is observed on B(E2) probabilities. A tentative explanation is given.Finally, the structure description of nuclei provided by the multiparticle-multihole configuration mixing method is utilized to study reaction mechanisms such as electron and proton inelastic scattering on sd-shell nuclei. Although the results also suffer from the lack of collectivity, the experimental trends are well reproduced and improved by the orbital optimization
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Verrière, Marc. "Description de la dynamique de la fission dans le formalisme de la méthode de la coordonnée génératrice dépendante du temps". Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLS113/document.
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La fission induite par neutron, découverte il y a plus de 70 ans, a de nombreuses applications, par exemple industrielles pour la production d'énergie, et intervient dans la nucléosynthèse. Cependant, sa description microscopique reste un problème ouvert. En effet, les degrés de liberté qui interviennent dans ce processus dynamique sont complexes. De plus, les noyaux fissiles ont un nombre élevé de nucléons en interaction (>200). Il s'agit donc d'un problème à N-corps quantique. Or, une résolution directe de ce dernier n'est pas possible à l'heure actuelle. Dans ce contexte, la description microscopique de la fission considérée ici est la suivante : la première étape consiste à déterminer un ensemble de configurations de champ moyen qui représentent différentes déformations du noyau, incluant ainsi explicitement les degrés de liberté collectifs qui leur sont associés. Dans la seconde étape, la dynamique est décrite dans cet espace de configurations en utilisant la méthode de la coordonnée génératrice dépendante du temps (TDGCM). L'approximation des recouvrements gaussiens (GOA) est alors utilisée. Cependant, elle introduit une erreur de modèle et limite les extensions comme par exemple la prise en compte explicite de degrés de liberté intrinsèques. Ce travail de thèse a pour objectif de décrire le processus de fission avec la TDGCM sans recourir à la GOA. Cela implique de résoudre l'équation de la dynamique en TDGCM appelée équation de Hill-Wheeler dépendante du temps (TD-HW). Les méthodes d'évaluations des matrices des recouvrements et du hamiltonien collectif sont présentées dans le cas d'une interaction de Gogny. La matrice des recouvrements représente la métrique de l'espace des configurations, et la matrice du hamiltonien collectif contient les couplages énergétiques entre les configurations. Les configurations sont exprimées dans des bases de particules deux à deux distinctes, introduisant des instabilités numériques dans les méthodes d'évaluation standard. Un formalisme adapté à ces bases est proposé permettant d'éliminer ces instabilités. Deux méthodes de résolution de TD-HW sont présentées. La première consiste à calculer l'opérateur d'évolution associé à l'équation de Hill-Wheeler dépendante du temps. Elle est adaptée à un faible nombre de configurations. La seconde utilise un schéma de discrétisation en temps permettant l'inclusion d'un plus grand nombre de configurations dans le modèle. Ce formalisme est ensuite appliqué à la description de la réaction de fission induite par neutron sur le plutonium 239, et une comparaison avec la TDGCM+GOA est effectuéeNuclear fission, where an atomic nucleus separates into two fragments while emitting a large amount of energy, is at the core of many applications in society (energy production) and national security (deterrence, non-proliferation). It is also a key ingredient of the mechanisms of formation of elements in the universe. Yet, nearly 80 years after its experimental discovery its theoretical description in terms of the basic constituents of the nucleus (protons and neutrons) and their interaction remains a challenge. In this thesis, we describe the fission process as follows. In a first step, we use large supercomputers to compute the deformation properties of the nucleus based on our knowledge of nuclear forces. In a second step, we simulate the time evolution of the system from its ground state up to the fragments separation with a fully quantum-mechanical approach called the time-dependent generator coordinate method (TDGCM). While results are in good qualitative agreement with experimental data, the implementation of the TDGCM so far had been greatly simplified using what is known as the Gaussian overlap approximation (GOA). We also developed the formalism and a numerical implementation of the exact TDGCM - without the GOA. This will allow the first systematic validation of that approximation and an assessment of the resulting theoretical uncertainties. The second chapter presents the description of the neutron induced fission process using the TDGCM+GOA. The third one introduces the developments carried out in this thesis allowing the description of the fission process with the TDGCM without the GOA. The last chapter shows the first results obtained with this approach
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White, Christopher David. "Numerical Methods for Many-Body Quantum Dynamics". Thesis, 2019. https://thesis.library.caltech.edu/11558/1/white_christopher_2019.pdf.
