Thèses sur le sujet « TIME QUANTUM »
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1
Oppenheim, Jonathan A. « Quantum time ». Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/NQ48689.pdf.
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Laflamme, Raymond. « Time and quantum cosmology ». Thesis, University of Cambridge, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.278123.
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Cramer, Claes Richard. « Quantum aspects of time-machines ». Thesis, University of York, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.265661.
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Vona, Nicola. « On time in quantum mechanics ». Diss., Ludwig-Maximilians-Universität München, 2014. http://nbn-resolving.de/urn:nbn:de:bvb:19-166201.
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Although time measurements are routinely performed in laboratories, their theoretical description is still an open problem.
Similarly, also the validity and the status of the energy-time uncertainty relation is unsettled.
In the first part of this work the necessity of positive operator valued measures (POVM) as descriptions of every quantum experiment is reviewed, as well as the suggestive role played by the probability current in time measurements.
Furthermore, it is shown that no POVM exists, which approximately agrees with the probability current on a very natural set of wave functions; nevertheless, the choice of the set is crucial, and on more restrictive sets the probability current does provide a good arrival time prediction.
Some ideas to experimentally detect quantum effects in time measurements are discussed.
In the second part of the work the energy-time uncertainty relation is considered, in particular for a model of alpha decay for which the variance of the energy can be calculated explicitly, and the variance of time can be estimated.
This estimate is tight for systems with long lifetimes, in which case the uncertainty relation is shown to be satisfied.
Also the linewidth-lifetime relation is shown to hold, but contrary to the common expectation, it is found that the two relations behave independently, and therefore it is not possible to interpret one as a consequence of the other.
To perform the mentioned analysis quantitative scattering estimates are necessary.
To this end, bounds of the form $\|\1_Re^{-iHt}\psi\|_2^2 \leq C t^{-3}$ have been derived, where $\psi$ denotes the initial state, $H$ the Hamiltonian, $R$ a positive constant, and $C$ is explicitly known.
As intermediate step, bounds on the derivatives of the $S$-matrix in the form $\|\1_K S^{(n)}\|_\infty \leq C_{n,K} $ have been established, with $n=1,2,3$, and the constants $C_{n,K}$ explicitly known.Obwohl Zeitmessungen tagtäglich in vielen Laboren durchgeführt werden, ist ihre theoretische Beschreibung noch unklar. Gleichermaßen sind Gültigkeit und Bedeutung der Energie-Zeit-Unschärfe ungeklärt. Der erste Teil dieser Arbeit diskutiert die Notwendigkeit von positive operator valued measures (POVM) zur Beschreibung von allen Quantenexperimenten, sowie die bedeutende Rolle des Wahrscheinlichkeitsstroms in Zeitmessungen. Außerdem, wird gezeigt, dass kein POVM existiert, der den Wahrscheinlichkeitsstrom jeder Wellenfunktion in einer natürlichen Menge annähert. Die Wahl dieser Menge ist aber entscheidend, und auf beschränkten Mengen ist der Wahrscheinlichkeitsstrom eine gute Vorhersage für Zeitmessungen. Einige Ideen sind diskutiert, wie man Zeitexperimente durchführen kann, um Quanteneffekten zu detektieren. Der zweite Teil dieser Arbeit beschäftigt sich mit der Energie-Zeit-Unschärfe, insbesondere für ein Modell von Alpha-Zerfall, wobei man die Energievarianz explizit berechnen kann, und die Zeitvarianz abschätzt. Diese Abschätzung ist für Systeme mit langen Lebensdauern gut, und in diesem Fall wird gezeigt, dass die Energie-Zeit-Unschärfe gilt. Ebenso wird gezeigt, dass die linewidth-lifetime relation gilt. Im allgemein wird angenommen, dass diese zwei Relationen dieselben sind. Im Gegensatz dazu, wird in der Dissertation aber gezeigt, dass sie sich unabhängig voneinander verhalten. Für diese Resultate, braucht man quantitative Streuabschätzungen. Zu diesem Zweck werden Schranken in der Form $\|\1_Re^{-iHt}\psi\|_2^2 \leq C t^{-3}$ in der Dissertation gezeigt, wo $\psi$ der Anfangszustand ist, $H$ der Hamiltonoperator, $R$ eine positive Konstante, und $C$ explizit bekannt ist. Als Zwischenschritt werden Schranken für die Ableitungen der $S$-Matrix in der Form $\|\1_K S^{(n)}\|_\infty \leq C_{n,K} $ bewiesen, wobei $n=1,2,3$, und die Konstanten $C_{n,K}$ explizit bekannt sind.
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Poulios, Konstantinos. « Integrated photonic continuous-time quantum walks ». Thesis, University of Bristol, 2013. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.633256.
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The present thesis describes experimental work on non-classical interference of photons in integrated quantum photonic circuits. This non-classical interference of indistinguishable photons serves as the basis for implementing photonic quantum technologies and its demonstration on integrated platforms sparked a plethora of experimental research. The viability of multi-mode interference (MMI) devices is investigated as an alternative building block for quantum waveguide circuits. The visibility function for non-classical interference of two photons injected into a MMI device is derived theoretically, predicting near unit visibility for compact SiOxNy (SiON) devices. Theoretical results are complemented by experimental demonstration of very high visibilities in 2x2 MMI devices without the requirement of narrow-band photons . Taking advantage of the low de coherence properties of the photons and the inherent stability of integrated waveguide arrays, quantum walks (QWs) of correlated photons are experimentally demonstrated. Non-classical correlated detection events are observed for two photon QWs in an array of 21 evanescently coupled waveguides in a SiON chip. These correlations depend on the input state of the photons and violate a classical limit.
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Rodgers, Peter A. « Time-dependent pulses in quantum optics ». Thesis, Queen's University Belfast, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.356924.
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Childs, Andrew MacGregor 1977. « Quantum information processing in continuous time ». Thesis, Massachusetts Institute of Technology, 2004. http://hdl.handle.net/1721.1/16663.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2004.Includes bibliographical references (p. 127-138) and index.
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Quantum mechanical computers can solve certain problems asymptotically faster than any classical computing device. Several fast quantum algorithms are known, but the nature of quantum speedup is not well understood, and inventing new quantum algorithms seems to be difficult. In this thesis, we explore two approaches to designing quantum algorithms based on continuous-time Hamiltonian dynamics. In quantum computation by adiabatic evolution, the computer is prepared in the known ground state of a simple Hamiltonian, which is slowly modified so that its ground state encodes the solution to a problem. We argue that this approach should be inherently robust against low-temperature thermal noise and certain control errors, and we support this claim using simulations. We then show that any adiabatic algorithm can be implemented in a different way, using only a sequence of measurements of the Hamiltonian. We illustrate how this approach can achieve quadratic speedup for the unstructured search problem. We also demonstrate two examples of quantum speedup by quantum walk, a quantum mechanical analog of random walk. First, we consider the problem of searching a region of space for a marked item. Whereas a classical algorithm for this problem requires time proportional to the number of items regardless of the geometry, we show that a simple quantum walk algorithm can find the marked item quadratically faster for a lattice of dimension greater than four, and almost quadratically faster for a four-dimensional lattice. We also show that by endowing the walk with spin degrees of freedom, the critical dimension can be lowered to two. Second, we construct an oracular problem that a quantum walk can solve exponentially faster than any classical algorithm.
(cont.) This constitutes the only known example of exponential quantum speedup not based on the quantum Fourier transform. Finally, we consider bipartite Hamiltonians as a model of quantum channels and study their ability to process information given perfect local control. We show that any interaction can simulate any other at a nonzero rate, and that tensor product Hamiltonians can simulate each other reversibly. We also calculate the optimal asymptotic rate at which certain Hamiltonians can generate entanglement.
by Andrew MacGregor Childs.
