Mathematical Foundations Of Statistical Mechanics

Mathematical Foundations of Statistical Mechanics PDF
Author: Aleksandr I?Akovlevich Khinchin
Publisher: Courier Corporation
ISBN: 9780486601472
Size: 28.94 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 179
View: 6191

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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.

Mathematical Foundations Of Classical Statistical Mechanics

Mathematical Foundations of Classical Statistical Mechanics PDF
Author: D.Ya. Petrina
Publisher: CRC Press
ISBN: 9780415273541
Size: 59.72 MB
Format: PDF, ePub
Category : Science
Languages : en
Pages : 352
View: 1064

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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 equations for the sequences of correlation functions in the thermodynamic limit. This is the first detailed investigation of the thermodynamic limit for non-equilibrium systems and of the states of infinite systems in the cases of both canonical and grand canonical ensembles, for which the thermodynamic equivalence is proved. A comprehensive survey of results is also included; it concerns the properties of correlation functions for infinite systems and the corresponding equations. For this new edition, the authors have made changes to reflect the development of theory in the last ten years. They have also simplified certain sections, presenting them more systematically, and greatly increased the number of references. The book is aimed at theoretical physicists and mathematicians and will also be of use to students and postgraduate students in the field.

Mathematical Foundations Of Statistical Mechanics

Mathematical Foundations of Statistical Mechanics PDF
Author: A. Ya. Khinchin
Publisher: Courier Corporation
ISBN: 0486138739
Size: 49.32 MB
Format: PDF, Docs
Category : Science
Languages : en
Pages : 179
View: 1305

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Phase space, ergodic problems, central limit theorem, dispersion and distribution of sum functions. Chapters include Geometry and Kinematics of the Phase Space; Reduction to the Problem of the Theory of Probability; and more.

Mathematical Foundations Of Quantum Mechanics

Mathematical Foundations of Quantum Mechanics PDF
Author: John von Neumann
Publisher: Princeton University Press
ISBN: 9780691028934
Size: 36.61 MB
Format: PDF
Category : Science
Languages : en
Pages : 445
View: 6016

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This text shows that insights in quantum physics can be obtained by exploring the mathematical structure of quantum mechanics. It presents the theory of Hermitean operators and Hilbert spaces, providing the framework for transformation theory, and using th

Mathematical Foundations Of Quantum Statistical Mechanics

Mathematical Foundations of Quantum Statistical Mechanics PDF
Author: D.Y. Petrina
Publisher: Springer Science & Business Media
ISBN: 940110185X
Size: 16.18 MB
Format: PDF, ePub
Category : Science
Languages : en
Pages : 445
View: 3180

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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.

Mathematical Foundations Of Quantum Mechanics

Mathematical Foundations of Quantum Mechanics PDF
Author: George W. Mackey
Publisher: Courier Corporation
ISBN: 0486154475
Size: 73.58 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 160
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This graduate-level text introduces fundamentals of classical mechanics; surveys basics of quantum mechanics; and concludes with a look at group theory and quantum mechanics of the atom. 1963 edition.

Mathematical Foundations Of Quantum Statistics

Mathematical Foundations of Quantum Statistics PDF
Author: A. Y. Khinchin
Publisher: Courier Corporation
ISBN: 0486167658
Size: 29.51 MB
Format: PDF, ePub, Docs
Category : Mathematics
Languages : en
Pages : 256
View: 7151

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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.

Mathematical Foundation Of Quantum Mechanics

Mathematical Foundation of Quantum Mechanics PDF
Author: K.R. Parthasarathy
Publisher: Springer
ISBN: 9386279282
Size: 72.73 MB
Format: PDF
Category : Mathematics
Languages : en
Pages : 178
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This is a brief introduction to the mathematical foundations of quantum mechanics based on lectures given by the author to Ph.D.students at the Delhi Centre of the Indian Statistical Institute in order to initiate active research in the emerging field of quantum probability. The material in the first chapter is included in the author's book "An Introduction to Quantum Stochastic Calculus" published by Birkhauser Verlag in 1992 and the permission of the publishers to reprint it here is acknowledged. Apart from quantum probability, an understanding of the role of group representations in the development of quantum mechanics is always a fascinating theme for mathematicians. The first chapter deals with the definitions of states, observables and automorphisms of a quantum system through Gleason's theorem, Hahn-Hellinger theorem and Wigner's theorem. Mackey's imprimitivity theorem and the theorem of inducing representations of groups in stages are proved directly for projective unitary antiunitary representations in the second chapter. Based on a discussion of multipliers on locally compact groups in the third chapter all the well-known observables of classical quantum theory like linear momenta, orbital and spin angular momenta, kinetic and potential energies, gauge operators etc., are derived solely from Galilean covariance in the last chapter. A very short account of observables concerning a relativistic free particle is included. In conclusion, the spectral theory of Schrodinger operators of one and two electron atoms is discussed in some detail.

Statistical Mechanics Of Disordered Systems

Statistical Mechanics of Disordered Systems PDF
Author: Anton Bovier
Publisher: Cambridge University Press
ISBN: 0521849918
Size: 73.98 MB
Format: PDF, Mobi
Category : Mathematics
Languages : en
Pages : 312
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A self-contained 2006 graduate-level introduction to the statistical mechanics of disordered systems. In three parts, the book treats basic statistical mechanics; disordered lattice spin systems; and latest developments in the mathematical understanding of mean-field spin glass models. It assumes basic knowledge of classical physics and working knowledge of graduate-level probability theory.

Foundations Of Statistical Mechanics

Foundations of Statistical Mechanics PDF
Author: O. Penrose
Publisher: Elsevier
ISBN: 1483156486
Size: 21.94 MB
Format: PDF, ePub, Docs
Category : Science
Languages : en
Pages : 270
View: 508

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International Series of Monographs in Natural Philosophy, Volume 22: Foundations of Statistical Mechanics: A Deductive Treatment presents the main approaches to the basic problems of statistical mechanics. This book examines the theory that provides explicit recognition to the limitations on one's powers of observation. Organized into six chapters, this volume begins with an overview of the main physical assumptions and their idealization in the form of postulates. This text then examines the consequences of these postulates that culminate in a derivation of the fundamental formula for calculating probabilities in terms of dynamic quantities. Other chapters provide a careful analysis of the significant notion of entropy, which shows the links between thermodynamics and statistical mechanics and also between communication theory and statistical mechanics. The final chapter deals with the thermodynamic concept of entropy. This book is intended to be suitable for students of theoretical physics. Probability theorists, statisticians, and philosophers will also find this book useful.