Phase Transitions and Quantum Stabilization in Quantum Anharmonic Crystals

TL;DR

This paper develops a unified theoretical framework for understanding phase transitions and quantum effects in quantum anharmonic crystals, using path measure representations to analyze various crystal conditions.

Contribution

It introduces a comprehensive theory connecting phase transitions and quantum effects in anharmonic crystals, including non-invariant and asymmetric potentials.

Findings

Relationship between phase transitions and quantum effects analyzed

Representation of Gibbs states via path measures established

Comparison with existing literature results provided

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.