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C*-Algebras and Mathematical Foundations of Quantum Statistical Mechanics

2023-06-16 Science
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Release : 2023-06-16
Genre : Science
Kind : eBook
Book Rating : 498/5 ( reviews)

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Book Synopsis C*-Algebras and Mathematical Foundations of Quantum Statistical Mechanics by : Jean-Bernard Bru

Download or read book C*-Algebras and Mathematical Foundations of Quantum Statistical Mechanics written by Jean-Bernard Bru. This book was released on 2023-06-16. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Operator Algebras and Quantum Statistical Mechanics

2013-06-29 Science
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Release : 2013-06-29
Genre : Science
Kind : eBook
Book Rating : 441/5 ( reviews)

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Book Synopsis Operator Algebras and Quantum Statistical Mechanics by : Ola Bratteli

Download or read book Operator Algebras and Quantum Statistical Mechanics written by Ola Bratteli. This book was released on 2013-06-29. Available in PDF, EPUB and Kindle. Book excerpt: 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 Statistical Mechanics

2012-12-06 Science
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Release : 2012-12-06
Genre : Science
Kind : eBook
Book Rating : 85X/5 ( reviews)

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Book Synopsis Mathematical Foundations of Quantum Statistical Mechanics by : D.Y. Petrina

Download or read book Mathematical Foundations of Quantum Statistical Mechanics written by D.Y. Petrina. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: 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 Foundation of Quantum Mechanics

2005-10-15 Mathematics
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Release : 2005-10-15
Genre : Mathematics
Kind : eBook
Book Rating : 282/5 ( reviews)

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Book Synopsis Mathematical Foundation of Quantum Mechanics by : K.R. Parthasarathy

Download or read book Mathematical Foundation of Quantum Mechanics written by K.R. Parthasarathy. This book was released on 2005-10-15. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Operator Algebras and Quantum Statistical Mechanics

2003-01-09 Science
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Release : 2003-01-09
Genre : Science
Kind : eBook
Book Rating : 432/5 ( reviews)

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Book Synopsis Operator Algebras and Quantum Statistical Mechanics by : Ola Bratteli

Download or read book Operator Algebras and Quantum Statistical Mechanics written by Ola Bratteli. This book was released on 2003-01-09. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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