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

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 the 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.