Ph.D.
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Tomasevic, Marija. « Quantum Aspects of Space and Time ». Doctoral thesis, Universitat de Barcelona, 2021. http://hdl.handle.net/10803/672688.
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In this thesis, we explore different ways in which spacetime exhibits peculiar properties when subjected to the rules of quantum mechanics. These rules are naturally implemented at the level of semiclassical physics, where the dynamical nature of the spacetime metric is neglected. In particular, we explore how quantum effects modify some of the fundamental statements of General Relativity, ranging from different possible solutions, such as traversable wormholes and time machines, to some of the more foundational conjectures, with an emphasis to the one of cosmic censorship.
Chapter One takes a deeper look into the connection between geometry and entropy. We revisit the original reasoning leading to their entwinement, and we clarify the different notions of entropy that play a role in it. We emphasize the recurring theme and the pattern in such a relationship: how the union between area and entropy makes sense when put together on the same footing, hinting towards a deeper meaning in a complete theory of quantum gravity. This seemingly simple unification is then shown to lead to incredible results, ranging from improved conjectures about quantum gravity, to illuminating one of the most critical problems of modern theoretical physics - the black hole information paradox. In particular, we mainly focus on one example of semiclassical statements, the (quantum) Penrose inequality, and we show in detail the difficulties one has to overcome for a meaningful conjecture to hold. Furthermore, we revise the basic arguments underlying the recent progress regarding the black hole interior and lay out the possible paths to the interpretation of these striking results.
Chapter Two explores different solutions that classical General Relativity forbade, but quantum physics advanced. A number of no-go theorems get circumvented, and configurations previously thought of as impossible become available, and even natural. This is especially clear for solutions such as traversable wormholes and their inherent use in studies of entanglement structures. Indeed, such connections will be relevant in gauge/gravity duality for a fuller understanding of the holographic dictionary. But we can also see the way in which other no-go theorems become easier to infer. In essence, the creation of closed causal curves was understood as a problem of quantum gravity due to the incredibly high energies one seems to need for their demise. However, we show how simple, low-energy arguments are enough to shatter the fiction of time machines.
The final Chapter Three perhaps comes closer to the study of quantum gravity than the previous ones. We undertake the problem of naked singularities in gravity, and we see how including quantum effects solidifies some foundational statements while completely fragmenting other ones. In a nutshell, the strong cosmic censorship conjecture is shown to be on much firmer ground than previously thought. Quantum physics is used to destabilize the relevant Cauchy horizon once and for all. However, including quantum effects necessarily means we must abandon our na¨ıve understanding of the weak cosmic censorship and embark on a much stranger path towards a meaningful statement about naked singularities. In doing so, we discuss the purpose of cosmic censorship and its interpretation in the realm of quantum gravity.
We finish the dissertation with a summary and a further discussion on the nature of naked sin- gularities, providing a framework in which these questions can be meaningfully posed. After a brief overview of recent developments in this research line, we discuss the possible ways in which we can tackle such a perplexing problem. Namely, the role of critical phenomena in gravitational collapse is emphasized, and a proposal for a future study is outlined.Como es propio de toda teoría clásica, la Relatividad General no puede aspirar a ser más que una teoría efectiva, cuyo campo de estudio se reduce al de fenómenos emergentes de estructuras más elementales. Sin embargo, se trata de una teoría dificil de tratar al poseer propiedades no compartidas por el resto de teorías clásicas: una descripción holográfica. A pesar de no haber proporcionado todas las respuestas que buscábamos acerca de la naturaleza del espacio y del tiempo, la holografía ha jugado un papel fundamental; en especial mostrándonos una conexión entre nociones tan dispares como la información cuántica y la geometría, similar a la conexión que Gibbons y Hawking [1] dieron a conocer entre el área y la entropía. Esta tesis tiene como objetivo el estudio de casos en los que esta relación se vuelve manifiesta, usando el régimen semiclásico de gravedad. El primer capítulo profundiza en la conexión entre área y entropía y algunas de las consecuencias que esta implica: la formulación semiclásica de la Desigualdad de Penrose y las posibles intepretaciones relativas al interior de los agujeros negros. El segundo capítulo se adentra en el estudio de escenarios prohibidos por la Relatividad General pero que resultan accesibles, y naturales, al considerar efectos cuánticos. Se centra en los agujeros de gusano y su relación con el entrelazamiento cuántico (a través de la dualidad “gauge/gravity”), así como en la imposibilidad de transformarse en máquinas del tiempo. El capítulo tercero es el que más avanza hacia el régimen cuántico de la gravedad, explorando el problema de las singularidades desnudas y la Hipótesis de la Censura Cósmica. Se muestra cómo la versión fuerte sale reforzada tras un análisis semiclásico, mientras que la versión débil requiere de nuevas reinterpretaciones para su adaptación a la nueva realidad cuántica. Finalmente se ofrece un resumen junto con una discusión adicional sobre la naturaleza de las singularidades desnudas, con un pequeño repaso sobre los avances en este campo y las posibles rutas que tomar, haciendo hincapié en el papel del colapso crítico gravitatorio y proponiendo una línea de investigación más allá de esta tesis. Bibliografía: [1] G. W. Gibbons and S. W. Hawking, “Action integrals and partition functions in quantum gravity,” Phys. Rev. D 15 (May, 1977) 2752–2756. https://link.aps.org/doi/10.1103/PhysRevD.15.2752.
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Yearsley, James M. « Aspects of time in quantum theory ». Thesis, Imperial College London, 2011. http://hdl.handle.net/10044/1/9115.
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We consider a number of aspects of the problem of defining time observables in quantum theory. Time observables are interesting quantities in quantum theory because they often cannot be associated with self-adjoint operators. Their definition therefore touches on foundational issues in quantum theory. Various operational approaches to defining time observables have been proposed in the past. Two of the most common are those based on pulsed measurements in the form of strings of projection operators and continuous measurements in the form of complex potentials. One of the major achievements of this thesis is to prove that these two operational approaches are equivalent. However operational approaches are somewhat unsatisfying by themselves. To provide a definition of time observables which is not linked to a particular measurement scheme we employ the decoherent, or consistent, histories approach to quantum theory. We focus on the arrival time, one particular example of a time observable, and we use the relationship between pulsed and continuous measurements to relate the decoherent histories approach to one based on complex potentials. This lets us compute the arrival time probability distribution in decoherent histories and we show that it agrees with semiclassical expectations in the right limit. We do this both for a free particle and for a particle coupled to an environment. Finally, we consider how the results discussed in this thesis relate to those derived by coupling a particle to a model clock. We show that for a general class of clock models the probabilities thus measured can be simply related to the ideal ones computed via decoherent histories.
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Mosley, Shaun. « Real time dynamics ». Thesis, University of Nottingham, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.240232.
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Arzano, Michele Ng Yee Jack. « Aspects of quantum gravity quantum space-time and black hole thermodynamics / ». Chapel Hill, N.C. : University of North Carolina at Chapel Hill, 2006. http://dc.lib.unc.edu/u?/etd,144.
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Thesis (Ph. D.)--University of North Carolina at Chapel Hill, 2006.Title from electronic title page (viewed Oct. 10, 2007). "... in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Physics & Astronomy." Discipline: Physics and Astronomy; Department/School: Physics and Astronomy.
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Crystal, Lisa. « Quantum Times : Physics, Philosophy, and Time in the Postwar United States ». Thesis, Harvard University, 2013. http://dissertations.umi.com/gsas.harvard:10973.
