Multiple path transport in quantum networks

TL;DR

This paper derives an exact expression for current in quantum networks with multiple paths, extending adiabatic and non-adiabatic regimes analysis beyond traditional Landau-Zener models.

Contribution

It introduces a multiple-path continuity equation for quantum transport, generalizing previous adiabatic results to include non-adiabatic regimes and complex level mixing.

Findings

Exact current expression for quantum networks with multiple paths

Unified treatment of adiabatic and non-adiabatic regimes

Inclusion of Wigner-type energy level mixing effects

Abstract

We find an exact expression for the current ($I$) that flows via a tagged bond from a site ("dot") whose potential ($u$) is varied in time. We show that the analysis reduces to that of calculating time dependent probabilities, as in the stochastic formulation, but with splitting (branching) ratios that are not bounded within $[0,1]$. Accordingly our result can be regarded as a multiple-path version of the continuity equation. It generalizes results that have been obtained from adiabatic transport theory in the context of quantum "pumping" and "stirring". Our approach allows to address the adiabatic regime, as well as the Slow and Fast non-adiabatic regimes, on equal footing. We emphasize aspects that go beyond the familiar picture of sequential Landau-Zener crossings, taking into account Wigner-type mixing of the energy levels.