The Feynman–Kac representation and Dobrushin–Lanford–Ruelle states of a quantum bose-gas

Yuri Suhov; Mark Kelbert; Izabella Stuhl

doi:10.3390/math8101683

The Feynman–Kac representation and Dobrushin–Lanford–Ruelle states of a quantum bose-gas

Yuri Suhov, Mark Kelbert, Izabella Stuhl

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

This paper focuses on infinite-volume bosonic states for a quantum particle system (a quantum gas) in R^d . 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.

Original language	English (US)
Article number	1683
Pages (from-to)	1-41
Number of pages	41
Journal	Mathematics
Volume	8
Issue number	10
DOIs	https://doi.org/10.3390/math8101683
State	Published - Oct 2020

All Science Journal Classification (ASJC) codes

General Mathematics

Access to Document

10.3390/math8101683

Cite this

@article{687e6c4894564d798b5f0e9bd044f75d,

title = "The Feynman–Kac representation and Dobrushin–Lanford–Ruelle states of a quantum bose-gas",

abstract = "This 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 {\textquoteleft}box{\textquoteright}). 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.",

author = "Yuri Suhov and Mark Kelbert and Izabella Stuhl",

note = "Funding Information: Funding: This work was partially funded by the Russian Academic Excellence Program {\textquoteleft}5-100{\textquoteright}. Funding Information: Acknowledgments: Y.S. and I.S. are grateful to Math Department, Penn State University, for the hospitality and support. M.K. was supported by the Russian Academic Excellence Program {\textquoteleft}5-100{\textquoteright}. The authors thank anonymous reviewers for useful comments. Publisher Copyright: {\textcopyright} 2020 by the authors. Licensee MDPI, Basel, Switzerland.",

year = "2020",

month = oct,

doi = "10.3390/math8101683",

language = "English (US)",

volume = "8",

pages = "1--41",

journal = "Mathematics",

issn = "2227-7390",

publisher = "MDPI AG",

number = "10",

}

TY - JOUR

T1 - The Feynman–Kac representation and Dobrushin–Lanford–Ruelle states of a quantum bose-gas

AU - Suhov, Yuri

AU - Kelbert, Mark

AU - Stuhl, Izabella

N1 - Funding Information: Funding: This work was partially funded by the Russian Academic Excellence Program ‘5-100’. Funding Information: Acknowledgments: Y.S. and I.S. are grateful to Math Department, Penn State University, for the hospitality and support. M.K. was supported by the Russian Academic Excellence Program ‘5-100’. The authors thank anonymous reviewers for useful comments. Publisher Copyright: © 2020 by the authors. Licensee MDPI, Basel, Switzerland.

PY - 2020/10

Y1 - 2020/10

N2 - This 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.

AB - This 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.

UR - http://www.scopus.com/inward/record.url?scp=85093118251&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85093118251&partnerID=8YFLogxK

U2 - 10.3390/math8101683

DO - 10.3390/math8101683

M3 - Article

AN - SCOPUS:85093118251

SN - 2227-7390

VL - 8

SP - 1

EP - 41

JO - Mathematics

JF - Mathematics

IS - 10

M1 - 1683

ER -

The Feynman–Kac representation and Dobrushin–Lanford–Ruelle states of a quantum bose-gas

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this