Many-body physics and resolvent algebras

TL;DR

This paper demonstrates how resolvent algebra-based algebraic methods effectively analyze many-body bosonic systems, showing convergence of dynamics and correlations in large-region limits, and characterizing Bose-Einstein condensates.

Contribution

It introduces an algebraic approach using resolvent algebras to study many-body bosonic systems, highlighting convergence properties and symmetry-breaking phenomena.

Findings

Dynamics converge to homogeneous or inhomogeneous limits depending on particle filling.

Correlation functions of thermal states converge in the large-region limit.

Presence of condensates indicated by long-range temporal correlations.

Abstract

Some advantages of the algebraic approach to many body physics, based on resolvent algebras, are illustrated by the simple example of non-interacting bosons which are confined in compact regions with soft boundaries. It is shown that the dynamics of these systems converges to the spatially homogeneous dynamics for increasing regions and particle numbers and a variety of boundary forces. The corresponding correlation functions of thermal equilibrium states also converge in this limit. Depending on the filling of the regions with particles, the limits can either be spatially homogeneous, including the Bose-Einstein condensates, or they become inhomogeneous with varying, but finite local particle densities. In case of this spontaneous breakdown of the spatial symmetry, the presence of condensates can be established by exhibiting temporal correlations over large temporal distances (memory effects).