Correlators for the Wigner-Smith time-delay matrix of chaotic cavities

TL;DR

This paper analyzes the statistical properties of the Wigner-Smith time-delay matrix in chaotic quantum cavities, deriving correlators for power traces using random matrix theory and proposing a conjecture about their cumulants.

Contribution

It introduces a method to compute correlators of power traces of the Wigner-Smith matrix for large N and conjectures their cumulants are integer-valued at leading order.

Findings

Derived v-point correlators for power traces of Q.

Proposed a conjecture on integer-valued cumulants.

Provided recursive Mathematica code for generating functions.

Abstract

We study the Wigner-Smith time-delay matrix $Q$ of a ballistic quantum dot supporting $N$ scattering channels. We compute the $v$-point correlators of the power traces $\mathrm{Tr} Q^{\kappa}$ for arbitrary $v\geq1$ at leading order for large $N$ using techniques from the random matrix theory approach to quantum chromodynamics. We conjecture that the cumulants of the $\mathrm{Tr} Q^{\kappa}$'s are integer-valued at leading order in $N$ and include a MATHEMATICA code that computes their generating functions recursively.