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The concept of time in physics underwent significant changes in the decades following World War II. This dissertation considers several ways in which American physicists grappled with these changes, analyzing the extent to which philosophical methods and questions played a role in physicists' engagement with time. Two lines of questioning run through the dissertation. The first asks about the professional identities of postwar American physicists in relation to philosophy, as exemplified by their engagement with the concept of time. The second analyzes the heterogeneous nature of time in physics, and the range of presuppositions and assumptions that have constituted this "fundamental" physical concept. The first chapter looks to the development of atomic clocks and atomic time standards from 1948-1958, and the ways in which new timekeeping technologies placed concepts such as “clock”, “second,” and “measure of time” in a state of flux. The second chapter looks to the experimental discovery of CP violation by particle physicists in the early 1960s, raising questions about nature of time understood as the variable “t” in the equations of quantum mechanics. The third chapter considers attempts to unify quantum mechanics and general relativity in the late 1960s, which prompted physicists to question the “existence” of time in relation to the universe as a whole. In each episode considered, physicists engaged with the concept of time in a variety of ways, revealing a multiplicity of relationships between physics, philosophy, and time. Further, in each case physicists brought a unique set of assumptions to their concepts of time, revealing the variety ways in which fundamental conceptsfunctioned and changed in late twentieth century physics. The result is a heterogeneous picture of the practice of physics, as well as one of physics’ most basic concepts.History of Science
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Ahn, Kwang Jun. « Fully quantum mechanical description of ultrashort time dynamics of semiconductor quantum dots ». [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=978946391.
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Tempel, David Gabriel. « Time-Dependent Density Functional Theory for Open Quantum Systems and Quantum Computation ». Thesis, Harvard University, 2012. http://dissertations.umi.com/gsas.harvard:10208.
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First-principles electronic structure theory explains properties of atoms, molecules and solids from underlying physical principles without input from empirical parameters. Time-dependent density functional theory (TDDFT) has emerged as arguably the most widely used first-principles method for describing the time-dependent quantum mechanics of many-electron systems. In this thesis, we will show how the fundamental principles of TDDFT can be extended and applied in two novel directions: The theory of open quantum systems (OQS) and quantum computation (QC). In the first part of this thesis, we prove theorems that establish the foundations of TDDFT for open quantum systems (OQS-TDDFT). OQS-TDDFT allows for a first principles description of non-equilibrium systems, in which the electronic degrees of freedom undergo relaxation and decoherence due to coupling with a thermal environment, such as a vibrational or photon bath. We then discuss properties of functionals in OQS-TDDFT and investigate how these differ from functionals in conventional TDDFT using an exactly solvable model system. Next, we formulate OQS-TDDFT in the linear-response regime, which gives access to environmentally broadened excitation spectra. Lastly, we present a hybrid approach in which TDDFT can be used to construct master equations from first-principles for describing energy transfer in condensed phase systems. In the second part of this thesis, we prove that the theorems of TDDFT can be extended to a class of qubit Hamiltonians that are universal for quantum computation. TDDFT applied to universal Hamiltonians implies that single-qubit expectation values can be used as the basic variables in quantum computation and information theory, rather than wavefunctions. This offers the possibility of simplifying computations by using the principles of TDDFT similar to how it is applied in electronic structure theory. Lastly, we discuss a related result; the computational complexity of TDDFT.Physics
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Wanzambi, Ellinor, et Stina Andersson. « Quantum Computing : Implementing Hitting Time for Coined Quantum Walks on Regular Graphs ». Thesis, Uppsala universitet, Institutionen för informationsteknologi, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-444818.
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In recent years, quantum walks have been widely researched and haveshown exciting properties. One such is a quadratic speed-up in hittingtime compared to its classical counterpart. In this paper, we design aquantum circuit for the MNRS algorithm, which finds a marked node in agraph with a quantum walk, and use it to find a hitting time for themarked nodes in the walk. We do this by implementing the circuit on IBMquantum simulators and show that the execution on a noise-free simulatorresults in hitting times that agree with the theoretical expectations.We also run the algorithm on a mock backend that simulates the noise ofthe IBM Melbourne computer. As expected, the noise has an extensiveimpact on the output, resulting in outcomes far from the noise-freesimulation.IT 21
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Robinson, James W. « Time-integrated and time-resolved optical studies of InGaN quantum dots ». Thesis, University of Oxford, 2005. http://ora.ox.ac.uk/objects/uuid:26101861-dd7f-4cb7-aecf-f482855a3dea.
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The construction of a high-resolution optical microscope system for micro-photoluminescence (µ-PL) spectroscopy is described, and a range of time-integrated and time-resolved experimental work on single InGaN quantum dots (QDs) is presented. Time-integrated measurements demonstrate the existence of InGaN QDs in three different samples via the presence of sharp exciton recombination lines in the µ-PL spectra. The narrowest peaks display a linewidth Γ of ~230 µeV, implying a decoherence time T2 ≥5.7 ps. Time-resolved measurements on exciton recombination lines from single self-assembled InGaN QDs reveal typical lifetimes of ~2.0 ns (which decrease with increasing temperature), while typical lifetimes for excitons in single selectively-grown micropyramidal InGaN QDs are found to be ~0.4 ns. The shorter exciton recombination lifetime in selectively-grown QDs is believed to be due to a stronger coupling of these QDs to the underlying quantum well. Temporal fluctuations (on a timescale of seconds) in the energy, intensity and FWHM of µ-PL peaks arising from the recombination of excitons in single self-assembled InGaN QDs are observed. These are attributed to transient Stark shifts induced by a fluctuating local charge distribution as carriers become trapped in defect states in the vicinity of the QDs. Time-integrated power-dependent measurements are used to demonstrate the presence of biexciton states in single self-assembled InGaN QDs. The exciton–biexciton energy splitting is found to be ~41 meV, in agreement with values predicted by theoretical calculations. Time-resolved studies of the biexciton and exciton decay curves reveal a coupling as the exciton population is refilled by biexciton decays. The biexciton lifetime is found to be ~1.4 ns, compared to an exciton lifetime of ~1.0 ns. Lateral electric fields are applied to a single self-assembled InGaN QD using aluminium electrodes lithographically defined on the sample surface. Application of fields of the order of ~0.17 MVcm-1 is found to cause both a red-shift and a reduction in the intensity of the exciton recombination peak in the µ-PL spectrum.
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Möckel, Michael. « Real-time evolution of quenched quantum systems ». Naila, Berger Str. 19 : M. Möckel, 2009. http://d-nb.info/995957290/34.
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Wustmann, Waltraut. « Statistical mechanics of time-periodic quantum systems ». Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2010. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-38126.
