Operator Theory With A Random Potential And Some Questions Of Statistical Physics

Author : Viktor Nikolaevich Popov
Publisher : American Mathematical Soc.
Page : 278 pages
File Size : 41,5 Mb
Release : 1991
Category : Mathematics
ISBN : 0821831399

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Operator Theory with a Random Potential, and Some Questions of Statistical Physics by Viktor Nikolaevich Popov Pdf

This collection is devoted to problems of operator theory with a random potential and a number of problems of statistical physics. For the Schrodinger operator with a potential randomly depending on time, mean wave operators, and the mean scattering operator are computed, and it is shown that the averaged dynamics behaves like free dynamics in the limit of infinite time. Results of applying the method of functional integration to some problems of statistical physics are presented: the theory of systems with model Hamiltonians and their dynamics, ferromagnetic systems of spin 1/2, Coulomb and quantum crystals. This collection is intended for specialists in spectral theory and statistical physics.

Author : American Mathematical Society
Publisher : Unknown
Page : 852 pages
File Size : 42,8 Mb
Release : 1992
Category : Mathematics
ISBN : UCSD:31822015782311

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Notices of the American Mathematical Society by American Mathematical Society Pdf

Author : Ola Bratteli,Derek William Robinson
Publisher : Springer Science & Business Media
Page : 536 pages
File Size : 42,9 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.

Author : Ola Bratteli,Derek William Robinson
Publisher : Springer Science & Business Media
Page : 503 pages
File Size : 48,8 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.

Author : Lev A. Sakhnovich
Publisher : Springer Science & Business Media
Page : 246 pages
File Size : 53,5 Mb
Release : 2012-07-18
Category : Mathematics
ISBN : 9783034803564

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Levy Processes, Integral Equations, Statistical Physics: Connections and Interactions by Lev A. Sakhnovich Pdf

In a number of famous works, M. Kac showed that various methods of probability theory can be fruitfully applied to important problems of analysis. The interconnection between probability and analysis also plays a central role in the present book. However, our approach is mainly based on the application of analysis methods (the method of operator identities, integral equations theory, dual systems, integrable equations) to probability theory (Levy processes, M. Kac's problems, the principle of imperceptibility of the boundary, signal theory). The essential part of the book is dedicated to problems of statistical physics (classical and quantum cases). We consider the corresponding statistical problems (Gibbs-type formulas, non-extensive statistical mechanics, Boltzmann equation) from the game point of view (the game between energy and entropy). One chapter is dedicated to the construction of special examples instead of existence theorems (D. Larson's theorem, Ringrose's hypothesis, the Kadison-Singer and Gohberg-Krein questions). We also investigate the Bezoutiant operator. In this context, we do not make the assumption that the Bezoutiant operator is normally solvable, allowing us to investigate the special classes of the entire functions.

Author : Ola Bratteli
Publisher : Unknown
Page : 520 pages
File Size : 51,5 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662025213

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Operator Algebras and Quantum Statistical Mechanics 1 by Ola Bratteli Pdf

Author : Ola Bratteli,Derek William Robinson
Publisher : Springer
Page : 506 pages
File Size : 42,9 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.

Author : Konrad Schmüdgen
Publisher : Springer Science & Business Media
Page : 511 pages
File Size : 48,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642773037

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Mathematical Physics X by Konrad Schmüdgen Pdf

th This volume contains the proceedings of the X Congress of the Interna tional Association of Mathematical Physics, held at the University of Leipzig from 30 July until 9 August 1991. There were more than 400 participants, from 29 countries, making it a truly international gathering. The congress had the support of the Deutsche Forschungsgemeinschaft, the European Economic Community, the International Association of Math ematical Physics, the International Mathematical Union and the Interna tional Union of Pure and Applied Physics. There were also sponsors from in dustry and commerce: ATC Mann, Deutsche Bank AG, Miele & Cie GmbH, NEC Deutschland GmbH, Rank Xerox, Siemens AG and Stiftungsfonds IBM Deutschland. On behalf of the congress participants and the members of the International Association of Mathematical Physics, I would like to thank all these organisations for their very generous support. The congress took place under the auspices of the Ministerp6isident des Freistaates Sachsen, K. Biedenkopf. The conference began with an address by A. Uhlmann, Chairman of the Local Organizing Committee. This was followed by speeches of welcome from F. Magirius, City President of Leipzig; C. Weiss, Rector of the Uni versity of Leipzig; and A. Jaffe, President of the International Association of Mathematical Physics."

Author : Reinhard Lang
Publisher : Springer
Page : 133 pages
File Size : 55,6 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540466277

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Spectral Theory of Random Schrödinger Operators by Reinhard Lang Pdf

The interplay between the spectral theory of Schr|dinger operators and probabilistic considerations forms the main theme of these notes, written for the non-specialist reader and intended to provide a brief and elementaryintroduction to this field. An attempt is made to show basic ideas in statu nascendi and to follow their evaluation from simple beginnings through to more advanced results. The term "genetic" in the title refers to this proceedure. The author concentrates on 2 topics which, in the history of the subject, have been of major conceptual importance - on the one hand the Laplacian is a random medium and the left end of its spectrum (leading to large deviation problems for Brownian motion and the link to thenotion of entropy) and on the other, Schr|dinger operators with general ergodic potentials in one-dimensional space. Ideas and concepts are explained in the simplest, possible setting and by means of a few characteristic problems with heuristic arguments preceding rigorous proofs.

Author : Anonim
Publisher : Unknown
Page : 2456 pages
File Size : 52,8 Mb
Release : 1992
Category : American literature
ISBN : UOM:39015058373989

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The Cumulative Book Index by Anonim Pdf

A world list of books in the English language.

Author : Ola Bratteli
Publisher : Unknown
Page : 532 pages
File Size : 51,7 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 366203445X

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Operator Algebras and Quantum Statistical Mechanics by Ola Bratteli Pdf

Author : M. Picardello,W. Woess
Publisher : Cambridge University Press
Page : 378 pages
File Size : 52,6 Mb
Release : 1999-11-18
Category : Mathematics
ISBN : 0521773121

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Random Walks and Discrete Potential Theory by M. Picardello,W. Woess Pdf

Comprehensive and interdisciplinary text covering the interplay between random walks and structure theory.

Author : FRITZ,JAFFE,SZASZ
Publisher : Springer Science & Business Media
Page : 489 pages
File Size : 43,7 Mb
Release : 2013-11-22
Category : Science
ISBN : 9781489966537

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Statistical Physics and Dynamical Systems by FRITZ,JAFFE,SZASZ Pdf

Author : Anonim
Publisher : Unknown
Page : 742 pages
File Size : 50,6 Mb
Release : 1992
Category : Science
ISBN : UOM:39015023898821

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World Translations Index by Anonim Pdf

Author : Anonim
Publisher : Unknown
Page : 570 pages
File Size : 44,6 Mb
Release : 1967
Category : Electronic
ISBN : OSU:32435062863477

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OAR by Anonim Pdf