Hydrodynamic Scales Of Integrable Many Body Systems

Author : Herbert Spohn
Publisher : World Scientific
Page : 255 pages
File Size : 40,9 Mb
Release : 2024-02-27
Category : Science
ISBN : 9789811283543

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Hydrodynamic Scales Of Integrable Many-body Systems by Herbert Spohn Pdf

This book provides a broad introduction to integrable systems with many degrees of freedom. Within a much larger orbit, discussed are models such as the classical Toda lattice, Calogero fluid, and Ablowitz-Ladik discretized nonlinear Schrödinger equation. On the quantum mechanical side, featured are the Lieb-Liniger delta-Bose gas and the quantum Toda lattice. As a genuinely novel twist, the study deals with random initial data described by generalized Gibbs ensembles with parameters of slow spatial variation. This is the hydrodynamic scale, in spirit similar to the ballistic Euler scale of nonintegrable simple fluids. While integrable microscopic particle models are very diverse, the central theme of this book is to elucidate their structural similarity on hydrodynamic scales.

Author : Kuzemsky Alexander Leonidovich
Publisher : World Scientific
Page : 1260 pages
File Size : 49,7 Mb
Release : 2017-02-24
Category : Science
ISBN : 9789813145658

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Statistical Mechanics And The Physics Of Many-particle Model Systems by Kuzemsky Alexander Leonidovich Pdf

The book is devoted to the study of the correlation effects in many-particle systems. It presents the advanced methods of quantum statistical mechanics (equilibrium and nonequilibrium), and shows their effectiveness and operational ability in applications to problems of quantum solid-state theory, quantum theory of magnetism and the kinetic theory. The book includes description of the fundamental concepts and techniques of analysis following the approach of N N Bogoliubov's school, including recent developments. It provides an overview that introduces the main notions of quantum many-particle physics with the emphasis on concepts and models. This book combines the features of textbook and research monograph. For many topics the aim is to start from the beginning and to guide the reader to the threshold of advanced researches. Many chapters include also additional information and discuss many complex research areas which are not often discussed in other places. The book is useful for established researchers to organize and present the advanced material disseminated in the literature. The book contains also an extensive bibliography. The book serves undergraduate, graduate and postgraduate students, as well as researchers who have had prior experience with the subject matter at a more elementary level or have used other many-particle techniques.

Author : D. Christian Glattli,Marc Sanquer,J. Thanh Van Tran
Publisher : Unknown
Page : 542 pages
File Size : 46,5 Mb
Release : 2000
Category : Mesoscopic phenomena (Physics)
ISBN : UCSD:31822031061625

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Quantum Physics at Mesoscopic Scale by D. Christian Glattli,Marc Sanquer,J. Thanh Van Tran Pdf

Author : V. E. Korepin,Vladimir E. Korepin,N. M. Bogoliubov,A. G. Izergin
Publisher : Cambridge University Press
Page : 582 pages
File Size : 53,6 Mb
Release : 1997-03-06
Category : Mathematics
ISBN : 0521586461

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Quantum Inverse Scattering Method and Correlation Functions by V. E. Korepin,Vladimir E. Korepin,N. M. Bogoliubov,A. G. Izergin Pdf

The quantum inverse scattering method is a means of finding exact solutions of two-dimensional models in quantum field theory and statistical physics (such as the sine-Go rdon equation or the quantum non-linear Schrödinger equation). These models are the subject of much attention amongst physicists and mathematicians.The present work is an introduction to this important and exciting area. It consists of four parts. The first deals with the Bethe ansatz and calculation of physical quantities. The authors then tackle the theory of the quantum inverse scattering method before applying it in the second half of the book to the calculation of correlation functions. This is one of the most important applications of the method and the authors have made significant contributions to the area. Here they describe some of the most recent and general approaches and include some new results.The book will be essential reading for all mathematical physicists working in field theory and statistical physics.

Author : Cédric Bernardin,François Golse,Patrícia Gonçalves,Valeria Ricci,Ana Jacinta Soares
Publisher : Springer Nature
Page : 400 pages
File Size : 42,8 Mb
Release : 2021-05-30
Category : Mathematics
ISBN : 9783030697846

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From Particle Systems to Partial Differential Equations by Cédric Bernardin,François Golse,Patrícia Gonçalves,Valeria Ricci,Ana Jacinta Soares Pdf

This book includes the joint proceedings of the International Conference on Particle Systems and PDEs VI, VII and VIII. Particle Systems and PDEs VI was held in Nice, France, in November/December 2017, Particle Systems and PDEs VII was held in Palermo, Italy, in November 2018, and Particle Systems and PDEs VIII was held in Lisbon, Portugal, in December 2019. Most of the papers are dealing with mathematical problems motivated by different applications in physics, engineering, economics, chemistry and biology. They illustrate methods and topics in the study of particle systems and PDEs and their relation. The book is recommended to probabilists, analysts and to those mathematicians in general, whose work focuses on topics in mathematical physics, stochastic processes and differential equations, as well as to those physicists who work in statistical mechanics and kinetic theory.

