C Algebras And Mathematical Foundations Of Quantum Statistical Mechanics

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C*-Algebras and Mathematical Foundations of Quantum Statistical Mechanics

Jean-Bernard Bru,Walter Alberto de Siqueira Pedra
C Algebras and Mathematical Foundations of Quantum Statistical Mechanics Book PDF

Author : Jean-Bernard Bru,Walter Alberto de Siqueira Pedra
Publisher : Springer Nature
Page : 497 pages
File Size : 50,5 Mb
Release : 2023-06-16
Category : Science
ISBN : 9783031289491

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C*-Algebras and Mathematical Foundations of Quantum Statistical Mechanics by Jean-Bernard Bru,Walter Alberto de Siqueira Pedra Pdf

This textbook provides a comprehensive introduction to the mathematical foundations of quantum statistical physics. It presents a conceptually profound yet technically accessible path to the C*-algebraic approach to quantum statistical mechanics, demonstrating how key aspects of thermodynamic equilibrium can be derived as simple corollaries of classical results in convex analysis. Using C*-algebras as examples of ordered vector spaces, this book makes various aspects of C*-algebras and their applications to the mathematical foundations of quantum theory much clearer from both mathematical and physical perspectives. It begins with the simple case of Gibbs states on matrix algebras and gradually progresses to a more general setting that considers the thermodynamic equilibrium of infinitely extended quantum systems. The book also illustrates how first-order phase transitions and spontaneous symmetry breaking can occur, in contrast to the finite-dimensional situation. One of the unique features of this book is its thorough and clear treatment of the theory of equilibrium states of quantum mean-field models. This work is self-contained and requires only a modest background in analysis, topology, and functional analysis from the reader. It is suitable for both mathematicians and physicists with a specific interest in quantum statistical physics.

Mathematical Foundations of Quantum Statistical Mechanics

D.Y. Petrina
Mathematical Foundations of Quantum Statistical Mechanics Book PDF

Author : D.Y. Petrina
Publisher : Springer Science & Business Media
Page : 460 pages
File Size : 48,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789401101851

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Mathematical Foundations of Quantum Statistical Mechanics by D.Y. Petrina Pdf

This monograph is devoted to quantum statistical mechanics. It can be regarded as a continuation of the book "Mathematical Foundations of Classical Statistical Mechanics. Continuous Systems" (Gordon & Breach SP, 1989) written together with my colleagues V. I. Gerasimenko and P. V. Malyshev. Taken together, these books give a complete pre sentation of the statistical mechanics of continuous systems, both quantum and classical, from the common point of view. Both books have similar contents. They deal with the investigation of states of in finite systems, which are described by infinite sequences of statistical operators (reduced density matrices) or Green's functions in the quantum case and by infinite sequences of distribution functions in the classical case. The equations of state and their solutions are the main object of investigation in these books. For infinite systems, the solutions of the equations of state are constructed by using the thermodynamic limit procedure, accord ing to which we first find a solution for a system of finitely many particles and then let the number of particles and the volume of a region tend to infinity keeping the density of particles constant. However, the style of presentation in these books is quite different.

Operator Algebras and Quantum Statistical Mechanics 1

Ola Bratteli,Derek William Robinson
Operator Algebras and Quantum Statistical Mechanics 1 Book PDF

Author : Ola Bratteli,Derek William Robinson
Publisher : Springer Science & Business Media
Page : 510 pages
File Size : 52,7 Mb
Release : 2013-03-14
Category : Technology & Engineering
ISBN : 9783662025208

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Operator Algebras and Quantum Statistical Mechanics 1 by Ola Bratteli,Derek William Robinson Pdf

In this book we describe the elementary theory of operator algebras and parts of the advanced theory which are of relevance, or potentially of relevance, to mathematical physics. Subsequently we describe various applications to quantum statistical mechanics. At the outset of this project we intended to cover this material in one volume but in the course of develop ment it was realized that this would entail the omission ofvarious interesting topics or details. Consequently the book was split into two volumes, the first devoted to the general theory of operator algebras and the second to the applications. This splitting into theory and applications is conventional but somewhat arbitrary. In the last 15-20 years mathematical physicists have realized the importance of operator algebras and their states and automorphisms for problems of field theory and statistical mechanics. But the theory of 20 years aga was largely developed for the analysis of group representations and it was inadequate for many physical applications. Thus after a short honey moon period in which the new found tools of the extant theory were applied to the most amenable problems a longer and more interesting period ensued in which mathematical physicists were forced to redevelop the theory in relevant directions. New concepts were introduced, e. g. asymptotic abelian ness and KMS states, new techniques applied, e. g. the Choquet theory of barycentric decomposition for states, and new structural results obtained, e. g. the existence of a continuum of nonisomorphic type-three factors.

