Existence Of The Thermodynamic Limit And Asymptotic Behavior Of Some Irreversible Quantum Dynamical Systems
Download Existence Of The Thermodynamic Limit And Asymptotic Behavior Of Some Irreversible Quantum Dynamical Systems full books in PDF, epub, and Kindle. Read online free Existence Of The Thermodynamic Limit And Asymptotic Behavior Of Some Irreversible Quantum Dynamical Systems ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
| Author | : Anna Vershynina |
| Publisher | : |
| Total Pages | : |
| Release | : 2012 |
| Genre | : |
| ISBN | : 9781267663252 |
This dissertation discusses the properties of two open quantum systems with a general class of irreversible quantum dynamics. First we study Lieb-Robinson bounds in a quantum lattice systems. This bound gives an estimate for the speed of growth of the support of an evolved local observable up to an exponentially small error. In a second model we study the properties of a leaking cavity pumped by a random atomic beam. We begin by describing quantum systems on an infinite lattice with associated finite or infinite dimensional Hilbert space. The generator of the dynamics of this system is of the Lindblad-Kossakowski type and consists of two parts: the Hamiltonian interactions and the dissipative terms. We allow both of them to be time-dependent. This generator satisfies some suitable decay condition in space. We show that the dynamics with a such generator on a finite system is a well-defined quantum dynamics in a sense of a norm-continuous cocycle of unit preserving completely positive maps. Lieb-Robinson bounds for irreversible dynamics were first considered in the classical context and in for a class of quantum lattice systems with finite-range interactions. We extend those results by proving a Lieb-Robinson bound for lattice models with a more general class of quantum dynamics. Then we use Lieb-Robinson bounds for a finite lattice systems to prove the existence of the thermodynamic limit of the dynamics. We show that in a strong limit there exits a strongly continuous cocycle of unit preserving completely positive maps. Which means that the dynamics exists in an infinite system, where Lieb-Robinson bounds also holds. In the second part of the dissertation we consider a system that consists of a beam of two-level atoms that pass one by one through the microwave cavity. The atoms are randomly excited and there is exactly one atom present in the cavity at any given moment. We consider both the ideal and leaky cavity and study the time asymptotic behavior of the state of the cavity. We show that the number of photons increases indefinitely in the case of the ideal cavity. In the case of the leaking cavity the limiting state is independent of the initial state, it is not quasi-free and it is a non-equilibrium steady state. We also compute the associated energy flow.
| Author | : C. Lindblad |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 184 |
| Release | : 2001-11-30 |
| Genre | : Science |
| ISBN | : 9781402003202 |
The problem of deriving irreversible thermodynamics from the re versible microscopic dynamics has been on the agenda of theoreti cal physics for a century and has produced more papers than can be digested by any single scientist. Why add to this too long list with yet another work? The goal is definitely not to give a gen eral review of previous work in this field. My ambition is rather to present an approach differing in some key aspects from the stan dard treatments, and to develop it as far as possible using rather simple mathematical tools (mainly inequalities of various kinds). However, in the course of this work I have used a large number of results and ideas from the existing literature, and the reference list contains contributions from many different lines of research. As a consequence the reader may find the arguments a bit difficult to follow without some previous exposure to this set of problems.
| Author | : Jesus Biel |
| Publisher | : Springer |
| Total Pages | : 492 |
| Release | : 1972 |
| Genre | : Science |
| ISBN | : |
The Sitges International School of Physics is the second one to be held in Spain on the Many Body Problem. The first one took place on Mallorca during the summer 1969. The aim of the school was mainly to direct the interest of professors and students of Spanish Universities tow~rds this concrete field of re search. For this purpose 55 ~specially prepared lectures were given by an eminent collection of lecturers. Besides, a school of this class contri butes to the scientific formation of many students from other countries. Also, in a meeting of this kind, personal contacts are born that favour future co~laboration between scientists. In view of the success of the first two schools, we intend to foster future international meetings on this subject until interest in it is consolidated in Spain. All the lectures given are published here except those of Professor P.C. Martin whose lec tures have previously been published. I would like to thank all those people who helped to make this school a success, and in particular: Prof. J.L. Villar-Palasi, Minister of Educa tion of Spain for sponsoring the school. Dr. R. Diez-Hochleitner, Undersecretary of the Ministry of Education for receiving the project of this school with such enthusiasm. v PREFACE Prof. E.Costa-Novella, Director General of Universities in Spain and Dr. F.Arias-Salgado who showed such interest and patience while assuring the necessary finance would be found for the school.