Author : Herbert Spohn
Publisher : Springer Science & Business Media
Page : 346 pages
File Size : 40,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642843716

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Large Scale Dynamics of Interacting Particles by Herbert Spohn Pdf

This book deals with one of the fundamental problems of nonequilibrium statistical mechanics: the explanation of large-scale dynamics (evolution differential equations) from models of a very large number of interacting particles. This book addresses both researchers and students. Much of the material presented has never been published in book-form before.

Author : W.G. Hoover
Publisher : Elsevier
Page : 330 pages
File Size : 40,7 Mb
Release : 2012-12-02
Category : Science
ISBN : 9780444596598

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Computational Statistical Mechanics by W.G. Hoover Pdf

Computational Statistical Mechanics describes the use of fast computers to simulate the equilibrium and nonequilibrium properties of gases, liquids, and solids at, and away from equilibrium. The underlying theory is developed from basic principles and illustrated by applying it to the simplest possible examples. Thermodynamics, based on the ideal gas thermometer, is related to Gibb's statistical mechanics through the use of Nosé-Hoover heat reservoirs. These reservoirs use integral feedback to control temperature. The same approach is carried through to the simulation and analysis of nonequilibrium mass, momentum, and energy flows. Such a unified approach makes possible consistent mechanical definitions of temperature, stress, and heat flux which lead to a microscopic demonstration of the Second Law of Thermodynamics directly from mechanics. The intimate connection linking Lyapunov-unstable microscopic motions to macroscopic dissipative flows through multifractal phase-space structures is illustrated with many examples from the recent literature. The book is well-suited for undergraduate courses in advanced thermodynamics, statistical mechanic and transport theory, and graduate courses in physics and chemistry.

Author : Adam Smith
Publisher : Springer
Page : 143 pages
File Size : 41,5 Mb
Release : 2019-07-01
Category : Science
ISBN : 9783030208516

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Disorder-Free Localization by Adam Smith Pdf

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.

Author : Andreas Schadschneider,Debashish Chowdhury,Katsuhiro Nishinari
Publisher : Elsevier
Page : 585 pages
File Size : 51,6 Mb
Release : 2010-10-01
Category : Science
ISBN : 9780080560526

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Stochastic Transport in Complex Systems by Andreas Schadschneider,Debashish Chowdhury,Katsuhiro Nishinari Pdf

The first part of the book provides a pedagogical introduction to the physics of complex systems driven far from equilibrium. In this part we discuss the basic concepts and theoretical techniques which are commonly used to study classical stochastic transport in systems of interacting driven particles. The analytical techniques include mean-field theories, matrix product ansatz, renormalization group, etc. and the numerical methods are mostly based on computer simulations. In the second part of the book these concepts and techniques are applied not only to vehicular traffic but also to transport and traffic-like phenomena in living systems ranging from collective movements of social insects (for example, ants) on trails to intracellular molecular motor transport. These demonstrate the conceptual unity of the fundamental principles underlying the apparent diversity of the systems and the utility of the theoretical toolbox of non-equilibrium statistical mechanics in interdisciplinary research far beyond the traditional disciplinary boundaries of physics. Leading industry experts provide a broad overview of the interdisciplinary nature of physics Presents unified descriptions of intracellular, ant, and vehicular traffic from a physics point of view Applies theoretical methods in practical everyday situations Reference and guide for physicists, engineers and graduate students

Author : P. A. Davidson
Publisher : Cambridge University Press
Page : 456 pages
File Size : 48,6 Mb
Release : 2001-03-05
Category : Mathematics
ISBN : 0521794870

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An Introduction to Magnetohydrodynamics by P. A. Davidson Pdf

This book is an introductory text on magnetohydrodynamics (MHD) - the study of the interaction of magnetic fields and conducting fluids.

