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Bose–Einstein condensation for particles with repulsive short-range pair interactions in a Poisson random external potential in $\mathbb{R}^{d}$

Part of: Equilibrium statistical mechanics Applications to specific physical systems Stochastic processes

Published online by Cambridge University Press:  28 October 2022

Joachim Kerner  and
Maximilian Pechmann
Joachim Kerner*
Affiliation:
FernUniversität in Hagen
Maximilian Pechmann*
Affiliation:
University of Tennessee
*
*Postal address: Fakultät für Mathematik und Informatik, FernUniversität in Hagen, 58084 Hagen, Germany. Email: joachim.kerner@fernuni-hagen.de
**Postal address: Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA. Email: mpechmann@utk.edu
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Abstract

We study Bose gases in $d \ge 2$ dimensions with short-range repulsive pair interactions at positive temperature, in the canonical ensemble and in the thermodynamic limit. We assume the presence of hard Poissonian obstacles and focus on the non-percolation regime. For sufficiently strong interparticle interactions, we show that almost surely there cannot be Bose–Einstein condensation into a sufficiently localized, normalized one-particle state. The results apply to the canonical eigenstates of the underlying one-particle Hamiltonian.

Keywords

Interacting Bose gasstrong repulsive pair interactionshard Poissonian obstaclesnon-percolation regime

MSC classification

Primary: 82B44: Disordered systems (random Ising models, random Schrödinger operators, etc.)
Secondary: 60G55: Point processes 81V70: Many-body theory; quantum Hall effect
Type
Original Article
Information
Journal of Applied Probability , Volume 60 , Issue 2 , June 2023 , pp. 382 - 393
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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