Effective Non Hermiticity And Topology In Markovian Quadratic Bosonic Dynamics
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Effective Non Hermiticity And Topology In Markovian Quadratic Bosonic Dynamics
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Author : Vincent Paul Flynn
language : en
Publisher: Springer Nature
Release Date :
Effective Non Hermiticity And Topology In Markovian Quadratic Bosonic Dynamics written by Vincent Paul Flynn and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Effective Non Hermiticity And Topology In Markovian Quadratic Bosonic Dynamics
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Author : Vincent Paul Flynn
language : en
Publisher: Springer
Release Date : 2024-04-01
Effective Non Hermiticity And Topology In Markovian Quadratic Bosonic Dynamics written by Vincent Paul Flynn and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-01 with Science categories.
This thesis provides an in-depth investigation of effective non-Hermiticity and topology in many-mode, non-interacting, bosonic systems. It also establishes the extent to which one must move beyond the Hamiltonian, closed-system setting, in order to uncover signatures of genuine symmetry-protected topological (SPT) physics in "free" (mean-field) bosons. While SPT phases of free fermionic matter and their associated zero-energy boundary-localized modes have been thoroughly explored, similar physics in free bosonic systems still remains elusive. No fermionic counterpart exists for the distinctive dynamical behavior that arises from the effective non-Hermiticity, intrinsic even at equilibrium, to bosonic Hamiltonians. Therefore, a much needed paradigm shift is required to address major conceptual roadblocks in the search for SPT bosonic phases. The analysis within develops, in particular, the notion of topological metastability in quadratic bosonic systems subject to Markovian dissipation. The resulting dynamical paradigm was found to be characterized by both a sharp separation between transient and asymptotic dynamics and non-trivial topological invariants. It also features long-lived boundary-localized "Majorana boson" and "Dirac boson" modes, which realize tight bosonic analogues to the edge modes characteristic of fermionic SPT phases. This comprehensive look into non-interacting bosonic systems breaks important new ground for re-imagining quantum phenomena beyond equilibrium, with novel applications in quantum science.
Effective Evolution Equations From Quantum Dynamics
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Author : Niels Benedikter
language : en
Publisher: Springer
Release Date : 2015-11-04
Effective Evolution Equations From Quantum Dynamics written by Niels Benedikter and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-04 with Science categories.
These notes investigate the time evolution of quantum systems, and in particular the rigorous derivation of effective equations approximating the many-body Schrödinger dynamics in certain physically interesting regimes. The focus is primarily on the derivation of time-dependent effective theories (non-equilibrium question) approximating many-body quantum dynamics. The book is divided into seven sections, the first of which briefly reviews the main properties of many-body quantum systems and their time evolution. Section 2 introduces the mean-field regime for bosonic systems and explains how the many-body dynamics can be approximated in this limit using the Hartree equation. Section 3 presents a method, based on the use of coherent states, for rigorously proving the convergence towards the Hartree dynamics, while the fluctuations around the Hartree equation are considered in Section 4. Section 5 focuses on a discussion of a more subtle regime, in which the many-body evolution can be approximated by means of the nonlinear Gross-Pitaevskii equation. Section 6 addresses fermionic systems (characterized by antisymmetric wave functions); here, the fermionic mean-field regime is naturally linked with a semiclassical regime, and it is proven that the evolution of approximate Slater determinants can be approximated using the nonlinear Hartree-Fock equation. In closing, Section 7 reexamines the same fermionic mean-field regime, but with a focus on mixed quasi-free initial data approximating thermal states at positive temperature.
Open Quantum Systems
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Author : Ángel Rivas
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-10-01
Open Quantum Systems written by Ángel Rivas and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-01 with Science categories.
In this volume the fundamental theory of open quantum systems is revised in the light of modern developments in the field. A unified approach to the quantum evolution of open systems is presented by merging concepts and methods traditionally employed by different communities, such as quantum optics, condensed matter, chemical physics and mathematical physics. The mathematical structure and the general properties of the dynamical maps underlying open system dynamics are explained in detail. The microscopic derivation of dynamical equations, including both Markovian and non-Markovian evolutions, is also discussed. Because of the step-by-step explanations, this work is a useful reference to novices in this field. However, experienced researches can also benefit from the presentation of recent results.
Topological Quantum Computation
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Author : Zhenghan Wang
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Topological Quantum Computation written by Zhenghan Wang and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Complex manifolds categories.
