Vol. 3, No. 2, 2022
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Large deviations in the quantum quasi-1D jellium

Christian Hirsch, Sabine Jansen and Paul Jung
Vol. 3 (2022), No. 2, 381–429
DOI: 10.2140/pmp.2022.3.381
Abstract

Wigner’s jellium is a model for a gas of electrons. The model consists of N particles with negative unit charge in a sea of neutralizing homogeneous positive charge spread out according to Lebesgue measure, and interactions are governed by the Coulomb potential. We consider the quantum jellium on quasi-one-dimensional spaces with Maxwell–Boltzmann statistics. Using the Feynman–Kac representation, we replace particle locations with Brownian bridges. We then adapt the approach of Leblé and Serfaty (2017) to prove a process-level large deviation principle for the empirical fields of the Brownian bridges.

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Keywords
Coulomb systems, jellium, quasi-one-dimensional systems, large deviations principle, Feynman–Kac representation, screening, marked point process
Mathematical Subject Classification
Primary: 60F10, 60K35, 82B21
Secondary: 82B10
Milestones
Received: 11 March 2021
Revised: 29 September 2021
Accepted: 8 November 2021
Published: 8 July 2022
Authors
Christian Hirsch
Department of Mathematics
Aarhus University
Aarhus
Denmark		 Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence
University of Groningen
Groningen
The Netherlands		 CogniGron (Groningen Cognitive Systems and Materials Center)
University of Groningen
Groningen, The Netherlands
Sabine Jansen
Mathematisches Institut
Ludwig-Maximilians-Universität München
Munich
Germany		 Munich Center for Quantum Science and Technology (MCQST)
Munich
Germany
Paul Jung
Department of Mathematics and Statistics
Sam Houston State University
Huntsville, TX
United States