Operator Algebras and Quantum Statistical Mechanics

Ola Bratteli,Derek William Robinson
Operator Algebras and Quantum Statistical Mechanics Book PDF

Author : Ola Bratteli,Derek William Robinson
Publisher : Springer Science & Business Media
Page : 503 pages
File Size : 46,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783662023136

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Operator Algebras and Quantum Statistical Mechanics by Ola Bratteli,Derek William Robinson Pdf

In this book we describe the elementary theory of operator algebras and parts of the advanced theory which are of relevance, or potentially of relevance, to mathematical physics. Subsequently we describe various applications to quantum statistical mechanics. At the outset of this project we intended to cover this material in one volume but in the course of develop ment it was realized that this would entail the omission of various interesting topics or details. Consequently the book was split into two volumes, the first devoted to the general theory of operator algebras and the second to the applications. This splitting into theory and applications is conventional but somewhat arbitrary. In the last 15-20 years mathematical physicists have realized the importance of operator algebras and their states and automorphisms for problems offield theory and statistical mechanics. But the theory of 20 years ago was largely developed for the analysis of group representations and it was inadequate for many physical applications. Thus after a short honey moon period in which the new found tools of the extant theory were applied to the most amenable problems a longer and more interesting period ensued in which mathematical physicists were forced to redevelop the theory in relevant directions. New concepts were introduced, e. g. asymptotic abelian ness and KMS states, new techniques applied, e. g. the Choquet theory of barycentric decomposition for states, and new structural results obtained, e. g. the existence of a continuum of nonisomorphic type-three factors.

Operator Algebras and Quantum Statistical Mechanics

Ola Bratteli,Derek William Robinson
Operator Algebras and Quantum Statistical Mechanics Book PDF

Author : Ola Bratteli,Derek William Robinson
Publisher : Springer Science & Business Media
Page : 525 pages
File Size : 50,7 Mb
Release : 2013-06-29
Category : Science
ISBN : 9783662034446

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Operator Algebras and Quantum Statistical Mechanics by Ola Bratteli,Derek William Robinson Pdf

For almost two decades, this has been the classical textbook on applications of operator algebra theory to quantum statistical physics. Major changes in the new edition relate to Bose-Einstein condensation, the dynamics of the X-Y model and questions on phase transitions.

Mathematical Foundations of Statistical Mechanics

Aleksandr I?Akovlevich Khinchin
Mathematical Foundations of Statistical Mechanics Book PDF

Author : Aleksandr I?Akovlevich Khinchin
Publisher : Courier Corporation
Page : 212 pages
File Size : 46,7 Mb
Release : 1949-01-01
Category : Mathematics
ISBN : 0486601471

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Mathematical Foundations of Statistical Mechanics by Aleksandr I?Akovlevich Khinchin Pdf

Phase space, ergodic problems, central limit theorem, dispersion and distribution of sum functions. Chapters include Geometry and Kinematics of the Phase Space; Ergodic Problem; Reduction to the Problem of the Theory of Probability; Application of the Central Limit Theorem; Ideal Monatomic Gas; The Foundation of Thermodynamics; and more.

Operator Algebras and Quantum Statistical Mechanics

Ola Bratteli,Derek William Robinson
Operator Algebras and Quantum Statistical Mechanics Book PDF

Author : Ola Bratteli,Derek William Robinson
Publisher : Springer Science & Business Media
Page : 536 pages
File Size : 42,7 Mb
Release : 2003-01-09
Category : Science
ISBN : 3540614435

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Operator Algebras and Quantum Statistical Mechanics by Ola Bratteli,Derek William Robinson Pdf

For almost two decades, this has been the classical textbook on applications of operator algebra theory to quantum statistical physics. Major changes in the new edition relate to Bose-Einstein condensation, the dynamics of the X-Y model and questions on phase transitions.