Author : Abolfazl Bayat,Sougato Bose,Henrik Johannesson
Publisher : Springer Nature
Page : 549 pages
File Size : 52,7 Mb
Release : 2022-09-26
Category : Science
ISBN : 9783031039980

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Entanglement in Spin Chains by Abolfazl Bayat,Sougato Bose,Henrik Johannesson Pdf

This book covers recent developments in the understanding, quantification, and exploitation of entanglement in spin chain models from both condensed matter and quantum information perspectives. Spin chain models are at the foundation of condensed matter physics and quantum information technologies and elucidate many fundamental phenomena such as information scrambling, quantum phase transitions, and many-body localization. Moreover, many quantum materials and emerging quantum devices are well described by spin chains. Comprising accessible, self-contained chapters written by leading researchers, this book is essential reading for graduate students and researchers in quantum materials and quantum information. The coverage is comprehensive, from the fundamental entanglement aspects of quantum criticality, non-equilibrium dynamics, classical and quantum simulation of spin chains through to their experimental realizations, and beyond into machine learning applications.

Author : Bilen Emek Abali,Ivan Giorgio
Publisher : Springer Nature
Page : 491 pages
File Size : 44,6 Mb
Release : 2020-07-18
Category : Science
ISBN : 9783030504601

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Developments and Novel Approaches in Nonlinear Solid Body Mechanics by Bilen Emek Abali,Ivan Giorgio Pdf

This book features selected manuscripts presented at ICoNSoM 2019, exploring cutting-edge methods for developing novel models in nonlinear solid mechanics. Innovative methods like additive manufacturing—for example, 3D printing— and miniaturization mean that engineers need more accurate techniques for modeling solid body mechanics. The book focuses on the formulation of continuum and discrete models for complex materials and systems, particularly the design of metamaterials.

Author : Nick Proukakis
Publisher : World Scientific
Page : 579 pages
File Size : 46,8 Mb
Release : 2013
Category : Science
ISBN : 9781848168121

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Quantum Gases by Nick Proukakis Pdf

This volume provides a broad overview of the principal theoretical techniques applied to non-equilibrium and finite temperature quantum gases. Covering Bose-Einstein condensates, degenerate Fermi gases, and the more recently realised exciton-polariton condensates, it fills a gap by linking between different methods with origins in condensed matter physics, quantum field theory, quantum optics, atomic physics, and statistical mechanics.

Author : Édouard Brezin,Vladimir Kazakov,Didina Serban,Paul Wiegmann,Anton Zabrodin
Publisher : Springer Science & Business Media
Page : 519 pages
File Size : 40,7 Mb
Release : 2006-07-03
Category : Science
ISBN : 9781402045318

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Applications of Random Matrices in Physics by Édouard Brezin,Vladimir Kazakov,Didina Serban,Paul Wiegmann,Anton Zabrodin Pdf

Random matrices are widely and successfully used in physics for almost 60-70 years, beginning with the works of Dyson and Wigner. Although it is an old subject, it is constantly developing into new areas of physics and mathematics. It constitutes now a part of the general culture of a theoretical physicist. Mathematical methods inspired by random matrix theory become more powerful, sophisticated and enjoy rapidly growing applications in physics. Recent examples include the calculation of universal correlations in the mesoscopic system, new applications in disordered and quantum chaotic systems, in combinatorial and growth models, as well as the recent breakthrough, due to the matrix models, in two dimensional gravity and string theory and the non-abelian gauge theories. The book consists of the lectures of the leading specialists and covers rather systematically many of these topics. It can be useful to the specialists in various subjects using random matrices, from PhD students to confirmed scientists.

Author : Annick LESNE,Michel Laguës
Publisher : Springer Science & Business Media
Page : 406 pages
File Size : 48,9 Mb
Release : 2011-11-04
Category : Science
ISBN : 9783642151231

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Scale Invariance by Annick LESNE,Michel Laguës Pdf

During a century, from the Van der Waals mean field description (1874) of gases to the introduction of renormalization group (RG techniques 1970), thermodynamics and statistical physics were just unable to account for the incredible universality which was observed in numerous critical phenomena. The great success of RG techniques is not only to solve perfectly this challenge of critical behaviour in thermal transitions but to introduce extremely useful tools in a wide field of daily situations where a system exhibits scale invariance. The introduction of scaling, scale invariance and universality concepts has been a significant turn in modern physics and more generally in natural sciences. Since then, a new "physics of scaling laws and critical exponents", rooted in scaling approaches, allows quantitative descriptions of numerous phenomena, ranging from phase transitions to earthquakes, polymer conformations, heartbeat rhythm, diffusion, interface growth and roughening, DNA sequence, dynamical systems, chaos and turbulence. The chapters are jointly written by an experimentalist and a theorist. This book aims at a pedagogical overview, offering to the students and researchers a thorough conceptual background and a simple account of a wide range of applications. It presents a complete tour of both the formal advances and experimental results associated with the notion of scaling, in physics, chemistry and biology.