Counting statistics in finite Fermi systems: illustrations with the atomic nucleus

TL;DR

This paper investigates counting statistics in finite Fermi systems, especially atomic nuclei, analyzing how particle number fluctuations transition from Poissonian to Gaussian distributions across different system sizes and conditions.

Contribution

It introduces a projection operator method linked to the characteristic function to analyze counting statistics in finite Fermi systems, including superfluid and particle number restored cases.

Findings

Particle number fluctuations transition from Poissonian to Gaussian with increasing volume.

Restoring total particle number influences counting statistics when more than a few particles are involved.

Surface and interior regions show different fluctuation behaviors.

Abstract

We analyze here in details the probability to find a given number of particles in a finite volume inside a normal or superfluid finite system. This probability, also known as counting statistics, is obtained using projection operator techniques directly linked to the characteristic function of the probability distribution. The method is illustrated in atomic nuclei. The nature of the particle number fluctuations from small to large volumes compared to the system size are carefully analyzed in three cases: normal systems, superfluid systems and superfluid systems with total particle number restoration. The transition from Poissonian distribution in the small volume limit to Gaussian fluctuations as the number of particles participating to the fluctuations increases, is analyzed both in the interior and at the surface of the system. While the restoration of total number of particles is not necessary for small volume, we show that it affects the counting statistics as soon as more than very few particles are involved.