Random-walk topological transition revealed via electron counting

TL;DR

This paper uncovers topological effects in a classical stochastic random walk model, demonstrating that topological invariants can be observed through escape time distributions without relying on wave coherence.

Contribution

It introduces a topological invariant in a stochastic model, linking it to observable escape time distributions, thus bridging topological physics and classical stochastic processes.

Findings

Topological phase signatures appear in escape time distributions.

A topological invariant is defined in counting-field space.

Classical stochastic models can exhibit topological effects.

Abstract

The appearance of topological effects in systems exhibiting a non-trivial topological band structure strongly relies on the coherent wave nature of the equations of motion. Here, we reveal topological dynamics in a classical stochastic random walk version of the Su-Schrieffer-Heeger model with no relation to coherent wave dynamics. We explain that the commonly used topological invariant in the momentum space translates into an invariant in a counting-field space. This invariant gives rise to clear signatures of the topological phase in an associated escape time distribution.