Large deviations in the quantum quasi-1D jellium

TL;DR

This paper establishes a large deviation principle for the empirical fields of quantum jellium in quasi-one-dimensional spaces, using a Feynman-Kac representation and adapting methods from Leblé and Serfaty (2017).

Contribution

It introduces a process-level large deviation principle for quantum jellium in quasi-1D, extending classical Coulomb gas results to quantum settings with Brownian bridges.

Findings

Proves a large deviation principle for quantum jellium empirical fields.

Adapts Leblé and Serfaty's approach to quantum and quasi-1D context.

Utilizes Feynman-Kac representation with Brownian bridges.

Abstract

Wigner's jellium is a model for a gas of electrons. The model consists of $N$ unit negatively charged particles lying in a sea of neutralizing homogeneous positive charge spread out according to Lebesgue measure, and interactions are governed by the Coulomb potential. In this work 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 Lebl\'e and Serfaty (2017) to prove a process-level large deviation principle for the empirical fields of the Brownian bridges.