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Book Cover
Author Albeverio, Sergio.

Title The statistical mechanics of quantum lattice systems : a path integral approach. / Sergio Albeverio [and others].

Published Zurich : European Mathematical Society, [2009]


Location Call No. Status
 UniM ERC  530.133 ALBE    AVAILABLE
Physical description xiii, 379 pages ; 25 cm.
Series Tracts in mathematics.
EMS tracts in mathematics ; 8.
Bibliography Includes bibliographical references (pages [355]-371) and index.
Contents Quantum mechanics and stochastic analysis -- Lattice approximation and applications -- Euclidean Gibbs measures of quantum crystals -- Quantum anharmonic crystal as a physical model -- Thermodynamic pressure -- Phase transitions -- Quantum effects -- Bibliography -- List of symbols -- Index.
Summary "Quantum statistical mechanics plays a major role in many fields such as thermodynamics, plasma physics, solid-state physics, and the study of stellar structure. While the theory of quantum harmonic oscillators is relatively simple, the case of anharmonic oscillators, a mathematical model of a localized quantum particle, is more complex and challenging. Moreover, infinite systems of interacting quantum anharmonic oscillators possess interesting ordering properties with respect to quantum stabilization. This book presents a rigorous approach to the statistical mechanics of such systems, in particular with respect to their actions on a crystal lattice. The text is addressed to both mathematicians and physicists, especially those who are concerned with the rigorous mathematical background of their results and the kind of problems that arise in quantum statistical mechanics. The reader will find here a concise collection of facts, concepts, and tools relevant for the application of path integrals and other methods based on measure and integration theory to problems of quantum physics, in particular the latest results in the mathematical theory of quantum anharmonic crystals. The methods developed in the book are also applicable to other problems involving infinitely many variables, for example, in biology and economics."--Publisher's description.
Subject Statistical mechanics.
Oscillators, Crystal.
ISBN 9783037190708