Open system of interacting fermions: Statistical properties of cross sections and fluctuations

TL;DR

This paper investigates the statistical properties of cross sections in open interacting fermion systems, highlighting deviations from standard theories during the transition from isolated to overlapping resonances, influenced by intrinsic interactions and chaos.

Contribution

It introduces a detailed analysis of the crossover region using an effective non-Hermitian Hamiltonian and compares results with classical statistical theories, revealing significant deviations.

Findings

Deviations from Hauser-Feshbach and Ericson theories in the crossover region

Sensitivity of cross section fluctuations to continuum coupling

Impact of intrinsic interactions and chaos on scattering properties

Abstract

Statistical properties of cross sections are studied for an open system of interacting fermions. The description is based on the effective non-Hermitian Hamiltonian that accounts for the existence of open decay channels preserving the unitarity of the scattering matrix. The intrinsic interaction is modelled by the two-body random ensemble of variable strength. In particular, the crossover region from isolated to overlapping resonances accompanied by the effect of the width redistribution creating super-radiant and trapped states is studied in detail. The important observables, such as average cross section, its fluctuations, autocorrelation functions of the cross section and scattering matrix, are very sensitive to the coupling of the intrinsic states to the continuum around the crossover. A detailed comparison is made of our results with standard predictions of statistical theory of cross sections, such as the Hauser-Feshbach formula for the average cross section and Ericson theory of fluctuations and correlations of cross sections. Strong deviations are found in the crossover region, along with the dependence on intrinsic interactions and degree of chaos inside the system.