Disorder Free Localization
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Anderson Localization And Its Ramifications
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Author : Tobias Brandes
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-09-11
Anderson Localization And Its Ramifications written by Tobias Brandes 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 2003-09-11 with Science categories.
The phenomenon of localization of the electronic wave function in a random medium can be regarded as the key manifestation of quantum coherence in a condensed matter system. As one of the most remarkable phenomena in condensed matter physics discovered in the 20th century, the localization problem is an indispensable part of the theory of the quantum Hall effects and rivals superconductivity in its significance as a manifestation of quantum coherence at a macroscopic scale. The present volume, written by some of the leading experts in the field, is intended to highlight some of the recent progress in the field of localization, with particular emphasis on the effect of interactions on quantum coherence. The chapters are written in textbook style and should serve as a reliable and thorough introduction for advanced students or researchers already working in the field of mesoscopic physics.
Disorder Free Localization
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Author : Adam Smith
language : en
Publisher: Springer
Release Date : 2019-07-01
Disorder Free Localization written by Adam Smith and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-01 with Science categories.
This thesis is a contribution at the intersection of a number of active fields in theoretical and experimental condensed matter, particularly those concerned with disordered systems, integrable models, lattice gauge theories, and non-equilibrium quantum dynamics. It contributes an important new facet to our understanding of relaxation in isolated quantum systems by conclusively demonstrating localization without disorder for the first time, answering a long-standing question in this field. This is achieved by introducing a family of models – intimately related to paradigmatic condensed matter models – and studying their non-equilibrium dynamics through a combination of exact analytical mappings and an array of numerical techniques. This thesis also makes contributions relevant to the theory of quantum chaotic behaviour by calculating novel, and often intractable, entanglement measures and out-of-time-ordered correlators. A concrete and feasible proposal is also made for the experimental realization and dynamical study of the family of models, based on currently available technologies.
Scattering And Localization Of Classical Waves In Random Media
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Author : Ping Sheng
language : en
Publisher: World Scientific
Release Date : 1990
Scattering And Localization Of Classical Waves In Random Media written by Ping Sheng and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Science categories.
The past decade has witnessed breakthroughs in the understanding of the wave localization phenomena and its implications for wave multiple scattering in inhomogeneous media. This book brings together review articles written by noted researchers in this field in a tutorial manner so as to give the readers a coherent picture of its status. It would be valuable both as an up-to-date reference for active researchers as well as a readable source for students looking to gain an understanding of the latest results.
Higher Form Symmetry And Eigenstate Thermalization Hypothesis
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Author : Osamu Fukushima
language : en
Publisher: Springer Nature
Release Date : 2025-04-11
Higher Form Symmetry And Eigenstate Thermalization Hypothesis written by Osamu Fukushima and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-11 with Science categories.
The eigenstate thermalization hypothesis (ETH) is a successful framework providing criteria for thermalization in isolated quantum systems. Although numerical and theoretical analyses support the ETH as a fundamental mechanism for explaining thermalization in diverse systems, it remains a challenge to analytically identify whether particular systems satisfy the ETH. In quantum many-body systems and quantum field theories, phenomena that violate the ETH are expected to imply nontrivial thermalization processes, and are gathering increasing attention. This book elucidates how the existence of higher-form symmetries influences the dynamics of thermalization in isolated quantum systems. Under reasonable assumptions, it is analytically shown that a p-form symmetry in a (d+1)-dimensional quantum field theory leads to the breakdown of the ETH for many nontrivial (d−p)-dimensional observables. In the case of discrete higher-form (i.e., p ≥ 1) symmetry, this indicates the absence of thermalization for observables that are non-local but much smaller than the entire system size even though the system do have no local conserved quantities. The author provides numerical evidence for this argument for the (2+1)-dimensional Z2 lattice gauge theory. While local observables such as a plaquette operator thermalize even for mixed symmetry sectors, the non-local observable such as the one exciting a magnetic dipole instead relaxes to the generalized Gibbs ensemble that takes account of the Z2 1-form symmetry. The assumptions of the ETH-violation include the mixing of symmetry sectors within a given energy shell. This condition is rather challenging to verify because it requires information on the eigenstates in the middle of the spectrum. In the subsequent chapter, we further reconsider this assumption from the viewpoint of a projective phase to alleviate this difficulty. In the case of ZN symmetries, the difficulty can be circumvented considering ZN×ZN-symmetric theories with a projective phase, and then perturbing the Hamiltonian while preserving one of the ZN symmetries of interest. Additionally, the book also presents numerical analyses for (1+1)-dimensional spin chains and the (2+1)-dimensional Z2 lattice gauge theory to demonstrate this scenario.