Operator Algebras and Quantum Statistical Mechanics 1

Ola Bratteli,Derek William Robinson
Operator Algebras and Quantum Statistical Mechanics 1 Book PDF

Author : Ola Bratteli,Derek William Robinson
Publisher : Springer
Page : 506 pages
File Size : 52,5 Mb
Release : 2010-10-19
Category : Mathematics
ISBN : 3642057365

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Operator Algebras and Quantum Statistical Mechanics 1 by Ola Bratteli,Derek William Robinson Pdf

In this book we describe the elementary theory of operator algebras and parts of the advanced theory which are of relevance, or potentially of relevance, to mathematical physics. Subsequently we describe various applications to quantum statistical mechanics. At the outset of this project we intended to cover this material in one volume but in the course of develop ment it was realized that this would entail the omission ofvarious interesting topics or details. Consequently the book was split into two volumes, the first devoted to the general theory of operator algebras and the second to the applications. This splitting into theory and applications is conventional but somewhat arbitrary. In the last 15-20 years mathematical physicists have realized the importance of operator algebras and their states and automorphisms for problems of field theory and statistical mechanics. But the theory of 20 years aga was largely developed for the analysis of group representations and it was inadequate for many physical applications. Thus after a short honey moon period in which the new found tools of the extant theory were applied to the most amenable problems a longer and more interesting period ensued in which mathematical physicists were forced to redevelop the theory in relevant directions. New concepts were introduced, e. g. asymptotic abelian ness and KMS states, new techniques applied, e. g. the Choquet theory of barycentric decomposition for states, and new structural results obtained, e. g. the existence of a continuum of nonisomorphic type-three factors.

Operator Algebras and Quantum Statistical Mechanics II

Ola Bratteli,Derek William Robinson
Operator Algebras and Quantum Statistical Mechanics II Book PDF

Author : Ola Bratteli,Derek William Robinson
Publisher : Springer Science & Business Media
Page : 508 pages
File Size : 48,9 Mb
Release : 2013-04-17
Category : Science
ISBN : 9783662090893

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Operator Algebras and Quantum Statistical Mechanics II by Ola Bratteli,Derek William Robinson Pdf

For almost two decades, this has been the classical textbook on applications of operator algebra theory to quantum statistical physics. Major changes in the new edition relate to Bose-Einstein condensation, the dynamics of the X-Y model and questions on phase transitions.

Operator Algebras and Quantum Statistical Mechanics

Ola Bratteli,Derek W. Robinson
Operator Algebras and Quantum Statistical Mechanics Book PDF

Author : Ola Bratteli,Derek W. Robinson
Publisher : Springer Science & Business Media
Page : 544 pages
File Size : 53,7 Mb
Release : 1979
Category : Mathematics
ISBN : UOM:39015014241957

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Operator Algebras and Quantum Statistical Mechanics by Ola Bratteli,Derek W. Robinson Pdf

For almost two decades, this has been the classical textbook on applications of operator algebra theory to quantum statistical physics. Major changes in the new edition relate to Bose-Einstein condensation, the dynamics of the X-Y model and questions on phase transitions.

Mathematical Foundations of Quantum Statistics

A. Y. Khinchin
Mathematical Foundations of Quantum Statistics Book PDF

Author : A. Y. Khinchin
Publisher : Courier Corporation
Page : 256 pages
File Size : 44,8 Mb
Release : 2013-02-21
Category : Mathematics
ISBN : 9780486167657

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Mathematical Foundations of Quantum Statistics by A. Y. Khinchin Pdf

A coherent, well-organized look at the basis of quantum statistics’ computational methods, the determination of the mean values of occupation numbers, the foundations of the statistics of photons and material particles, thermodynamics.

