Trapped bosons, thermodynamic limit and condensation: a study in the framework of resolvent algebras

TL;DR

This paper demonstrates how resolvent algebras offer a robust framework for analyzing infinite bosonic systems, including phase transitions like Bose-Einstein condensation, without relying on ad hoc methods.

Contribution

It introduces resolvent algebras as a universal tool for studying equilibrium states of bosons, both trapped and untrapped, across various dimensions and interaction types.

Findings

Equilibrium states are well-defined on a fixed C*-algebra for all relevant temperatures and chemical potentials.

The framework clarifies the emergence of Bose-Einstein condensates in non-interacting systems.

It extends to interacting bosonic systems, providing a comprehensive analysis method.

Abstract

The virtues of resolvent algebras, compared to other approaches for the treatment of canonical quantum systems, are exemplified by infinite systems of non-relativistic bosons. Within this framework, equilibrium states of trapped and untrapped bosons are defined on a fixed C*-algebra for all physically meaningful values of the temperature and chemical potential. Moreover, the algebra provides the tools for their analysis without having to rely on 'ad hoc' prescriptions for the test of pertinent features, such as the appearance of Bose-Einstein condensates. The method is illustrated in case of non-interacting systems in any number of spatial dimensions and sheds new light on the appearance of condensates. Yet the framework also covers interactions and thus provides a universal basis for the analysis of bosonic systems.