论文标题
量子准1D jellium中的大偏差
Large deviations in the quantum quasi-1D jellium
论文作者
论文摘要
Wigner's Jellium是电子气体的模型。该模型由$ n $单元组成，负电荷的粒子位于中和均质的正电荷中，根据Lebesgue Mesure，相互作用受库仑电位的控制。在这项工作中，我们考虑了具有Maxwell-Boltzmann统计数据的准二维空间上的量子jellium。使用Feynman-KAC表示，我们用布朗桥代替粒子位置。然后，我们适应了Leblé和Serfaty（2017）的方法，以证明布朗尼桥的经验领域的过程级别的大偏差原理。
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 Leblé and Serfaty (2017) to prove a process-level large deviation principle for the empirical fields of the Brownian bridges.