| Author | : Fabio Benatti |
| Publisher | : Springer |
| Total Pages | : 362 |
| Release | : 2008-01-11 |
| Genre | : Science |
| ISBN | : 3540448748 |
The idea of editing the present volume in the Lecture Notes in Physics series arosewhileorganizingthe“ConferenceonIrreversibleQuantumDynamics”that took place at The Abdus Salam International Center for Theoretical Physics, Trieste, Italy, from July 29 to August 2, 2002. The aim of the Conference was to bring together di?erent groups of - searcherswhoseinterestsandpursuitsinvolveirreversibilityandtimeasymmetry in quantum mechanics. The Conference promoted open and in-depth exchanges of di?erent points of view, concerning both the content and character of qu- tum irreversibility and the methodologies used to study it. The following main themes were addressed: • Theoretical Aspects of Quantum Irreversible Dynamics • Open Quantum Systems and Applications • Foundational Aspects of Irreversible Quantum Dynamics • Asymmetric Time Evolution and Resonances Eachthemewasreviewedbyanexpertinthe?eld,accompaniedbymorespeci?c, research-like shorter talks. The whole topic of quantum irreversibility in all its manifold aspects has always raised a lot of interest, starting with the description of unstable systems in quantum mechanics and the issue of quantum measurement. Further, in - cent years a boost of activity concerning noise, dissipation and open systems has been prompted by the fast developing ?eld of quantum communication and information theory. These considerations motivated the editors to put together a volume that tries to summarize the present day status of the research in the ?eld, with the aim of providing the reader with an accessible and exhaustive introduction to it.
| Author | : B. Fain |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 222 |
| Release | : 2006-04-11 |
| Genre | : Science |
| ISBN | : 0306471280 |
The problem of irreversibility is ubiquitous in physics and chemistry. The present book attempts to present a unified theoretical and conceptual framework for the description of various irreversible phenomena in quantum mechanics. In a sense, this book supplements conventional textbooks on quantum mechanics by including the theory of irreversibilities. However, the content and style of this book are more appropriate for a monograph than a textbook. We have tried to arrange the material so that, as far as possible, the reader need not continually refer elsewhere. The references to the literature make no pretense of completeness. The book is by no means a survey of present theoretical work. We have tried to highlight the basic principles and their results, while the attention has been mainly paid to the problems in which the author himself has been involved. The book as a whole is designed for the reader with knowledge of theoretical physics (especially quantum mechanics) at university level. This book is based on the courses of lectures given at the Chemistry Department of Tel-Aviv University.
| Author | : Wassim M. Haddad |
| Publisher | : Princeton University Press |
| Total Pages | : 744 |
| Release | : 2019-06-04 |
| Genre | : Mathematics |
| ISBN | : 0691190143 |
A brand-new conceptual look at dynamical thermodynamics This book merges the two universalisms of thermodynamics and dynamical systems theory in a single compendium, with the latter providing an ideal language for the former, to develop a new and unique framework for dynamical thermodynamics. In particular, the book uses system-theoretic ideas to bring coherence, clarity, and precision to an important and poorly understood classical area of science. The dynamical systems formalism captures all of the key aspects of thermodynamics, including its fundamental laws, while providing a mathematically rigorous formulation for thermodynamical systems out of equilibrium by unifying the theory of mechanics with that of classical thermodynamics. This book includes topics on nonequilibrium irreversible thermodynamics, Boltzmann thermodynamics, mass-action kinetics and chemical reactions, finite-time thermodynamics, thermodynamic critical phenomena with continuous and discontinuous phase transitions, information theory, continuum and stochastic thermodynamics, and relativistic thermodynamics. A Dynamical Systems Theory of Thermodynamics develops a postmodern theory of thermodynamics as part of mathematical dynamical systems theory. The book establishes a clear nexus between thermodynamic irreversibility, the second law of thermodynamics, and the arrow of time to further unify discreteness and continuity, indeterminism and determinism, and quantum mechanics and general relativity in the pursuit of understanding the most fundamental property of the universe—the entropic arrow of time.
