Engineering stable quantum currents at bulk boundaries

TL;DR

This paper investigates quantum transport phenomena in lattice systems, demonstrating the existence of stable quantum currents and spectrum properties that are topologically robust and model-independent.

Contribution

It provides new proofs of charge transport and spectrum coverage, and constructs explicit quantum coins for stable directed currents in quantum walks.

Findings

Existence of non-trivial charge transport.

Absolutely continuous spectrum covers the entire unit circle.

Explicit constructions of coins for stable quantum currents.

Abstract

We study transport properties of discrete quantum dynamical systems on the lattice, in particular Coined Quantum Walks and the Chalker--Coddington model. We prove existence of a non trivial charge transport and that the absolutely continuous spectrum covers the whole unit circle under mild assumptions. For Quantum Walks we exhibit explicit constructions of coins which imply existence of stable directed quantum currents along classical curves. The results are of topological nature and independent of the details of the model.