The Statistical Mechanics of Quantum Lattice Systems: A Path Integral Approach

Cover
European Mathematical Society, 2009 - 379 Seiten
0 Rezensionen
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.
 

Was andere dazu sagen - Rezension schreiben

Es wurden keine Rezensionen gefunden.

Inhalt

Introduction
1
Quantum Mechanics and Stochastic Analysis
15
Lattice Approximation and Applications
155
Euclidean Gibbs Measures of Quantum Crystals
191
Quantum Anharmonic Crystal as a Physical Model
249
Thermodynamic Pressure
262
Phase Transitions
280
Quantum Effects
336
Bibliography
355
List of Symbols
373
Urheberrecht

Andere Ausgaben - Alle anzeigen

Häufige Begriffe und Wortgruppen

Bibliografische Informationen