Mathematical Foundations Of Statistical Mechanics

Mathematical Foundations of Statistical Mechanics PDF
Author: Aleksandr I?Akovlevich Khinchin
Publisher: Courier Corporation
ISBN: 9780486601472
Size: 23.26 MB
Format: PDF, Mobi
Category : Mathematics
Languages : en
Pages : 179
View: 2056

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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 Quantum Statistical Mechanics

Mathematical Foundations of Quantum Statistical Mechanics PDF
Author: D.Y. Petrina
Publisher: Springer Science & Business Media
ISBN: 940110185X
Size: 21.43 MB
Format: PDF, Kindle
Category : Science
Languages : en
Pages : 445
View: 6887

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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 Classical Statistical Mechanics

Mathematical Foundations of Classical Statistical Mechanics PDF
Author: D.Ya. Petrina
Publisher: CRC Press
ISBN: 9780415273541
Size: 58.13 MB
Format: PDF, ePub, Docs
Category : Science
Languages : en
Pages : 352
View: 3670

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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 Quantum Statistical Mechanics

Mathematical Foundations of Quantum Statistical Mechanics PDF
Author: D.Y. Petrina
Publisher: Springer
ISBN: 9780792332589
Size: 11.97 MB
Format: PDF
Category : Science
Languages : en
Pages : 445
View: 5428

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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: John Von Neumann
Publisher: Princeton University Press
ISBN: 0691028931
Size: 64.72 MB
Format: PDF, ePub
Category : Mathematics
Languages : en
Pages : 445
View: 677

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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 Statistical Mechanics

Mathematical Foundations of Statistical Mechanics PDF
Author: A. Ya. Khinchin
Publisher: Courier Corporation
ISBN: 0486138739
Size: 25.22 MB
Format: PDF, Kindle
Category : Science
Languages : en
Pages : 179
View: 4546

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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.

Foundations Of Statistical Mechanics

Foundations of Statistical Mechanics PDF
Author: Walter Grandy
Publisher: Springer Science & Business Media
ISBN: 9789027724892
Size: 43.54 MB
Format: PDF, Docs
Category : Science
Languages : en
Pages : 380
View: 477

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In a certain sense this book has been twenty-five years in the writing, since I first struggled with the foundations of the subject as a graduate student. It has taken that long to develop a deep appreciation of what Gibbs was attempting to convey to us near the end of his life and to understand fully the same ideas as resurrected by E.T. Jaynes much later. Many classes of students were destined to help me sharpen these thoughts before I finally felt confident that, for me at least, the foundations of the subject had been clarified sufficiently. More than anything, this work strives to address the following questions: What is statistical mechanics? Why is this approach so extraordinarily effective in describing bulk matter in terms of its constituents? The response given here is in the form of a very definite point of view-the principle of maximum entropy (PME). There have been earlier attempts to approach the subject in this way, to be sure, reflected in the books by Tribus [Thermostat ics and Thermodynamics, Van Nostrand, 1961], Baierlein [Atoms and Information Theory, Freeman, 1971], and Hobson [Concepts in Statistical Mechanics, Gordon and Breach, 1971].

Mathematical Foundations Of Quantum Mechanics

Mathematical Foundations of Quantum Mechanics PDF
Author: George W. Mackey
Publisher: Courier Corporation
ISBN: 0486435172
Size: 51.50 MB
Format: PDF, ePub
Category : Mathematics
Languages : en
Pages : 137
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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.

Statistical Mechanics And Fractals

Statistical Mechanics and Fractals PDF
Author: Roland L. Dobrushin
Publisher: Springer
ISBN: 3540482059
Size: 77.69 MB
Format: PDF, Mobi
Category : Mathematics
Languages : en
Pages : 102
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This book is composed of two texts, by R.L. Dobrushin and S. Kusuoka, each representing the content of a course of lectures given by the authors. They are pitched at graduate student level and are thus very accessible introductions to their respective subjects for students and non specialists. CONTENTS: R.L. Dobrushin: On the Way to the Mathematical Foundations of Statistical Mechanics.- S. Kusuoka: Diffusion Processes on Nested Fractals.

Desert Geomorphology

Desert Geomorphology PDF
Author: Ronald U. Cooke
Publisher: CRC Press
ISBN: 9781857280173
Size: 15.68 MB
Format: PDF, Mobi
Category : Science
Languages : en
Pages : 534
View: 4994

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Including recent research findings from terrestrial satellite imagery, the study of planetary landscapes, and advances in laboratory work, this also covers the environmental processes involved in desertification and the solution of planning and