Scaling Limits In Statistical Mechanics And Microstructures In Continuum Mechanics
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Scaling Limits In Statistical Mechanics And Microstructures In Continuum Mechanics
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Author : Errico Presutti
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-11-01
Scaling Limits In Statistical Mechanics And Microstructures In Continuum Mechanics written by Errico Presutti and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-01 with Mathematics categories.
Collective behavior in systems with many components, blow-ups with emergence of microstructures are proofs of the double, continuum and atomistic, nature of macroscopic systems, an issue which has always intrigued scientists and philosophers. Modern technologies have made the question more actual and concrete with recent, remarkable progresses also from a mathematical point of view. The book focuses on the links connecting statistical and continuum mechanics and, starting from elementary introductions to both theories, it leads to actual research themes. Mathematical techniques and methods from probability, calculus of variations and PDE are discussed at length.
Statistical Mechanics Of Lattice Systems
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Author : Sacha Friedli
language : en
Publisher: Cambridge University Press
Release Date : 2017-11-23
Statistical Mechanics Of Lattice Systems written by Sacha Friedli and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-23 with Mathematics categories.
A self-contained, mathematical introduction to the driving ideas in equilibrium statistical mechanics, studying important models in detail.
Making Sense Of Statistical Mechanics
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Author : Jean Bricmont
language : en
Publisher: Springer Nature
Release Date : 2022-02-11
Making Sense Of Statistical Mechanics written by Jean Bricmont and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-11 with Science categories.
Many people, including physicists, are confused about what the Second Law of thermodynamics really means, about how it relates to the arrow of time, and about whether it can be derived from classical mechanics. They also wonder what entropy really is: Is it all about information? But, if so, then, what is its relation to fluxes of heat? One might ask similar questions about probabilities: Do they express subjective judgments by us, humans, or do they reflect facts about the world, i.e. frequencies. And what notion of probability is used in the natural sciences, in particular statistical mechanics? This book addresses all of these questions in the clear and pedagogical style for which the author is known. Although valuable as accompaniment to an undergraduate course on statistical mechanics or thermodynamics, it is not a standard course book. Instead it addresses both the essentials and the many subtle questions that are usually brushed under the carpet in such courses. As one of the most lucid accounts of the above questions, it provides enlightening reading for all those seeking answers, including students, lecturers, researchers and philosophers of science.
Quantum Mathematics Ii
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Author : Michele Correggi
language : en
Publisher: Springer Nature
Release Date : 2023-12-08
Quantum Mathematics Ii written by Michele Correggi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-08 with Science categories.
This book is the second volume that provides an unique overview of the most recent and relevant contributions in the field of mathematical physics with a focus on the mathematical features of quantum mechanics. It is a collection of review papers together with brand new works related to the activities of the INdAM Intensive Period "INdAM Quantum Meetings (IQM22)", which took place at the Politecnico di Milano in Spring 2022 at Politecnico di Milano. The range of topics covered by the book is wide, going ranging from many-body quantum mechanics to quantum field theory and open quantum systems.
Physics Avoidance
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Author : Mark Wilson
language : en
Publisher: Oxford University Press
Release Date : 2017-10-20
Physics Avoidance written by Mark Wilson and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-20 with Philosophy categories.
Mark Wilson presents a series of explorations of our strategies for understanding the world. 'Physics avoidance' refers to the fact that we frequently cannot reason about nature in the straightforward manner we anticipate, but must seek alternative policies that allow us to address the questions we want answered in a tractable way. Within both science and everyday life, we find ourselves relying upon thought processes that reach useful answers in opaque and roundabout manners. Conceptual innovators are often puzzled by the techniques they develop, when they stumble across reasoning patterns that are easy to implement but difficult to justify. But simple techniques frequently rest upon complex foundations--a young magician learns how to execute a card-guessing trick without understanding how its progressive steps squeeze in on a proper answer. As we collectively improve our inferential skills in this gradually evolving manner, we often wander into unfamiliar explanatory landscapes in which simple words encode physical information in complex and unanticipated ways. Like our juvenile conjurer, we fail to recognize the true strategic rationales underlying our achievements and may turn instead to preposterous rationalizations for our policies. We have learned how to reach better conclusions in a more fruitful way, but we remain baffled by our own successes. At its best, philosophical reflection illuminates the natural developmental processes that generate these confusions and explicates their complexities. But current thinking within philosophy of science and language works to opposite effect by relying upon simplistic conceptions of 'cause', 'law of nature', 'possibility', and 'reference' that ignore the strategic complexities in which these concepts become entangled within real-life usage. To avoid these distortions, better descriptive tools are wanted. The nine new essays within this volume illustrate this need for finer discriminations through a range of revealing cases, of both historical and contemporary significance.
Theory Of Simple Glasses
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Author : Giorgio Parisi
language : en
Publisher: Cambridge University Press
Release Date : 2020-01-09
Theory Of Simple Glasses written by Giorgio Parisi and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-09 with Science categories.
This self-contained text describes the modern mean field theory of simple structural glasses using a quantum statistical mechanical approach. Describing the theory in clear and simple terms, this is a valuable resource for graduate students and researchers working in condensed matter physics and statistical mechanics.
C Algebras And Mathematical Foundations Of Quantum Statistical Mechanics
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Author : Jean-Bernard Bru
language : en
Publisher: Springer Nature
Release Date : 2023-06-16
C Algebras And Mathematical Foundations Of Quantum Statistical Mechanics written by Jean-Bernard Bru and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-16 with Science categories.
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.
Feynman Kac Type Formulae And Gibbs Measures
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Author : József Lörinczi
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-01-20
Feynman Kac Type Formulae And Gibbs Measures written by József Lörinczi and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-20 with Mathematics categories.
This is the second updated and extended edition of the successful book on Feynman-Kac theory. It offers a state-of-the-art mathematical account of functional integration methods in the context of self-adjoint operators and semigroups using the concepts and tools of modern stochastic analysis. The first volume concentrates on Feynman-Kac-type formulae and Gibbs measures.
Gibbs Measures And Phase Transitions
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Author : Hans-Otto Georgii
language : en
Publisher: Walter de Gruyter
Release Date : 2011
Gibbs Measures And Phase Transitions written by Hans-Otto Georgii and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
From a review of the first edition: "This book [...] covers in depth a broad range of topics in the mathematical theory of phase transition in statistical mechanics. [...] It is in fact one of the author's stated aims that this comprehensive monograph should serve both as an introductory text and as a reference for the expert." (F. Papangelou
Feynman Kac Type Theorems And Gibbs Measures On Path Space
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Author : József Lörinczi
language : en
Publisher: Walter de Gruyter
Release Date : 2011-08-29
Feynman Kac Type Theorems And Gibbs Measures On Path Space written by József Lörinczi and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-29 with Mathematics categories.
This monograph offers a state-of-the-art mathematical account of functional integration methods in the context of self-adjoint operators and semigroups using the concepts and tools of modern stochastic analysis. These ideas are then applied principally to a rigorous treatment of some fundamental models of quantum field theory. In this self-contained presentation of the material both beginners and experts are addressed, while putting emphasis on the interdisciplinary character of the subject.