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The asymptotic state of a quantum system, which is in contact with a heat bath, is strongly disturbed by a time-periodic driving in comparison to a time-independent system. In this thesis an extensive picture of the asymptotic state of time-periodic quantum systems is drawn by relating it to the structure of the corresponding classical phase space. To this end the occupation probabilities of the Floquet states are analyzed with respect to their semiclassical property of being either regular or chaotic. The regular Floquet states are occupied with exponential weights e^{-betaeff Ereg} similar to the canonical weights e^{-beta E} of time-independent systems. The regular energies Ereg are defined by the quantization of the time-periodic system, whose classical properties also determine the effective temperature 1/betaeff. In contrast, the chaotic Floquet states acquire almost equal probabilities, irrespective of their time-averaged energy. Beyond these semiclassical properties the existence of avoided crossings in the spectrum is an intrinsic quantum property of time-periodic systems. Avoided crossings can strongly influence the entire occupation distribution. As an impressive application a novel switching mechanism is proposed in a periodically driven double well potential coupled to a heat bath. By a weak variation of the driving amplitude its asymptotic state is switched from the ground state in one well to a state with higher average energy in the other wellDer asymptotische Zustand eines Quantensystems, das in Kontakt mit einem Wärmebad steht, wird durch einen zeitlich periodischen Antrieb gegenüber einem zeitunabhängigen System nachhaltig verändert. In dieser Arbeit wird ein umfassendes Bild über den asymptotischen Zustand zeitlich periodischer Quantensysteme entworfen, indem es diesen zur Struktur des zugehörigen klassischen Phasenraums in Beziehung setzt. Dazu werden die Besetzungswahrscheinlichkeiten der Floquet-Zustände hinsichtlich ihrer semiklassischen Eigenschaft analysiert, nach welcher sie entweder regulär oder chaotisch sind. Die regulären Floquet-Zustände sind mit exponentiellen Gewichten e^{-betaeff Ereg} ähnlich der kanonischen Verteilung e^{-beta E} zeitunabhängiger Systeme besetzt. Dabei sind die reguläre Energien Ereg durch die Quantisierung des Systems vorgegeben, dessen klassische Eigenschaften auch die effektive Temperatur 1/betaeff bestimmen. Die chaotischen Zustände dagegen haben fast einheitliche Besetzungswahrscheinlichkeiten, welche unabhängig von ihrer mittleren Energie sind. Über diese semiklassischen Eigenschaften hinaus ist das Auftreten von vermiedenen Kreuzungen im Spektrum eine intrinsisch quantenmechanische Eigenschaft zeitlich periodischer Systeme. Diese können die gesamte Besetzungsverteilung nachhaltig beeinflussen und finden eine eindrucksvolle Anwendung in Form eines neuartigen Schaltmechanismus in einem harmonisch modulierten Doppelmuldenpotential in Kontakt mit einem Wärmebad. Der asymptotische Zustand kann unter geringer Variation der Antriebsamplitude vom Grundzustand der einen Mulde in einen Zustand höherer mittlerer Energie in der anderen Mulde geschaltet werden
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Möckel, Michael. « Real-time evolution of quenched quantum systems ». Diss., lmu, 2009. http://nbn-resolving.de/urn:nbn:de:bvb:19-103950.
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Arnault, Pablo. « Discrete-time quantum walks and gauge theories ». Thesis, Paris 6, 2017. http://www.theses.fr/2017PA066135/document.
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Un ordinateur quantique (OQ), i.e. utilisant les ressources de la physique Q, superposition et intrication, pourrait fournir un gain exponentiel de temps de calcul. Une simulation utilisant ces ressources est appelée simulation Q (SQ). L’avantage des SQs sur les simulations classiques est bien établi au niveau théorique, i.e. software. Leur avantage pratique requiert un hardware Q. L’OQ, sous-entendu universel (cf. plus bas), n’a pas encore vu le jour, mais les efforts en ce sens sont croissants et variés. Aussi la SQ a-t-elle déjà été illustrée par de nombreuses expériences de principe, grâce à des calculateurs ou simulateurs Qs de taille réduite. Les marches Qs (MQs) sont des schémas de SQ particulièrement étudiés, étant des briques élémentaires pour concevoir n’importe quel algorithme Q, i.e. pour le calcul Q universel. La présente thèse est un pas de plus vers une simulation des théories Qs des champs basée sur les MQs à temps discret (MQTD). En effet, il est montré, dans certains cas, comment les MQTD peuvent simuler, au continu, l'action d'un champ de jauge Yang-Mills sur de la matière fermionique, et la rétroaction de cette-dernière sur la dynamique du champ de jauge. Les schémas proposés préservent l’invariance de jauge au niveau de la grille d’espace-temps, i.e. pas seulement au continu. Il est proposé (i) des équations de Maxwell sur grille, compatibles avec la conservation du courant sur la grille, et (ii) une courbure non-abélienne définie sur la grille. De plus, il est montré comment cette matière fermionique à base de MQTD peut être couplée à des champs gravitationnels relativistes du continu, i.e. des espaces-temps courbes, en dimension 1+2A quantum (Q) computer (QC), i.e. utilizing the resources of Q physics, superposition of states and entanglement, could fournish an exponential gain in computing time. A simulation using such resources is called a Q simulation (QS). The advantage of QSs over classical ones is well established at the theoretical, i.e. software level. Their practical benefit requires their implementation on a Q hardware. The QC, i.e. the universal one (see below), has not seen the light of day yet, but the efforts in this direction are both growing and diverse. Also, QS has already been illustrated by numerous experimental proofs of principle, thanks too small-size and specific-task Q computers or simulators. Q walks (QWs) are particularly-studied QS schemes, being elementary bricks to conceive any Q algorithm, i.e. to achieve so-called universal Q computation. The present thesis is a step more towards a simulation of Q field theories based on discrete-time QWs (DTQWs). Indeed, it is shown, in certain cases, how DTQWs can simulate, in the continuum, the action of Yang-Mills gauge fields on fermionic matter, and the retroaction of the latter on the gauge-field dynamics. The suggested schemes preserve gauge invariance on the spacetime lattice, i.e. not only in the continuum. In the (1+2)D Abelian case, consistent lattice equivalents to both Maxwell’s equations and the current conservation are suggested. In the (1+1)D non-Abelian case, a lattice version of the non-Abelian field strength is suggested. Moreover, it is shown how this fermionic matter based on DTQWs can be coupled to relativistic gravitational fields of the continuum, i.e. to curved spacetimes, in several spatial dimensions
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Maciejko, Joseph. « Time-dependent quantum transport in mesoscopic structures ». Thesis, McGill University, 2006. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=99346.
Texte intégralRésumé :
In this thesis, we present a theory to calculate the time-dependent current flowing through an arbitrary noninteracting nanoscale phase-coherent device connected to arbitrary noninteracting external leads, in response to sharp step- and square-shaped voltage pulses. Our analysis is based on the Keldysh nonequilibrium Green's functions formalism, and provides an exact analytical solution to the transport equations in the far from equilibrium, nonlinear response regime. The essential feature of our solution is that it does not rely on the commonly used wideband approximation where the coupling between device scattering region and leads is taken to be independent of energy, and as such provides a way to perform transient transport calculations from first principles on realistic systems, taking into account the detailed electronic structure of the device scattering region and the leads. As an illustration of the general theory, we perform a toy model calculation for a quantum dot with Lorentzian linewidth and show how interesting finite-bandwidth effects arise in the time-dependent current dynamics. Finally, we describe possible generalizations of our theory to the cases of superconducting leads (an example of broken symmetry) and one-dimensional leads in the Luttinger liquid regime (an example of an interacting system).
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Hussain, A. « Time-dependent quantum dynamics of molecule predissociation ». Thesis, University of Cambridge, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.604841.
Texte intégralRésumé :
The work in this thesis uses wavepacket techniques on a discrete grid to solve the time-dependent Schroedinger equation numerically for a series of problems within the field of photodissociation dynamics. The systems studied focus on the phenomenon of 'predissociation', either electronically, via a non-adiabatic curve-crossing between (diabatically) bound and (diabatically) unbound Born-Oppenheimer potential energy surfaces (PESs), or vibrationally, in a system where there are several active vibrational modes, and the vibrational energy is enough to rupture one of the bonds provided enough can be concentrated in a single mode via intramolecular vibrational relaxation (IVR). The curve-crossing between the (bound) B and (repulsive) Y states of the I-Br molecule is studied in detail, being an example of electronic coupling that obeys neither the weak or strong limiting case. The dynamics of the B state are explored in detail, both via the propagation of coherent wavepackets, and by the propagation of the limiting (zero-coupling) vibrational eigenstates, to investigate the state-selectivity of the perturbation. It is found that the vibrational lifetimes vary dramatically with quantum number, with adjacent states often having half-lives that differ by two or three orders of magnitude. Finally, a series of calculations are performed simulating a set of pump-probe experiments that have been carried out on this system, and using the data previously generated on the B-state vibrational lifetimes to assist in the analysis. Qualitative agreement with experiment is achieved, and the data on vibrational lifetimes explains the main features of the ionisation traces; there is evidence that the model potentials (taken from the literature) are part of the explanation for any discrepancies.
