Quantum-to-classical crossover of mesoscopic conductance fluctuations

TL;DR

This paper investigates how conductance fluctuations in mesoscopic systems transition from quantum to classical behavior as the system size increases, using theoretical models and simulations.

Contribution

It provides a detailed analysis of the size dependence of conductance fluctuations and identifies the quantum-to-classical crossover governed by Ehrenfest and ergodic times.

Findings

Universal quantum fluctuations dominate for small systems.

Conductance fluctuations scale as M^2 for large systems.

Quantum-to-classical crossover depends on Ehrenfest and ergodic time ratio.

Abstract

We calculate the system-size-over-wave-length ($M$) dependence of sample-to-sample conductance fluctuations, using the open kicked rotator to model chaotic scattering in a ballistic quantum dot coupled by two $N$-mode point contacts to electron reservoirs. Both a fully quantum mechanical and a semiclassical calculation are presented, and found to be in good agreement. The mean squared conductance fluctuations reach the universal quantum limit of random-matrix-theory for small systems. For large systems they increase $\propto M^2$ at fixed mean dwell time $\tau_D \propto M/N$. The universal quantum fluctuations dominate over the nonuniversal classical fluctuations if $N < \sqrt{M}$. When expressed as a ratio of time scales, the quantum-to-classical crossover is governed by the ratio of Ehrenfest time and ergodic time.