Exact ground state number fluctuations of trapped ideal and interacting fermions

TL;DR

This paper introduces a new method to precisely calculate ground state particle number fluctuations in small trapped fermion systems, including interactions, using spectrum partitioning and number theory, improving efficiency over previous methods.

Contribution

It develops a novel approach combining spectrum partitioning and number partitioning theory to compute exact particle number fluctuations in both ideal and interacting fermions.

Findings

Exact fluctuations computed for non-interacting fermions.

Fluctuations also calculated for fermions with inverse-square interactions.

Method improves computational efficiency over direct combinatorics.

Abstract

We consider a small and fixed number of fermions in an isolated one-dimensional trap (microcanonical ensemble). The ground state of the system is defined at T=0, with the lowest single-particle levels occupied. The number of particles in this ground state fluctuates as a function of excitation energy. By breaking up the energy spectrum into particle and hole sectors, and mapping the problem onto the classic number partitioning theory, we formulate a new method to calculate the exact particle number fluctuation more efficiently than the direct combinatorics method. The exact ground state number fluctuation for particles interacting via an inverse-square pair-wise interaction is also calculated.