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Worsley, Richard Edward. « Time-resolved relaxation processes in quantum wells ». Thesis, University of Southampton, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.295867.
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Bugler-Lamb, Samuel Lloyd. « The quantum vacuum near time-dependent dielectrics ». Thesis, University of Exeter, 2017. http://hdl.handle.net/10871/29879.
Texte intégralRésumé :
The vacuum, as described by Quantum Field Theory, is not as empty as classical physics once led us to believe. In fact, it is characterised by an infinite energy stored in the ground state of its constituent fields. This infinite energy has real, tangible effects on the macroscopic clusters of matter that make up our universe. Moreover, the configuration of these clusters of matter within the vacuum in turn influences the form of the vacuum itself and so forth. In this work, we shall consider the changes to the quantum vacuum brought about by the presence of time-dependent dielectrics. Such changes are thought to be responsible for phenomena such as the simple and dynamical Casimir effects and Quantum Friction. After introducing the physical and mathematical descriptions of the electromagnetic quantum vacuum, we will begin by discussing some of the basic quasi-static effects that stem directly from the existence of an electromagnetic ground state energy, known as the \textit{zero-point energy}. These effects include the famous Hawking radiation and Unruh effect amongst others. We will then use a scenario similar to that which exhibits Cherenkov radiation in order to de-mystify the 'negative frequency' modes of light that often occur due to a Doppler shift in the presence of media moving at a constant velocity by showing that they are an artefact of the approximation of the degrees of freedom of matter to a macroscopic permittivity function. Here, absorption and dissipation of electromagnetic energy will be ignored for simplicity. The dynamics of an oscillator placed within this moving medium will then be considered and we will show that when the motion exceeds the speed of light in the dielectric, the oscillator will begin to absorb energy from the medium. It will be shown that this is due to the reversal of the 'radiation damping' present for lower velocity of stationary cases. We will then consider how the infinite vacuum energy changes in the vicinity, but outside, of this medium moving with a constant velocity and show that the presence of matter removes certain symmetries present in empty space leading to transfers of energy between moving bodies mediated by the electromagnetic field. Following on from this, we will then extend our considerations by including the dissipation and dispersion of electromagnetic energy within magneto-dielectrics by using a canonically quantised model referred to as 'Macroscopic QED'. We will analyse the change to the vacuum state of the electromagnetic field brought about by the presence of media with an arbitrary time dependence. It will be shown that this leads to the creation of particles tantamount to exciting the degrees of freedom of both the medium and the electromagnetic field. We will also consider the effect these time-dependencies have on the two point functions of the field amplitudes using the example of the electric field. Finally, we will begin the application of the macroscopic QED model to the path integral methods of quantum field theory with the purpose of making use of the full range of perturbative techniques that this entails, leaving the remainder of this adaptation for future work.
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Šafránek, Dominik. « Gaussian quantum metrology and space-time probes ». Thesis, University of Nottingham, 2016. http://eprints.nottingham.ac.uk/37124/.
Texte intégralRésumé :
In this thesis we focus on Gaussian quantum metrology in the phase-space formalism and its applications in quantum sensing and the estimation of space-time parameters. We derive new formulae for the optimal estimation of multiple parameters encoded into Gaussian states. We discuss the discontinuous behavior of the figure of merit -- the quantum Fisher information. Using derived expressions we devise a practical method of finding optimal probe states for the estimation of Gaussian channels and we illustrate this method on several examples. We show that the temperature of a probe state affects the estimation generically and always appears in the form of four multiplicative factors. We also discuss how well squeezed thermal states perform in the estimation of space-time parameters. Finally we study how the estimation precision changes when two parties exchanging a quantum state with the encoded parameter do not share a reference frame. We show that using a quantum reference frame could counter this effect.
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Gaury, Benoit. « Emerging concepts in time-resolved quantum nanoelectronics ». Thesis, Grenoble, 2014. http://www.theses.fr/2014GRENY026/document.
Texte intégralRésumé :
Grâce aux progrès techniques récents, les sources d'électrons uniques sontpassées de la théorie au laboratoire. Des expériencesconceptuellement nouvelles où l'on sonde directement la dynamique quantiqueinterne des systèmes sont désormais possibles. Dans cette thèse nousdéveloppons les outils analytiques et numériques pour analyser et comprendre cesproblèmes. Les simulations requièrent une résolution spatiale appropriée pourles systèmes, et des temps simulés suffisament longs pour sonder leurs tempscaractéristiques. Jusqu'à présent l'approche théorique standard utilisée pour traiter de tels problèmes numériquement---connue sous les dénominations de formalisme Keldysh ou NEGF (Fonctions de Green Hors Equilibre)---n'a pas été très fructueuse, principalement à cause du coût en temps de calcul prohibitif. Nous proposons une reformulation decette technique sous la forme des fonctions d'onde électroniques du système dansune représentation énergie--temps. Le coût de calcul de notre algorithmenumérique est maintenant linéaire avec le temps simulé et le volume du système,rendant possible la simulation de système contenant $10^5-10^6$ atomes/sites.Nous utilisons cet outil pour proposer de nouveaux effets intrigants ainsi quedes expériences. Nous introduisons la modification dynamique du motifd'interférence d'un système quantique. Nous montrons, par exemple, que la montéed'une tension DC $V$ sur un interféromètre électronique produit un régimetransitoire où le courant oscille comme $cos(eVt/hbar)$. Nous prévoyons unegrande variété d'effets nouveaux lorsque les circuits de nanoélectronique sontsondés très rapidement. Les outils et concepts développés dans cette thèseauront un rôle clé dans l'analyse et les propositions des expériences à venirWith the recent technical progress, single electron sources have moved fromtheory to the lab. Conceptually new types of experiments where one probesdirectly the internal quantum dynamics of the devices are within grasp. In thisthesis we develop the analytical and numerical tools for handling suchsituations. The simulations require appropriate spatial resolution for thesystems, and simulated times long enough so that one can probe their internalcharacteristic times. So far the standard theoretical approach used to treatsuch problems numerically---known as Keldysh or NEGF (Non Equilibrium Green'sFunctions) formalism---has not been very successful mainly because of aprohibitive computational cost. We propose a reformulation of the NEGFtechnique in terms of the electronic wave functions of the system in anenergy--time representation. The numerical algorithm we obtain scales nowlinearly with the simulated time and the volume of the system, and makessimulation of systems with $10^5-10^6$ atoms/sites feasible. We leverage thistool to propose new intriguing effects and experiments. In particular weintroduce the concept of dynamical modification of interference pattern of aquantum system. For instance, we show that when raising a DC voltage $V$ to anelectronic interferometer, the transient current responseoscillates as $cos(eVt/hbar)$. We expect a wealth of new effects whennanoelectronic circuits are probed fast enough. The tools and conceptsdeveloped in this work shall play a key role in the analysis and proposal ofupcoming experiments
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Weston, Joseph. « Numerical methods for time-resolved quantum nanoelectronics ». Thesis, Université Grenoble Alpes (ComUE), 2016. http://www.theses.fr/2016GREAY040/document.
