FK-DLR states of a quantum bose-gas with a card-core interaction

TL;DR

This paper introduces FK-DLR functionals for a quantum Bose gas with a finite-range, hard-core interaction, laying the groundwork for proving shift-invariance of these states in future work.

Contribution

It defines a new class of FK-DLR functionals for infinite-volume bosonic states with hard-core interactions, advancing the mathematical understanding of quantum gas states.

Findings

Defined FK-DLR functionals for quantum Bose gases

Established a framework for analyzing shift-invariance in future work

Connected the functionals to limiting Gibbs states

Abstract

The paper focuses on infinite-volume bosonic states for a quantum particle system (a quantum gas) in a Euclidean space. The kinetic energy part of the Hamiltonian is the standard Laplacian (with a Dirichlet's boundary condition at the border of a `box'). The particles interact with each other through a two-body finite-range potential depending on the distance between them and featuring a hard core of a positive diameter. We introduce a class of so-called FK-DLR functionals containing all limiting Gibbs states of the system. In the next paper we will prove that any FK-DLR functional is shift-invariant, regardless of whether it is unique or not.