Random-walk topological transition revealed via electron counting

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.

11 pages including supplementary information, comments are welcome

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• Unified Light-Matter Floquet Theory and its Application to Quantum Communication
• Higher-Order Photon Statistics as a New Tool to Reveal Hidden Excited States in a Plasmonic Cavity
• Machine Learning of Knot Topology in Non-Hermitian Band Braids
• Selectable diffusion direction with topologically protected edge modes
• Quantum versus Population Dynamics over Cayley Graphs