The resolvent algebra for oscillating lattice systems: Dynamics, ground and equilibrium states

TL;DR

This paper develops a C*-algebraic framework for oscillating lattice systems, analyzing their dynamics, and constructing equilibrium and ground states, with considerations for singular interactions and non-harmonic oscillations.

Contribution

It introduces a resolvent algebra approach to lattice systems, demonstrating the existence of regular equilibrium and ground states under bounded interactions.

Findings

Global dynamics act as automorphisms on the algebra

Existence of weakly dense subalgebra with continuous dynamics

Construction of regular equilibrium and ground states

Abstract

Within the C*-algebraic framework of the resolvent algebra for canonical quantum systems, the structure of oscillating lattice systems with bounded nearest neighbor interactions is studied in any number of dimensions. The global dynamics of such systems acts on the resolvent algebra by automorphisms and there exists a (in any regular representation) weakly dense subalgebra on which this action is pointwise norm continuous. Based on this observation, equilibrium (KMS) states as well as ground states are constructed which are shown to be regular. It is also indicated how to deal with singular interactions and non-harmonic oscillations.