Texte intégralRésumé :
De récents progrès dans la nanoélectronique quantique ont donné lieu à denouvelles expériences avec des sources cohérentes d'électrons unique. Lorsqu'undispositif électronique quantique est manipulé sur une échelle de temps pluscourte que le temps de vol caractéristique d'un électron à travers ledispositif, toute une gamme de possibilités qui sont conceptuellement nouvellesdeviennent possible. Pour traiter de telles situations physiques, des avancéescorrespondantes sont nécessaires dans les techniques de simulation, pour aiderà comprendre, ainsi qu'à concevoir, la prochaine génération d'expériences dansce domaine.Les techniques les plus avancées pour simuler ce genre de physique nécessitentun temps de calcul qui croît de linéairement avec la taille dusystème, mais de manière quadratique avec la durée simulée.Ceci est particulièrement problématique pour les cas où un électron restedans le dispositif pendant une durée beaucoup plus longue que le temps devol balistique. Dans cette thèse on propose d'améliorer un algorithmeexistant, basé sur des fonctions d'onde, pour traiter le transport quantiquerésolu en temps dont le temps de calcul croît linéairement avec la taille du système ainsique la durée simulée. Par la suite on exploite cet algorithme pour étudierplusieurs systèmes physiques intéressants. En particulier on trouve quel'application d'un train d'impulsions de tension à un interféromètre à électronspeut stabiliser la modification dynamique du schéma d'interférence.On exploite cet effet pour faire de la spectroscopied'états d'Andreev et de Majorana existant dans des structure hybridessupraconducteur-nanofil.Les algorithmes numériques sont implémentés en tant qu'extension du logicielde transport quantique Kwant. Cette implémentation est utilisée pour tousles résultats numériques présentés dans la thèse, ainsi que d'autres projetsde recherche couvrants une grande gamme de physique: effet Hall quantique,isolants topologiques de Floquet, interféromètres de type Fabry-Pérot, etjonctions supraconductricesRecent technical progress in the field of quantum nanoelectronics have lead toexciting new experiments involving coherent single electron sources.When quantum electronic devices are manipulated on time scales shorterthan the characteristic time of flight of electrons through the device, a wholeclass of conceptually new possibilities become available. In order totreat such physical situations, corresponding advances in numerical techniquesand their software implementation are required both as a tool to aidunderstanding, and also to help when designing the next generation ofexperiments in this domain.Recent advances in numerical methods have lead to techniques for which thecomputation times scales linearly with the system volume, but as thesquare of the simulation time desired. This is particularly problematicfor cases where the characteristic dwell time of electrons in the centraldevice is much longer than the ballistic time of flight. Here, we proposean improvement to an existing wavefunction based algorithm fortreating time-resolved quantum transport which scales linearly in both thesystem volume and desired simulation time. We use this technique tostudy a number of interesting physical cases. In particular we find that theapplication of a train of voltage pulses to an electronic interferometercan be used to stabilise the dynamical modification of the interferencethat was recently proposed. We use this to perform spectroscopy on Majoranaand Andreev resonances in hybrid superconductor-nanowire structures.The numerical algorithms are implemented as an extension to the Kwantquantum transport software. This implementation is used for all the numericalresults presented here, in addition to other work, covering a wide varietyof physical applications: quantum Hall effect, Floquet topological insulators,Fabry-Perot interferometers and superconducting junction
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Rossignol, Benoît. « Time-resolved quantum nanoelectronics in electromagnetic environments ». Thesis, Université Grenoble Alpes, 2020. http://www.theses.fr/2020GRALY004.
Texte intégralRésumé :
La nanoélectronique quantique est dans une phase de grande expansion, soutenue principalement par le développement de l'informatique quantique. Une grande précision est nécessaire pour atteindre les objectifs actuels, mais d'un autre côté, les expériences sont aussi plus complexes que jamais. Les outils numériques semblent nécessaires pour réaliser la compréhension exigée tout en traitant une telle complexité. Les échelles de temps concernées sont de plus en plus courtes et se rapprochent des échelles de temps quantiques intrinsèques de l'appareil, comme le temps de vol. Les travaux antérieurs de notre groupe ont simulé le transport d'électrons en fonction du temps à une échelle quantique. Cette thèse vise à améliorer les algorithmes précédents pour obtenir une plus grande précision et une meilleure description des systèmes en incluant l'environnement électronique.Ce travail est divisé en trois domaines principaux. Tout d'abord, nous améliorons les outils de simulation numérique en fonction du temps pour prendre en compte un environnement électronique d'une manière cohérente. Le nouvel algorithme peut atteindre une précision arbitraire d'une manière contrôlée. Deuxièmement, le nouvel algorithme est utilisé pour démontrer l'existence de nouveaux phénomènes physiques. Nous étudions les jonctions Josephson dans différents environnements pour mettre en valeur le rôle des quasi-particules, l'effet d'une impulsion très courte, et pour étudier les techniques de caractérisation de la jonction topologique.Enfin, différents développements sont à l'étude afin d'intégrer le phénomène de décohérence et le bruit quantique dans les simulationsQuantum nanoelectronics is in a phase of great expansion, supported mainlyby the development of quantum computing. A high degree of precision isrequired to achieve current objectives, but on the other hand, the experi-ences are also more complex than ever. Nuremical tools seem necessary toachieve the required understanding while dealing with such complexity. Thetime scales involved are getting shorter and are getting closer to the intrinsicquantum time scales of the device, such as time of flight. Our group’s pre-vious work has simulated time-dependent electron transport on a quantumscale. This thesis aims to improve the previous algorithms to obtain greateraccuracy and a better description of the systems by including the electronicenvironment. This work is divided into three main areas. First, we improveof numerical time-dependent simulation tools to take into account an elec-tronic environment in a self-consistent way. The new algorithm can achievearbitrary accuracy in a controlled way. Second, the new algorithm is used todemonstrate the existence of new physical phenomena. We study Josephsonjunctions in different environments to enhance the role of quasi-particles, theeffect of a very short pulse, and to study topological junction characteriza-tion techniques. Finally, various developments are being studied to integratethe phenomenon of decoherence and quantum noise into the simulations
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Kirchner, Ulrich. « A space-time approach to quantum mechanics ». Master's thesis, University of Cape Town, 1999. http://hdl.handle.net/11427/14639.
Texte intégralRésumé :
Includes bibliographical references.We present a systematic development and application of Geometric Algebra, an extended vector calculus. The entire algebraic structure, which is a graded Clifford algebra, is developed. To illustrate the derived results, examples are given for two and three dimensions. Here it becomes clear, how rotations and Lorentz boosts can be formulated in the Geometric Algebra. Further we realize that the Geometric Algebra contains elements, which can be used as representations of the complex unit. Having derived the necessary tools, we turn our attention to physics. We give applications to classical mechanics, quantum mechanics, ï¬ eld theory, curved manifolds, electromagnetism, and gravity as a gauge theory.
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Fabre, Nicolas. « Quantum information in time-frequency continuous variables ». Thesis, Université de Paris (2019-....), 2020. http://www.theses.fr/2020UNIP7044.
Texte intégralRésumé :
Cette thèse aborde l’encodage de degrés de liberté continus temps-fréquence de photon uniques. Les similitudes mathématiques avec les quadratures du champ électromagnétique amène à généraliser des protocoles exprimées dans ces variables dans notre encodage. On introduit un nouveau type de qubit robuste contre des erreurs du type déplacement dans l’espace des phases temps-fréquence. Un nouvel espace des phases doublement cylindriques est étudié et est une représentation particulièrement adaptée pour des états ayant une symétrie de translation. On étudie également comment construire une distribution de phase fonctionnelle permettant de décrire un état quantique possédant des degrés de libertés continus spectraux et en quadratureThis thesis tackles the time-frequency continuous variables degree of freedom encoding of single photons and examine the formal mathematical analogy with the quadrature continuous variables of the electromagnetic field. We define a new type of qubit which is robust against time-frequency displacement errors. We define a new double-cylinder phase space which is particularly adapted for states which have a translational symmetry. We also study how to build a functional phase space distribution which allows to describe a quantum state with spectral and quadrature continuous variables degrees of freedom
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Escobedo, Crisol J. « The problem of time in quantum mechanics ». To access this resource online via ProQuest Dissertations and Theses @ UTEP, 2009. http://0-proquest.umi.com.lib.utep.edu/login?COPT=REJTPTU0YmImSU5UPTAmVkVSPTI=&clientId=2515.
