Random Interaction Matrix Ensembles in Mesoscopic Physics

TL;DR

This paper investigates mesoscopic systems using a random interaction matrix model, revealing key properties like ground state energy staggering and conductance distribution, with analytical formulas explaining spectral variances.

Contribution

It introduces the RIMM model for fermion systems with spin, incorporating pairing and exchange interactions, and derives analytical formulas for spectral variances.

Findings

Reproduces odd-even staggering in ground state energies

Explains delay in ground state magnetization

Describes conductance peak spacing distributions

Abstract

We analyze several ground state related properties of mesoscopic systems using the random interaction matrix model EGOE(1+2)-$\cs$ (or RIMM) for many fermion systems with spin degree of freedom and the Hamiltonian containing pairing and exchange interactions in addition to the mean-field one-body and random two-body parts. RIMM reproduces the essential features of various properties: odd-even staggering in ground state energies as a function of particle number, delay in ground state magnetization and conductance peak spacing distributions. The analytical formula, we have derived, for the ensemble averaged spectral variances provides a simple understanding of some of these properties.