Anderson localization from classical trajectories

TL;DR

This paper demonstrates that Anderson localization in ballistic quasi-one-dimensional conductors can be explained solely through classical trajectories, linking classical chaos to quantum interference effects.

Contribution

It introduces a classical trajectory-based framework to understand Anderson localization in ballistic conductors, bridging classical chaos and quantum interference.

Findings

Classical trajectories proliferate exponentially at large scales.

Interference among similar trajectories suppresses conductance.

The mechanism is described via transition probabilities and phase space analysis.

Abstract

We show that Anderson localization in quasi-one dimensional conductors with ballistic electron dynamics, such as an array of ballistic chaotic cavities connected via ballistic contacts, can be understood in terms of classical electron trajectories only. At large length scales, an exponential proliferation of trajectories of nearly identical classical action generates an abundance of interference terms, which eventually leads to a suppression of transport coefficients. We quantitatively describe this mechanism in two different ways: the explicit description of transition probabilities in terms of interfering trajectories, and an hierarchical integration over fluctuations in the classical phase space of the array cavities.