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This thesis describes two studies of the dynamics of many-body quantum systems with extensive numerical support.
In Part I we first give a new algorithm for simulating the dynamics of one-dimensional systems that thermalize (that is, come to local thermal equilibrium). The core of this algorithm is a new truncation for matrix product operators, which reproduces local properties faithfully without reproducing non-local properties (e.g. the information required for OTOCs). To the extent that the dynamics depends only on local operators, timesteps interleaved with this truncation will reproduce that dynamics.
We then apply this to algorithm to Floquet systems: first to clean, non-integrable systems with a high-frequency drive, where we find that the system is well-described by a natural diffusive phenomenology; and then to disordered systems with low-frequency drive, which display diffusion — not subdiffusion — at appreciable disorder strengths.
In Part II, we study the utility of many-body localization as a medium for a thermodynamic engine. We first construct a small ("mesoscale") engine that gives work at high efficiency in the adiabatic limit, and show that thanks to the slow spread of information in many body localized systems, these mesoscale engines can be chained together without specially engineered insulation. Our construction takes advantage of precisely the fact that MBL systems do not thermalize. We then show that these engines still have high efficiency when run at finite speed, and we compare to competitor engines.
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Pastori, Lorenzo. "Entanglement and Topology in Quantum Many-Body Dynamics". 2020. https://tud.qucosa.de/id/qucosa%3A76132.
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A defining feature of quantum many-body systems is the presence of entanglement among their constituents. Besides providing valuable insights on several physical properties, entanglement is also responsible for the computational complexity of simulating quantum systems with variational methods. This thesis explores several aspects of entanglement in many-body systems, with the primary goal of devising efficient approaches for the study of topological properties and quantum dynamics of lattice models.
The first focus of this work is the development of variational wavefunctions inspired by artificial neural networks. These can efficiently encode long-range and extensive entanglement in their structure, as opposed to the case of tensor network states. This feature makes them promising tools for the study of topologically ordered phases, quantum critical states as well as dynamical properties of quantum systems. In this thesis, we characterize the representational power of a specific class of artificial neural network states, constructed from Boltzmann machines. First, we show that wavefunctions obtained from restricted Boltzmann machines can efficiently parametrize chiral topological phases, such as fractional quantum Hall states. We then turn our attention to deep Boltzmann machines. In this framework, we propose a new class of variational wavefunctions, coined generalized transfer matrix states, which encompass restricted Boltzmann machine and tensor network states. We investigate the entanglement properties of this ansatz, as well as its capability of representing physical states.
Understanding how the entanglement properties of a system evolve in time is the second focus of this thesis. In this context, we first investigate the manifestation of topological properties in the unitary dynamics of systems after a quench, using the degeneracy of the entanglement spectrum as a possible signature. We then analyze the phenomenon of entanglement growth, which limits to short timescales the applicability of tensor network methods in out-of-equilibrium problems. We investigate whether these limitations can be overcome by exploiting the dependence of entanglement entropies on the chosen computational basis. Specifically, we study how the spreading of quantum correlations can be contained by means of time-dependent basis rotations of the state, using exact diagonalization to simulate its dynamics after a quench. Going beyond the case of sudden quenches, we then show how, in certain weakly interacting problems, the asymptotic value of the entanglement entropy can be tuned by modifying the velocity at which the parameters in the Hamiltonian are changed. This enables the simulation of longer timescales using tensor network approaches. We present preliminary results obtained with matrix product states methods, with the goal of studying how equilibration affects the transport properties of interacting systems at long times.
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Davidson, Shainen. "Novel phase-space methods to simulate strongly-interacting many-body quantum dynamics". Thesis, 2017. https://hdl.handle.net/2144/24091.
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Understanding the collective behaviour of many-body quantum systems is an important subject in many areas of physics. With advances in ultra-cold gas experiments, the dynamics of strongly-interacting systems can now be studied in the lab. However, there is a paucity of theoretical techniques available to simulate such systems. One technique is phase-space methods, often known as the Truncated Wigner Approximation; however, its applicability in its naive form is limited. In this work, we expound on techniques to expand the regimes in which it can be effective. This involves creating a novel phase-space that is tailored to the problem at hand, and associated classical equations of motion. We show techniques for lattice systems with local finite Hilbert spaces, for fermionic systems, and for many-body localized systems. In all cases, we benchmark the accuracy of the approximation against exact results.
