A hierarchical model of quantum anharmonic oscillators: critical point convergence

TL;DR

This paper investigates a hierarchical quantum anharmonic oscillator model using Euclidean methods, proving the convergence of Matsubara functions at the critical point in the thermodynamic limit.

Contribution

It establishes a rigorous theorem on the convergence of Matsubara functions for a hierarchical quantum anharmonic oscillator model.

Findings

Proves critical point convergence of Matsubara functions in the model.

Develops a measure-based Euclidean approach for quantum particle systems.

Provides a mathematical foundation for phase transition analysis in quantum anharmonic oscillators.

Abstract

A hierarchical model of interacting quantum particles performing anharmonic oscillations is studied in the Euclidean approach, in which the local Gibbs states are constructed as measures on infinite dimensional spaces. The local states restricted to the subalgebra generated by fluctuations of displacements of particles are in the center of the study. They are described by means of the corresponding temperature Green (Matsubara) functions. The result of the paper is a theorem, which describes the critical point convergence of such Matsubara functions in the thermodynamic limit.