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Large deviations in the
quantum quasi-1D jellium
Christian Hirsch, Sabine Jansen and Paul Jung |
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Vol. 3 (2022), No. 2, 381–429
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Abstract |
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Wigner’s jellium is a model for a gas of electrons. The model consists of 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. |
Keywords
Coulomb systems, jellium, quasi-one-dimensional systems,
large deviations principle, Feynman–Kac representation,
screening, marked point process
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Mathematical Subject Classification
Primary: 60F10, 60K35, 82B21
Secondary: 82B10
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Milestones
Received: 11 March 2021
Revised: 29 September 2021
Accepted: 8 November 2021
Published: 8 July 2022
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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 |
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| Paul Jung | ||
| Department of Mathematics and
Statistics Sam Houston State University Huntsville, TX United States |
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