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Lyons, Glenn. « Time asymmetry ». Thesis, University of Cambridge, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.309076.
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Shaghaghi, Mehran. « Topics in quantum physics : Schrodinger's cat problem - time measurement accuracies in quantum mechanics ». Thesis, University of British Columbia, 2007. http://hdl.handle.net/2429/204.
Texte intégralRésumé :
In this thesis I address two different topics in quantum theory. The first one is the long discussed Schrodinger's cat problem, and the issues related to having a macroscopic superposition state. I show that the quantum theory provides full explanation to the problem. In the second part, I discuss the time measurement related issues in quantum mechanics. Since there does not exist any time operator in quantum mechanics generally, time is not directly measurable. Therefore we should devise other methods to register time. We study different time-energy relations and will find that accurate clocks have high energy uncertainties. If we use accurate clocks in quantum systems to observe their time evolutions, their high energy uncertainties interfere with system's normal evolution and slows it down. I also provide a formal proof to a previously suggested limiting accuracy relation on the measurements of the time-of-arrival experiments.
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Barsegov, Valeri Abulevich. « Quantum decoherence and time symmetry breaking : quantum-classical correspondence in non-adiabatic transitions / ». Full text (PDF) from UMI/Dissertation Abstracts International, 2000. http://wwwlib.umi.com/cr/utexas/fullcit?p3004212.
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Gibbs, James Michael. « Spacetime as a quantum graph ». Diss., Georgia Institute of Technology, 1994. http://hdl.handle.net/1853/29195.
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Bonifacio, Paolo. « Spacetime conformal fluctuations and quantum dephasing ». Thesis, Available from the University of Aberdeen Library and Historic Collections Digital Resources, 2009. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?application=DIGITOOL-3&owner=resourcediscovery&custom_att_2=simple_viewer&pid=33587.
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Ioannou, Lawrence Mario. « Continuous-time quantum algorithms searching and adiabatic computation / ». Waterloo, Ont. : University of Waterloo, [Dept. of Combinatorics and Optimization], 2002. http://etd.uwaterloo.ca/etd/dgpiche2002.pdf.
Texte intégralRésumé :
Thesis (M.Math.) - University of Waterloo, 2002."A thesis presented to the University of Waterloo in fulfilment of the thesis requirement for the degree of Master of Mathematics in Combinatorics and Optimization". Includes bibliographical references.
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Ioannou, Lawrence. « Continuous-time Quantum Algorithms : Searching and Adiabatic Computation ». Thesis, University of Waterloo, 2002. http://hdl.handle.net/10012/1129.
Texte intégralRésumé :
One of the most important quantum algorithms is Grover's search algorithm [G96]. Quantum searching can be used to speed up the search for solutions to NP-complete problems e. g. 3SAT. Even so, the best known quantum algorithms for 3SAT are considered inefficient.
Soon after Grover's discovery, Farhi and Gutmann [FG96] devised a "continuous-time analogue" of quantum searching. More recently Farhi et. al. [FGGS00] proposed a continuous-time 3SAT algorithm which invokes the adiabatic approximation [M76]. Their algorithm is difficult to analyze, hence we do not know whether it can solve typical 3SAT instances faster than Grover's search algorithm can.
I begin with a review of the discrete- and continuous-time models of quantum computation. I then make precise the notion of "efficient quantum algorithms", motivating sufficient conditions for discrete- and continuous-time algorithms to be considered efficient via discussion of standard techniques for discrete-time simulation of continuous-time algorithms. After reviewing three quantum search algorithms [F00,FG96,G96], I develop the adiabatic 3SAT algorithm as a natural extension of Farhi and Gutmann's search algorithm. Along the way, I present the adiabatic search algorithm [vDMV01] and remark on its discrete-time simulation. Finally I devise a generalization of the adiabatic algorithm and prove some lower bounds for various cases of this general framework.
UPDATE (February 2003): Please see article http://arxiv. org/abs/quant-ph/0302138 for a resolution to the problem of simulating the continuous-time adiabatic search algorithm with a quantum circuit using only O(sqrt(N)) resources.
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Špalek, Robert. « Quantum algorithms, lower bounds and time-space tradeoffs) ». Amsterdam : Amsterdam : Institute for Logic, Language and Computation ; Universiteit van Amsterdam [Host], 2006. http://dare.uva.nl/document/27681.
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Khosravi, Elham [Verfasser]. « Time-dependent phenomena in quantum transport / Elham Khosravi ». Berlin : Freie Universität Berlin, 2013. http://d-nb.info/1034300261/34.
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Zhang, Yu, et 張余. « Time-dependent study of quantum transport and dissipation ». Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2014. http://hdl.handle.net/10722/207190.
Texte intégralRésumé :
Dissipative time-dependent quantum transport theory with electron-phonon interaction in either weak or strong coupling regime is established. This theory goes beyond the conventional quantum master equation method and Kadanoff-Baym kinetic equations. It provides an efficient method for the simulation of transient quantum transport under arbitrary bias voltage with different electron-phonon coupling strength.
First, time-dependent quantum transport theory for non-interacting system and its combination with first-principles method is developed. Based on the Padé expansion to Fermi function, and wide-band limit approximation of lead self-energy, a set of equations of motion is developed for efficient evaluation of density matrix and related quantities. To demonstrate its applicability, this method is employed to study the transient transport through a carbon nanotube based electronic device.
Second, a dissipative time-dependent quantum transport theory is established in the weak electron-phonon coupling regime. In addition to the self-energy caused by leads, a new self-energy is introduced to characterize the dissipative effect induced by electron-phonon interaction. In the weak coupling regime, the lowest order expansion is employed for practical implementation. The corresponding closed set of equations of motion is derived, which provides an efficient and accurate treatment of transient quantum transport with electron-phonon interaction in the weak coupling regime. Numerical examples are demonstrated and its combination with first-principles method is also discussed.
Next, a dissipative quantum transport theory for strong electron-phonon interaction is established by employing small polaron transformation. The corresponding equation of motions are developed, which is used to study the quantum interference effect and phonon-induced decoherence dynamics. Numerical studies demonstrate the formation of quantum interference effect caused by the transport electrons through two quasi-degenerate states with different couplings to the leads. The quantum interference can be suppressed by phonon scattering, which indicates the importance of considering electron-phonon interaction in these systems with prominent quantum interference effect when the electron-phonon coupling is strong.
Last, the dissipative quantum transport theory for weak electron-phonon coupling regime is used to simulate the photovoltaic devices. Within the nonequilibrium Greens function formalism, a quantum mechanical method for nanostructured photovoltaic devices is presented. The method employs density-functional tight-binding theory for electronic structure, which make is possible to simulate the performance of photovoltaic devices without relying on empirical parameters. Numerical studies of silicon nanowirebased devices of realistic sizes with more than ten thousand atoms are performed and the results indicate that atomistic details and nonequilibrium conditions have clear impact on the photoresponse of the devices.published_or_final_version
Chemistry
Doctoral
Doctor of Philosophy
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Sherlock, Benjamin Edward. « Ultracold quantum gases in time-averaged adiabatic potentials ». Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:3c0b680e-b752-4278-8033-787f8519f244.