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Chhenh, Chunhoa. "Corner transfer matrix derived variational methods in lattice statistical mechanics and quantum many-body systems". Phd thesis, 2011. http://hdl.handle.net/1885/150093.
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The concept of the corner transfer matrix (CTM) was first discovered by Baxter in 1968, when he derived a set of variational matrix equations, which for finite matrix sizes, could be numerically solved to obtain a sequence of approximations for the statistical mechanical properties of a system of monomers and dimers on a rectangular lattice [1]. It was not until 1978, however, in a seminal paper entitled "Variational Approximations for Square Lattice Models in Statistical Mechanics" [4], that Baxter outlined his CTM variational method, which brought to light the potential power of the former objects to obtain numerics and series expansions for unsolved models and to calculate the order parameter of solved ones. Subsequent numerical work led to the realisation that the method, though general, was not very efficient; and increasing efficiency required making model specific modifications, which restricted the transferability of the resulting algorithm to other models. The CTM variational method was thus not widely adopted, despite holding much promise. More recently, however, Nishino and Okunishi discovered that White's density matrix renormalisation group (DMRG) algorithm [55, 56] could be efficiently extended to study two-dimensional classical lattice models, if the density matrix was approximated by Baxters CTMs. Numerical tests of their algorithm, the corner transfer matrix renormalisation group (CTMRG) method, were met with much success. Notable among these is its implementation within the infinite projected entangled-pair states (iPEPS) algorithm of Orus and Vidal to simulate the ground state of infinite two-dimensional quantum systems. In this thesis we review CTM derived variational methods: Baxter's original CTM iterative method, and developments of the CTM concept within the DMRG algorithm by Nishino and Okunishi, which led to the CTMRG method to calculate critical phenomena of classical and quantum systems. This will begin with elucidating the theoretical formalisms of both methods in two dimensions and their generalisations to three dimensions; followed by review of important application, namely, within the iPEPS algorithm of Orus and Vidal to numerically study infinite planar quantum systems.
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Engels-Putzka, Anna [Verfasser]. "An efficient implementation of second quantization-based many-body methods for electrons and its application to coupled-cluster with arbitrary excitation level / vorgelegt von Anna Engels-Putzka". 2009. http://d-nb.info/1007520558/34.
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Wu, I.-Huan, e 吳宜洹. "Extension of Kinetic Energy Partition Method to Many-body Systems". Thesis, 2019. http://ndltd.ncl.edu.tw/handle/pgkx63.
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碩士國立臺灣大學
應用力學研究所
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This study extends a novel and systematic scheme, kinetic energy partition (KEP) method, developed by our group for solving the general quantum eigenvalue problems. The key point of the KEP method is to split the mass factor into effective ones, each to be associated with partial kinetic energy terms, and the full Hamiltonian of the system can be wrote as the sum of subsystem Hamiltonians. Starting from the simple one-particle problems, we gradually increase the complexity in particle number, dimension and interaction patterns. For the many-body system, we propose to use the idea of “negative mass” to deal with the repulsive interaction potential, and in order to reduce the number of basis sets with continuous-energy. In addition, to simplify the procedure of KEP method, we employ an adiabatic approximation. We will test the utility of the KEP method with the models such as Moshinsky atoms, Hookium atom and Dirackium atom which error within 5%. Furthermore, to challenge the three-body problem first, use the one-dimensional Moshinsky atoms to prove it has the opportunity to confront the quantum many-body problems. Moreover, the other part is variational kinetic energy partition method (VKEP). We study the theoretical background of the KEP method by studying its relation with the variational principles. Owing to the new variational parameters provided by the KEP method, we believe VKEP method can improve KEP method to make it more precise. We use the simplest case of double delta potential to verify its feasibility.
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Nandy, Pratik. "Complexity and Entanglement: From quantum gravity to many-body systems". Thesis, 2022. https://etd.iisc.ac.in/handle/2005/5851.
