Universal Quantum Signatures of Chaos in Ballistic Transport

TL;DR

This paper derives universal statistical properties of conductance in ballistic quantum dots with chaotic dynamics, using random matrix theory to describe different symmetry classes and their impact on transport phenomena.

Contribution

It introduces a universal framework for analyzing conductance fluctuations in chaotic quantum dots via Dyson's circular ensembles, providing explicit formulas for various symmetry classes.

Findings

Universal conductance fluctuation formulas derived for different symmetry classes.

Distribution P(g) of conductance g computed, showing class-dependent behavior.

Results applicable to quantum dots with ballistic transport and chaotic classical dynamics.

Abstract

The conductance of a ballistic quantum dot (having chaotic classical dynamics and being coupled by ballistic point contacts to two electron reservoirs) is computed on the single assumption that its scattering matrix is a member of Dyson's circular ensemble. General formulas are obtained for the mean and variance of transport properties in the orthogonal (beta=1), unitary (beta=2), and symplectic (beta=4) symmetry class. Applications include universal conductance fluctuations, weak localization, sub-Poissonian shot noise, and normal-metal-superconductor junctions. The complete distribution P(g) of the conductance g is computed for the case that the coupling to the reservoirs occurs via two quantum point contacts with a single transmitted channel. The result P(g)=g^(-1+beta/2) is qualitatively different in the three symmetry classes. ***Submitted to Europhysics Letters.****