Mesoscopic Fluctuations of the Pairing Gap

TL;DR

This paper develops a theoretical framework using periodic orbit theory to analyze mesoscopic fluctuations of the pairing gap in finite quantum systems, highlighting differences between regular and chaotic classical dynamics.

Contribution

It introduces a unified approach to describe pairing gap fluctuations across various mesoscopic systems, including nuclei, metallic grains, and ultracold gases, based on classical motion properties.

Findings

Fluctuation sizes depend on classical dynamics (regular or chaotic).

The theory accurately describes pairing gap variations with system size and particle number.

Application to nuclei, metallic grains, and ultracold gases demonstrates broad relevance.

Abstract

A description of mesoscopic fluctuations of the pairing gap in finite-sized quantum systems based on periodic orbit theory is presented. The size of the fluctuations are found to depend on quite general properties. We distinguish between systems where corresponding classical motion is regular or chaotic, and describe in detail fluctuations of the BCS gap as a function of the size of the system. The theory is applied to different mesoscopic systems: atomic nuclei, metallic grains, and ultracold fermionic gases. We also present a detailed description of pairing gap variation with particle number for nuclei based on a deformed cavity potential.