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In recent years, complexity and entanglement have emerged as two fundamental computational measures and played a significant role in shaping our understanding of various phenomena, from the geometric nature of quantum gravity to the critical phenomena in many-body systems. In the first part of the thesis, we primarily focus on complexity in three different aspects. We modify Nielsen’s original arguments of traditional quantum gate counting, utilizing higher-order integrators of the Suzuki-Trotter method. This provides a volume-law scaling of complexity that is consistent with holographic proposals. Then we discuss the higher-dimension generalization of path integral complexity and its holographic interpretation using the AdS/BCFT correspondence. Later, we turn our attention to subregion complexity, which is a version of complexity that plays a significant role in understanding the black hole information problem. In the second part of the thesis, we zoom in to the entanglement for both pure states and mixed states. First, we discuss the capacity of entanglement in diverse scenarios, from operator excitations in quantum field theory to the phenomena of quantum chaos in many-body systems. We then delve into the details of the mixed state entanglement, introducing a measure known as the balance partial entanglement. In several examples, we show that it generalizes the reflected entropy and equals the entanglement wedge cross-section from the gravity perspective.University Grants Commission
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Hickel, Tilmann [Verfasser]. "Theory of many body effects in the Kondo lattice model : projection operator method / von Tilmann Hickel". 2005. http://d-nb.info/980739764/34.
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Esler, Kenneth Paul. "Advancements in the path integral Monte Carlo method for many-body quantum systems at finite temperature /". 2006. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3242842.
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Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2006.Source: Dissertation Abstracts International, Volume: 67-11, Section: B, page: 6459. Adviser: David M. Ceperley. Includes bibliographical references. Available on microfilm from Pro Quest Information and Learning.
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Neff, Thomas [Verfasser]. "Short ranged central and tensor correlations in nuclear many-body systems : towards ab initio calculations using realistic interactions within the unitary correlation operator method / von Thomas Neff". 2002. http://d-nb.info/964685604/34.
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Laflamme, Janssen Jonathan. "Méthode de calcul à N-corps basée sur la G0W0 : étude du couplage électron-phonon dans le C60 et développement d’une approche accélérée pour matériaux organiques". Thèse, 2013. http://hdl.handle.net/1866/10809.
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La présente thèse porte sur les limites de la théorie de la fonctionnelle de la densité et les moyens de surmonter celles-ci.
Ces limites sont explorées dans le contexte d'une implémentation traditionnelle utilisant une base d'ondes planes.
Dans un premier temps, les limites dans la taille des systèmes pouvant être simulés sont observées.
Des méthodes de pointe pour surmonter ces dernières sont ensuite utilisées pour simuler des systèmes de taille nanométrique.
En particulier, le greffage de molécules de bromophényle sur les nanotubes de carbone est étudié avec ces méthodes, étant donné l'impact substantiel que pourrait avoir une meilleure compréhension de ce procédé sur l'industrie de l'électronique.
Dans un deuxième temps, les limites de précision de la théorie de la fonctionnelle de la densité sont explorées.
Tout d'abord, une étude quantitative de l'incertitude de cette méthode pour le couplage électron-phonon est effectuée et révèle que celle-ci est substantiellement plus élevée que celle présumée dans la littérature.
L'incertitude sur le couplage électron-phonon est ensuite explorée dans le cadre de la méthode G0W0 et cette dernière se révèle être une alternative substantiellement plus précise.
Cette méthode présentant toutefois de sévères limitations dans la taille des systèmes traitables, différents moyens théoriques pour surmonter ces dernières sont développés et présentés dans cette thèse.
La performance et la précision accrues de l'implémentation résultante laissent présager de nouvelles possibilités dans l'étude et la conception de certaines catégories de matériaux, dont les supraconducteurs, les polymères utiles en photovoltaïque organique, les semi-conducteurs, etc.This thesis studies the limitations of density functional theory. These limits are explored in the context of a traditional implementation using a plane waves basis set. First, we investigate the limit of the size of the systems that can be treated. Cutting edge methods that assess these limitations are then used to simulate nanoscale systems. More specifically, the grafting of bromophenyl molecules on the sidewall of carbon nanotubes is studied with these methods, as a better understanding of this procedure could have substantial impact on the electronic industry. Second, the limitations of the precision of density functional theory are explored. We begin with a quantitative study of the uncertainty of this method for the case of electron-phonon coupling calculations and find it to be substantially higher than what is widely presumed in the literature. The uncertainty on electron-phonon coupling calculations is then explored within the G0W0 method, which is found to be a substantially more precise alternative. However, this method has the drawback of being severely limitated in the size of systems that can be computed. In the following, theoretical solutions to overcome these limitations are developed and presented. The increased performance and precision of the resulting implementation opens new possibilities for the study and design of materials, such as superconductors, polymers for organic photovoltaics and semiconductors.