| Author | : Vasily E. Tarasov |
| Publisher | : MDPI |
| Total Pages | : 278 |
| Release | : 2020-06-03 |
| Genre | : Business & Economics |
| ISBN | : 303936118X |
This book is devoted to the application of fractional calculus in economics to describe processes with memory and non-locality. Fractional calculus is a branch of mathematics that studies the properties of differential and integral operators that are characterized by real or complex orders. Fractional calculus methods are powerful tools for describing the processes and systems with memory and nonlocality. Recently, fractional integro-differential equations have been used to describe a wide class of economical processes with power law memory and spatial nonlocality. Generalizations of basic economic concepts and notions the economic processes with memory were proposed. New mathematical models with continuous time are proposed to describe economic dynamics with long memory. This book is a collection of articles reflecting the latest mathematical and conceptual developments in mathematical economics with memory and non-locality based on applications of fractional calculus.
| Author | : Stanislaw Sieniutycz |
| Publisher | : Elsevier |
| Total Pages | : 740 |
| Release | : 2016-05-20 |
| Genre | : Technology & Engineering |
| ISBN | : 0128093390 |
Thermodynamic Approaches in Engineering Systems responds to the need for a synthesizing volume that throws light upon the extensive field of thermodynamics from a chemical engineering perspective that applies basic ideas and key results from the field to chemical engineering problems. This book outlines and interprets the most valuable achievements in applied non-equilibrium thermodynamics obtained within the recent fifty years. It synthesizes nontrivial achievements of thermodynamics in important branches of chemical and biochemical engineering. Readers will gain an update on what has been achieved, what new research problems could be stated, and what kind of further studies should be developed within specialized research. Presents clearly structured chapters beginning with an introduction, elaboration of the process, and results summarized in a conclusion Written by a first-class expert in the field of advanced methods in thermodynamics Provides a synthesis of recent thermodynamic developments in practical systems Presents very elaborate literature discussions from the past fifty years
| Author | : Annick Lesne |
| Publisher | : Wiley |
| Total Pages | : 0 |
| Release | : 1998-05-08 |
| Genre | : Mathematics |
| ISBN | : 9780471966890 |
Originally conceived some thirty years ago in the context ofquantum electrodynamics, renormalization methods have progressivelydeveloped into an indispensable analytical tool used in widelyvarying domains of physics and applied mathematics, such as * phase transitions and critical phenomena * dynamical systems and chaos * developed turbulence * fractal structures and complex systems * percolation * polymer physics * diffusion in disordered media * measure theory and stochastic processes. By explaining the fundamental principles of renormalization theorysuch as scale invariance and universality which lie behind all thetechnical variations, this book aims to guide the reader to a moreunified understanding of today s physics. The book is based on avery accessible main text, supplemented by several more specializedsections; it is intended for graduate students and for researcherswho are seeking an introduction to a new area of electrodynamics ora general overview of the physical phenomena to whichrenormalization methods are applied.
| Author | : Stuart A. Rice |
| Publisher | : John Wiley & Sons |
| Total Pages | : 346 |
| Release | : 2007-04-10 |
| Genre | : Science |
| ISBN | : 0470121904 |
This series provides the chemical physics field with a forum for critical, authoritative evaluations of advances in every area of the discipline. This stand-alone special topics volume reports recent advances in electron-transfer research with significant, up-to-date chapters by internationally recognized researchers.
