Ehrenfest-time dependence of counting statistics for chaotic ballistic systems

TL;DR

This paper investigates how the Ehrenfest time influences the statistical properties of scattering matrices in chaotic ballistic systems, revealing exponential damping effects and contributions from correlated trajectories using semiclassical methods.

Contribution

It provides a detailed semiclassical analysis of Ehrenfest-time effects on scattering matrix correlations, confirming predictions from effective random matrix theory and identifying new trajectory contributions.

Findings

Ehrenfest time causes exponential damping in correlation functions.

Correlated trajectory bands contribute additional effects.

Transport quantities like delay time distributions are significantly affected.

Abstract

Transport properties of open chaotic ballistic systems and their statistics can be expressed in terms of the scattering matrix connecting incoming and outgoing wavefunctions. Here we calculate the dependence of correlation functions of arbitrarily many pairs of scattering matrices at different energies on the Ehrenfest time using trajectory based semiclassical methods. This enables us to verify the prediction from effective random matrix theory that one part of the correlation function obtains an exponential damping depending on the Ehrenfest time, while also allowing us to obtain the additional contribution which arises from bands of always correlated trajectories. The resulting Ehrenfest-time dependence, responsible e.g. for secondary gaps in the density of states of Andreev billiards, can also be seen to have strong effects on other transport quantities like the distribution of delay times.