Topological quantum computation is a computational paradigm based on topological phases of matter, which are governed by topological quantum field theories. In this approach, information is stored in the lowest energy states of many-anyon systems and processed by braiding non-abelian anyons. The computational answer is accessed by bringing anyons together and observing the result. Besides its theoretical esthetic appeal, the practical merit of the topological approach lies in its error-minimizing hypothetical hardware: topological phases of matter are fault-avoiding or deaf to most local noises, and unitary gates are implemented with exponential accuracy. Experimental realizations are pursued in systems such as fractional quantum Hall liquids and topological insulators. This book expands on the author's CBMS lectures on knots and topological quantum computing and is intended as a primer for mathematically inclined graduate students. With an emphasis on introducing basic notions and current research, this book gives the first coherent account of the field, covering a wide range of topics: Temperley-Lieb-Jones theory, the quantum circuit model, ribbon fusion category theory, topological quantum field theory, anyon theory, additive approximation of the Jones polynomial, anyonic quantum computing models, and mathematical models of topological phases of matter.
Introduction To Topological Quantum Computation
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Author : Jiannis K. Pachos
language : en
Publisher: Cambridge University Press
Release Date : 2012-04-12
Introduction To Topological Quantum Computation written by Jiannis K. Pachos and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-12 with Computers categories.
Ideal for graduate students and researchers from various sub-disciplines, this book provides an excellent introduction to topological quantum computation.
Pt Symmetry
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Author : Carl M Bender
language : en
Publisher: World Scientific Publishing
Release Date : 2018-11-22
Pt Symmetry written by Carl M Bender and has been published by World Scientific Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-22 with Science categories.
Originated by the author in 1998, the field of PT (parity-time) symmetry has become an extremely active and exciting area of research. PT-symmetric quantum and classical systems have theoretical, experimental, and commercial applications, and have been the subject of many journal articles, PhD theses, conferences, and symposia. Carl Bender's work has influenced major advances in physics and generations of students. This book is an accessible entry point to PT symmetry, ideal for students and scientists looking to begin their own research projects in this field.
Quantum Mechanics Via Lie Algebras
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Author : Arnold Neumaier
language : en
Publisher:
Release Date : 2020-10-04
Quantum Mechanics Via Lie Algebras written by Arnold Neumaier and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-04 with Science categories.
Quantum Quenching Annealing And Computation
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Author : Anjan Kumar Chandra
language : en
Publisher: Springer
Release Date : 2010-07-23
Quantum Quenching Annealing And Computation written by Anjan Kumar Chandra and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-23 with Science categories.
The process of realizing the ground state of some typical (frustrated) quantum many-body systems, starting from the ‘disordered’ or excited states, can be formally mapped to the search of solutions for computationally hard problems. The dynamics through the critical point, in between, are therefore extremely crucial. In the context of such computational optimization problems, the dynamics (of rapid quenching or slow annealing), while tuning the appropriate elds or uctuations, in particular while crossing the quantum critical point, are extremely intriguing and are being investigated these days intensively. Several successful methods and tricks are now well established. This volume gives a collection of introductory reviews on such developments written by well-known experts. It concentrates on quantum phase transitions and their dynamics as the transition or critical points are crossed. Both the quenching and annealing dynamics are extensively covered. We hope these timely reviews will inspire the young researchers to join and c- tribute to this fast-growing, intellectually challenging, as well as technologically demanding eld. We are extremely thankful to the contributors for their intensive work and pleasant cooperations. We are also very much indebted to Kausik Das for his help in compiling this book. Finally, we express our gratitude to Johannes Zittartz, Series Editor, LNP, and Christian Caron of physics editorial department of Springer for their encouragement and support.
Quantum Field Theory Of Non Equilibrium States
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Author : Jørgen Rammer
language : en
Publisher: Cambridge University Press
Release Date : 2011-03-03
Quantum Field Theory Of Non Equilibrium States written by Jørgen Rammer and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-03 with Science categories.
Quantum field theory is the application of quantum mechanics to systems with infinitely many degrees of freedom. This 2007 textbook presents quantum field theoretical applications to systems out of equilibrium. It introduces the real-time approach to non-equilibrium statistical mechanics and the quantum field theory of non-equilibrium states in general. It offers two ways of learning how to study non-equilibrium states of many-body systems: the mathematical canonical way and an easy intuitive way using Feynman diagrams. The latter provides an easy introduction to the powerful functional methods of field theory, and the use of Feynman diagrams to study classical stochastic dynamics is considered in detail. The developed real-time technique is applied to study numerous phenomena in many-body systems. Complete with numerous exercises to aid self-study, this textbook is suitable for graduate students in statistical mechanics and condensed matter physics.