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This thesis describes the experimental realisation and characterisation of three non-trivial trapping geometries for ultracold atoms. The double-well, ring and to some degree shell trap are examples of a highly versatile class of traps called time-averaged adiabatic potentials (TAAPs). In this experiment the TAAPs arise from the combination of three independent magnetic fields; a static quadrupole field dressed by a uniform radio-frequency field is time-averaged by a bias field oscillating at in the kHz regime. The result is a very smooth potential, within which ultracold atoms can be evaporatively cooled to quantum degeneracy, and subsequently manipulated into new geometries without destroying the quantum coherence. The vertically offset double-well potential provided the first example of ultracold atoms confined in a TAAP. The same potential is used to demonstrate efficient evaporative cooling across the Bose-Einstein condensate (BEC) phase transition using only the Landau-Zener loss mechanism. Switching off the time-averaging fields loads atoms from the double-well TAAP into the rf-dressed shell trap. A characterisation of this potential measured low heating rates and lifetimes of up to 58s. With efforts ongoing to increase the trap anisotropy, this potential shows promise for research into the static and rapidly rotating 2D systems. In the presence of a single time-averaging field, the shell geometry is transformed into a ring-shaped trap with an adjustable radius. The ring trap can be controllably tilted and progress towards multiply connected condensates is being made. A rotation scheme to spin up atoms in the ring trap has been demonstrated, presenting the opportunity to investigate the dynamics of superflow in degenerate quantum gases.
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Dakovski, Georgi L. « TIME-RESOLVED TERAHERTZ SPECTROSCOPY OF SEMICONDUCTOR QUANTUM DOTS ». Case Western Reserve University School of Graduate Studies / OhioLINK, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=case1192470456.
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Qubain, Edward George. « A quantum phase space with classical time evolution / ». Full text (PDF) from UMI/Dissertation Abstracts International, 2001. http://wwwlib.umi.com/cr/utexas/fullcit?p3008424.
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McDonald, Christopher. « Electron Dynamics in Finite Quantum Systems ». Thèse, Université d'Ottawa / University of Ottawa, 2013. http://hdl.handle.net/10393/26105.
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The multiconfiguration time-dependent Hartree-Fock (MCTDHF) and multiconfiguration time-dependent Hartree (MCTDH) methods are employed to investigate nonperturbative multielectron dynamics in finite quantum systems. MCTDHF is a powerful tool that allows for the investigation of multielectron dynamics in strongly perturbed quantum systems. We have developed an MCTDHF code that is capable of treating problems involving three dimensional (3D) atoms and molecules exposed to strong laser fields. This code will allow for the theoretical treatment of multielectron phenomena in attosecond science that were previously inaccessible. These problems include complex ionization processes in pump-probe experiments on noble gas atoms, the nonlinear effects that have been observed in Ne atoms in the presence of an x-ray free-electron laser (XFEL) and the molecular rearrangement of cations after ionization. An implementation of MCTDH that is optimized for two electrons, each moving in two dimensions (2D), is also presented. This implementation of MCTDH allows for the efficient treatment of 2D spin-free systems involving two electrons; however, it does not scale well to 3D or to systems containing more that two electrons.
Both MCTDHF and MCTDH were used to treat 2D problems in nanophysics and attosecond science. MCTDHF is used to investigate plasmon dynamics and the quantum breathing mode for several electrons in finite lateral quantum dots. MCTDHF is also used to study the effects of manipulating the potential of a double lateral quantum dot containing two electrons; applications to quantum computing are discussed. MCTDH is used to examine a diatomic model molecular system exposed to a strong laser field; nonsequential double ionization and high harmonic generation are studied and new processes identified and explained. An implementation of MCTDHF is developed for nonuniform tensor product grids; this will allow for the full 3D implementation of MCTDHF and will provide a means to investigate a wide variety of problems that cannot be currently treated by any other method. Finally, the time it takes for an electron to tunnel from a bound state is investigated; a definition of the tunnel time is established and the Keldysh time is connected to the wavefunction dynamics.
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Zhan, Hongxin [Verfasser]. « Time-dependent quantum transport and quantum correlations of interacting electrons and photons / Hongxin Zhan ». Konstanz : KOPS Universität Konstanz, 2019. http://d-nb.info/1202713912/34.
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Lu, Feng. « Studies of a quantum scheduling algorithm and on quantum error correction ». Doctoral diss., University of Central Florida, 2007. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/3540.
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Quantum computation has been a rich field of study for decades because it promises possible spectacular advances, some of which may run counter to our classically rooted intuitions. At the same time, quantum computation is still in its infancy in both theoretical and practical areas. Efficient quantum algorithms are very limited in number and scope; no real breakthrough has yet been achieved in physical implementations. Grover's search algorithm can be applied to a wide range of problems; even problems not generally regarded as searching problems can be reformulated to take advantage of quantum parallelism and entanglement leading to algorithms which show a square root speedup over their classical counterparts. This dissertation discusses a systematic way to formulate such problems and gives as an example a quantum scheduling algorithm for an R||C_max problem. This thesis shows that quantum solution to such problems is not only feasible but in some cases advantageous. The complexity of the error correction circuitry forces us to design quantum error correction codes capable of correcting only a single error per error correction cycle. Yet, time-correlated errors are common for physical implementations of quantum systems; an error corrected during a certain cycle may reoccur in a later cycle due to physical processes specific to each physical implementation of the qubits. This dissertation discusses quantum error correction for a restricted class of time-correlated errors in a spin-boson model. The algorithm proposed allows the correction of two errors per error correction cycle, provided that one of them is time-correlated. The algorithm can be applied to any stabilizer code, perfect or non-perfect, and simplified the circuit complexity significantly comparing to the classic quantum error correction codes.Ph.D.
School of Electrical Engineering and Computer Science
Engineering and Computer Science
Computer Science PhD
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Galiautdinov, Andry. « Quantum theory of elementary processes ». Diss., Georgia Institute of Technology, 2002. http://hdl.handle.net/1853/28007.
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Ilg, Matthias. « An investigation of spatially bounded, time independent quantum systems ». Thesis, Georgia Institute of Technology, 1991. http://hdl.handle.net/1853/28046.
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Siegert, Jörg. « Semiconductor Quantum Dots Studied by Time-Resolved Luminescence Techniques ». Licentiate thesis, KTH, Microelectronics and Information Technology, IMIT, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-1789.
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In this thesis time-resolved photoluminescence spectroscopyis presented as a powerful tool to study the carrier dynamicsin various self-assembled quantum dot (QD) structures, whichare potentially attractive for device applications.
The experiments reveal the impact of proton irradiation onInGaAs QDs and comparable quantum wells. Nonradiativerecombination at defectsan important material parameterandmeasureof the structure optical qualityis found to play a much less important role for the QD samples.The superior radiation hardness can be explained as a result ofthe three-dimensional carrier confinement in QDs. Comparisonsbetween the structures show a decrease of photoluminescenceintensity for quantum wells but a slight increase for QDsirradiated at low to intermediate doses. This somewhatunexpected characteristic is described by an enhanced carriertransfer into the dots via the defects introduced in thematerial by the protons.
In a different structure carrier dynamics in spatiallyaligned of InAs QDs are investigated. Alignment along lines isachieved by misfit dislocations deliberately introduced in thesubstrate. Photoluminescence spectra of the dots exhibit muchsmaller inhomogeneous broadening than for the reference sampleas a result of an improved QD uniformity. Samples with varyingbuffer layer thicknesses were grown to study the influence ofdislocation related traps on the observed fastphotoluminescence decay. It is found that the fast carriertrapping is predominantly caused by point defects close to theQDs or at the QD/barrier interfaces.
Additional numerical simulations confirm the roles of thetwo independently acting traps in nonradiativerecombination.