#### 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
##### 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.

##### 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