Supersymmetry In Disorder And Chaos
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Author : Konstantin Efetov
language : en
Publisher: Cambridge University Press
Release Date : 1999-09-13
Supersymmetry In Disorder And Chaos written by Konstantin Efetov 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 1999-09-13 with Mathematics categories.
This book provides a comprehensive treatment of the ideas and applications of supersymmetry.
Light Localisation And Lasing
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Author : Mher Ghulinyan
language : en
Publisher: Cambridge University Press
Release Date : 2015
Light Localisation And Lasing written by Mher Ghulinyan 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 2015 with Science categories.
This book presents research on quasi-random and random photonic systems for graduate students and researchers in optics, photonics and optical engineering.
Ultracold Atoms In Optical Lattices
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Author : Maciej Lewenstein
language : en
Publisher: Oxford University Press (UK)
Release Date : 2012-03-08
Ultracold Atoms In Optical Lattices written by Maciej Lewenstein and has been published by Oxford University Press (UK) this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-08 with Science categories.
This book explores the physics of atoms frozen to ultralow temperatures and trapped in periodic light structures. It introduces the reader to the spectacular progress achieved on the field of ultracold gases and describes present and future challenges in condensed matter physics, high energy physics, and quantum computation.
50 Years Of Anderson Localization
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Author : Elihu Abrahams
language : en
Publisher: World Scientific
Release Date : 2010
50 Years Of Anderson Localization written by Elihu Abrahams and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Science categories.
This unique volume celebrates the five decades of the impact of Anderson localization on modern physics. In addition to the historical perspective on its origin, it provides a comprehensive description of the experimental and theoretical aspects of Anderson localization.
Diffuse Waves In Complex Media
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Author : Jean-Pierre Fouque
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Diffuse Waves In Complex Media written by Jean-Pierre Fouque 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 2012-12-06 with Science categories.
The NATO Advanced Study Institute on Diffuse Waves in Complex Media was held at the "Centre de Physique des Houches" in France from March 17 to 27, 1998. The Schools' scientific content, wave propagation in heterogeneous me dia, has covered many areas of fundamental and applied research. On the one hand, the understanding of wave propagation has considerably improved during the last thirty years. New developments and concepts such as, speckle correlations, weak and strong localization, time reversal, near-field propagation are under active research. On the other hand, wave propagation in random media is now being investigated in many different fields such as applied mathematics, acoustics, optics, atomic physics, geo physics or medical sciences. Each community often uses its own langage to describe the same phenomena. The aim of the School was to gather worldwide specialists to illuminate various aspects of wave propagation in random media. This volume presents fourteen expository articles corresponding to courses and seminars given during the School. They are arranged as follows. The first three articles deal with the phenomena of localization of waves: B. van Tiggelen (p. 1) gives a critical review of the physics of localization, J. Lacroix (p. 61) presents the mathematical theory and A. Klein (p. 73) describes recent results for randomized periodic media.
Random Operators
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Author : Michael Aizenman
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-12-11
Random Operators written by Michael Aizenman 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 2015-12-11 with Mathematics categories.
This book provides an introduction to the mathematical theory of disorder effects on quantum spectra and dynamics. Topics covered range from the basic theory of spectra and dynamics of self-adjoint operators through Anderson localization--presented here via the fractional moment method, up to recent results on resonant delocalization. The subject's multifaceted presentation is organized into seventeen chapters, each focused on either a specific mathematical topic or on a demonstration of the theory's relevance to physics, e.g., its implications for the quantum Hall effect. The mathematical chapters include general relations of quantum spectra and dynamics, ergodicity and its implications, methods for establishing spectral and dynamical localization regimes, applications and properties of the Green function, its relation to the eigenfunction correlator, fractional moments of Herglotz-Pick functions, the phase diagram for tree graph operators, resonant delocalization, the spectral statistics conjecture, and related results. The text incorporates notes from courses that were presented at the authors' respective institutions and attended by graduate students and postdoctoral researchers.