Lectures on the Mathematics of Quantum Mechanics I

Gianfausto Dell'Antonio
Lectures on the Mathematics of Quantum Mechanics I Book PDF

Author : Gianfausto Dell'Antonio
Publisher : Springer
Page : 459 pages
File Size : 48,7 Mb
Release : 2015-05-25
Category : Science
ISBN : 9789462391185

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Lectures on the Mathematics of Quantum Mechanics I by Gianfausto Dell'Antonio Pdf

The first volume (General Theory) differs from most textbooks as it emphasizes the mathematical structure and mathematical rigor, while being adapted to the teaching the first semester of an advanced course in Quantum Mechanics (the content of the book are the lectures of courses actually delivered.). It differs also from the very few texts in Quantum Mechanics that give emphasis to the mathematical aspects because this book, being written as Lecture Notes, has the structure of lectures delivered in a course, namely introduction of the problem, outline of the relevant points, mathematical tools needed, theorems, proofs. This makes this book particularly useful for self-study and for instructors in the preparation of a second course in Quantum Mechanics (after a first basic course). With some minor additions it can be used also as a basis of a first course in Quantum Mechanics for students in mathematics curricula. The second part (Selected Topics) are lecture notes of a more advanced course aimed at giving the basic notions necessary to do research in several areas of mathematical physics connected with quantum mechanics, from solid state to singular interactions, many body theory, semi-classical analysis, quantum statistical mechanics. The structure of this book is suitable for a second-semester course, in which the lectures are meant to provide, in addition to theorems and proofs, an overview of a more specific subject and hints to the direction of research. In this respect and for the width of subjects this second volume differs from other monographs on Quantum Mechanics. The second volume can be useful for students who want to have a basic preparation for doing research and for instructors who may want to use it as a basis for the presentation of selected topics.

Mathematical Foundations of Quantum Theory

A. R. Marlow
Mathematical Foundations of Quantum Theory Book PDF

Author : A. R. Marlow
Publisher : Unknown
Page : 392 pages
File Size : 55,7 Mb
Release : 1978
Category : Science
ISBN : UOM:39015017151930

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Mathematical Foundations of Quantum Theory by A. R. Marlow Pdf

Mathematical Foundations of Quantum Theory is a collection of papers presented at the 1977 conference on the Mathematical Foundations of Quantum Theory, held in New Orleans. The contributors present their topics from a wide variety of backgrounds and specialization, but all shared a common interest in answering quantum issues. Organized into 20 chapters, this book's opening chapters establish a sound mathematical basis for quantum theory and a mode of observation in the double slit experiment. This book then describes the Lorentz particle system and other mathematical structures with which fun ...

Spectral Theory and Quantum Mechanics

Valter Moretti
Spectral Theory and Quantum Mechanics Book PDF

Author : Valter Moretti
Publisher : Springer
Page : 950 pages
File Size : 49,5 Mb
Release : 2018-01-30
Category : Mathematics
ISBN : 9783319707068

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Spectral Theory and Quantum Mechanics by Valter Moretti Pdf

This book discusses the mathematical foundations of quantum theories. It offers an introductory text on linear functional analysis with a focus on Hilbert spaces, highlighting the spectral theory features that are relevant in physics. After exploring physical phenomenology, it then turns its attention to the formal and logical aspects of the theory. Further, this Second Edition collects in one volume a number of useful rigorous results on the mathematical structure of quantum mechanics focusing in particular on von Neumann algebras, Superselection rules, the various notions of Quantum Symmetry and Symmetry Groups, and including a number of fundamental results on the algebraic formulation of quantum theories. Intended for Master's and PhD students, both in physics and mathematics, the material is designed to be self-contained: it includes a summary of point-set topology and abstract measure theory, together with an appendix on differential geometry. The book also benefits established researchers by organizing and presenting the profusion of advanced material disseminated in the literature. Most chapters are accompanied by exercises, many of which are solved explicitly."

Mathematical Foundations of Classical Statistical Mechanics

D.Ya. Petrina,V.I. Gerasimenko,P V Malyshev
Mathematical Foundations of Classical Statistical Mechanics Book PDF

Author : D.Ya. Petrina,V.I. Gerasimenko,P V Malyshev
Publisher : CRC Press
Page : 352 pages
File Size : 48,8 Mb
Release : 2002-04-11
Category : Mathematics
ISBN : 9781482265026

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Mathematical Foundations of Classical Statistical Mechanics by D.Ya. Petrina,V.I. Gerasimenko,P V Malyshev Pdf

This monograph considers systems of infinite number of particles, in particular the justification of the procedure of thermodynamic limit transition. The authors discuss the equilibrium and non-equilibrium states of infinite classical statistical systems. Those states are defined in terms of stationary and nonstationary solutions to the Bogolyubov