Residual Coulomb interaction fluctuations in chaotic systems: the boundary, random plane waves, and semiclassical theory

TL;DR

This paper investigates fluctuation properties of residual Coulomb interactions in chaotic systems, emphasizing boundary effects, limitations of random plane wave models, and the effectiveness of semiclassical theory in capturing these phenomena.

Contribution

It introduces a semiclassical framework to accurately describe boundary-related fluctuations in chaotic eigenstates, improving upon random plane wave approximations.

Findings

Fluctuation scale is larger with Neumann boundary conditions.

Random plane wave models have significant limitations near boundaries.

Semiclassical theory effectively corrects these modeling errors.

Abstract

New fluctuation properties arise in problems where both spatial integration and energy summation are necessary ingredients. The quintessential example is given by the short-range approximation to the first order ground state contribution of the residual Coulomb interaction. The dominant features come from the region near the boundary where there is an interplay between Friedel oscillations and fluctuations in the eigenstates. Quite naturally, the fluctuation scale is significantly enhanced for Neumann boundary conditions as compared to Dirichlet. Elements missing from random plane wave modeling of chaotic eigenstates lead surprisingly to significant errors, which can be corrected within a purely semiclassical approach.