The Feynman–Kac Representation and Dobrushin–Lanford–Ruelle States of a Quantum Bose-Gas


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Authors
Suhov, Yuri 
Stuhl, Izabella 
Abstract

jats:pThis paper focuses on infinite-volume bosonic states for a quantum particle system (a quantum gas) in Rd. The kinetic energy part of the Hamiltonian is the standard Laplacian (with a 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 diameter a>0. We introduce a class of so-called FK-DLR functionals containing all limiting Gibbs states of the system. As a justification of this concept, we prove that for d=2, any FK-DLR functional is shift-invariant, regardless of whether it is unique or not. This yields a quantum analog of results previously achieved by Richthammer.</jats:p>

Description
Keywords
49 Mathematical Sciences
Journal Title
Mathematics
Conference Name
Journal ISSN
2227-7390
2227-7390
Volume Title
8
Publisher
MDPI AG