Distribution of the local density of states, reflection coefficient and Wigner delay time in absorbing ergodic systems at the point of chiral symmetry

TL;DR

This paper derives the probability distribution of the local density of states, reflection coefficient, and Wigner delay time in absorbing chiral symmetric systems using random matrix theory, relevant for quantum chaotic two-sublattice systems.

Contribution

It provides a novel analytical calculation of these distributions specifically for absorbing systems at chiral symmetry using the chiral Unitary Ensemble.

Findings

Distribution of local density of states at E=0 derived

Reflection coefficient distribution obtained

Wigner time delay distribution characterized

Abstract

Employing the chiral Unitary Ensemble of random matrices we calculate the probability distribution of the local density of states for zero-dimensional ("quantum chaotic") two-sublattice systems at the point of chiral symmetry E=0 and in the presence of uniform absorption. The obtained result can be used to find the distributions of the reflection coefficent and of the Wigner time delay for such systems.