Universal quantum signature of mixed dynamics in antidot lattices

TL;DR

This paper reveals a universal quantum signature in antidot lattices, showing that conductivity fluctuations follow a non-Gaussian distribution with power-law moments derived from bifurcating periodic orbits, applicable in mixed regular and chaotic systems.

Contribution

It introduces a universal quantum signature based on bifurcating periodic orbits in mixed dynamical systems, linking classical bifurcations to quantum transport fluctuations.

Findings

Conductivity fluctuations have a non-Gaussian distribution.

Moments of fluctuations follow a power-law dependence with fractional exponents.

The exponents are universal when long orbits contribute.

Abstract

We investigate phase coherent ballistic transport through antidot lattices in the generic case where the classical phase space has both regular and chaotic components. It is shown that the conductivity fluctuations have a non-Gaussian distribution, and that their moments have a power-law dependence on a semiclassical parameter, with fractional exponents. These exponents are obtained from bifurcating periodic orbits in the semiclassical approximation. They are universal in situations where sufficiently long orbits contribute.