Spectral statistics of the k-body random-interaction model

TL;DR

This paper critically examines the spectral statistics of the k-body random-interaction model, questioning previous claims of Poissonian behavior and highlighting the need for more rigorous mathematical treatment.

Contribution

It challenges prior conclusions by analyzing the divergence issues in the binary-correlation method and emphasizes that the spectral statistics remain unresolved.

Findings

Previous methods involve divergent series that require careful regularization.

Borel summation alone is insufficient to define the series rigorously.

The spectral statistics of the model are still an open problem.

Abstract

We reconsider the question of the spectral statistics of the k-body random-interaction model, investigated recently by Benet, Rupp, and Weidenmueller, who concluded that the spectral statistics are Poissonian. The binary-correlation method that these authors used involves formal manipulations of divergent series. We argue that Borel summation does not suffice to define these divergent series without further (arbitrary) regularization, and that this constitutes a significant gap in the demonstration of Poissonian statistics. Our conclusion is that the spectral statistics of the k-body random-interaction model remains an open question.