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PHASE TRANSITIONS AND QUANTUM STABILIZATION IN QUANTUM ANHARMONIC CRYSTALS

ALINA KARGOL

Instytut Matematyki, Uniwersytet Marii Curie-Skłodowskiej, 20-031 Lublin, Poland

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YURI KONDRATIEV

Fakultät für Mathematik, Universität Bielefeld, D-33615 Bielefeld, Germany

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, and

YURI KOZITSKY

Instytut Matematyki, Uniwersytet Marii Curie-Skłodowskiej, 20-031 Lublin, Poland

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https://doi.org/10.1142/S0129055X08003353Cited by:5 (Source: Crossref)

Abstract

A unified theory of phase transitions and quantum effects in quantum anharmonic crystals is presented. In its framework, the relationship between these two phenomena is analyzed. The theory is based on the representation of the model Gibbs states in terms of path measures (Euclidean Gibbs measures). It covers the case of crystals without translation invariance, as well as the case of asymmetric anharmonic potentials. The results obtained are compared with those known in the literature.

Keywords:

AMSC: 82B10, 82B26, 81S40

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