Semiclassical Approach to Chaotic Quantum Transport

TL;DR

This paper introduces a semiclassical method for calculating universal transport properties in chaotic quantum systems, accounting for trajectory pairs and quadruplets, and considers effects of symmetry and magnetic fields.

Contribution

It presents a novel semiclassical framework that systematically computes transport quantities using trajectory pairs and quadruplets, including symmetry crossover effects.

Findings

Energy-averaged conductance governed by pairs of trajectories

Conductance variance and shot noise require quadruplet trajectories

Diagrammatic rules enable calculation of trajectory contributions

Abstract

We describe a semiclassical method to calculate universal transport properties of chaotic cavities. While the energy-averaged conductance turns out governed by pairs of entrance-to-exit trajectories, the conductance variance, shot noise and other related quantities require trajectory quadruplets; simple diagrammatic rules allow to find the contributions of these pairs and quadruplets. Both pure symmetry classes and the crossover due to an external magnetic field are considered.