Spectral intensity distribution of trapped fermions

TL;DR

This paper compares exact and LDA calculations of the spectral intensity distribution function (SIDF) for trapped non-interacting fermions, highlighting the conditions under which LDA provides accurate results.

Contribution

It provides a detailed comparison of exact and LDA methods for SIDF in trapped fermions across different dimensions and particle numbers.

Findings

LDA approximations improve with increasing dimensions.

Exact and LDA SIDFs agree better at higher particle numbers.

Behavior of SIDF correlates with the density of states in the free system.

Abstract

To calculate static response properties of a many body system, local density approximation (LDA) can be safely applied. But applicability of LDA is limited for the case of dynamical response functions since dynamics of the system needs to be considered as well. To examine this in the context of cold atoms, we consider a system of non-interacting spin-$1/2$ fermions confined by a harmonic trapping potential. We have calculated a very important response function, the spectral intensity distribution function (SIDF), both exactly and using LDA at zero temperature and compared with each other for different dimensions, trap frequencies and momenta. The behavior of the SIDF at a particular momentum can be explained by noting the behavior of the density of states (DOS) of the free system (without trap) in that particular dimension. The agreement between exact and LDA SIDFs becomes better with increase in dimensions and number of particles.