Transport moments beyond the leading order

TL;DR

This paper develops a semiclassical diagrammatic technique to calculate higher-order moments of transport properties in chaotic systems, extending beyond leading order and including energy-dependent and nonlinear statistics.

Contribution

It introduces a novel semiclassical approach to compute transport moments beyond leading order, incorporating correlations and energy dependence, bridging semiclassical and random matrix theory results.

Findings

Derived moments of transmission and reflection eigenvalues for systems with/without time reversal symmetry.

Calculated moments of Wigner delay times and density of states in chaotic Andreev billiards.

Established patterns for higher-order corrections and matched with random matrix theory for generating functions.

Abstract

For chaotic cavities with scattering leads attached, transport properties can be approximated in terms of the classical trajectories which enter and exit the system. With a semiclassical treatment involving fine correlations between such trajectories we develop a diagrammatic technique to calculate the moments of various transport quantities. Namely, we find the moments of the transmission and reflection eigenvalues for systems with and without time reversal symmetry. We also derive related quantities involving an energy dependence: the moments of the Wigner delay times and the density of states of chaotic Andreev billiards, where we find that the gap in the density persists when subleading corrections are included. Finally, we show how to adapt our techniques to non-linear statistics by calculating the correlation between transport moments. In each setting, the answer for the $n$-th moment is obtained for arbitrary $n$ (in the form of a moment generating function) and for up to the three leading orders in terms of the inverse channel number. Our results suggest patterns which should hold for further corrections and by matching with the low order moments available from random matrix theory we derive likely higher order generating functions.