Many body density of states in the edge of the spectrum: non-interacting limit

TL;DR

This paper derives the ensemble-averaged many-body density of states in the non-interacting limit using random matrix models, providing analytical insights into spectral properties of complex quantum systems.

Contribution

It introduces a method to compute the many-body density of states by convolving single-particle densities modeled as Gaussian or Wishart ensembles, advancing theoretical understanding.

Findings

Derived explicit formulas for many-body density of states

Connected spectral properties to random matrix ensembles

Provided analytical tools for non-interacting quantum systems

Abstract

In noninteracting limit, the density of states of a many body system can be expressed as the convolution of single body density of states of its subunits. Here we use the formulation to derive the ensemble averaged many body density of states for the cases in which subunits can be modelled by Gaussian or Wishart random matrix ensembles.