Non-adiabatic quantum pumping by a randomly moving quantum dot

TL;DR

This paper investigates non-adiabatic quantum charge pumping in a randomly moving quantum dot, revealing that in the long-term, the charge fluctuations grow faster than adiabatic predictions due to non-adiabatic effects.

Contribution

It introduces a separation of wavefunction components in non-adiabatic regimes and derives exact propagator expressions for diffusive and ballistic quantum dot motions.

Findings

Wavefunction splits into Berry-phase and non-adiabatic parts at large times

Disorder-averaged current is mainly determined by the Berry phase

Charge fluctuations grow faster than adiabatic theory predicts

Abstract

We look at the time dependent fluctuations of the electrical charge in an open 1D quantum system represented by a quantum dot experiencing random lateral motion. In essentially non-adiabatic settings we study both diffusive and ballistic (Levy) regimes of the barrier motion where the electric current as well as the net pumped electric charge experience random fluctuations over the static background. We show that in the large-time limit, $t \to \infty$, the wavefunction is naturally separated into the Berry-phase component (resulting from the singular part of the wave amplitude in the co-moving frame) and the non-adiabatic correction (arising from fast oscillating, slow decaying tails of the same amplitude). Based on this separation we report two key results: Firstly, the disorder averaged wave function and current are asymptotically mainly determined by the same Berry phase contribution that applies in the case of adiabatic motion. Secondly, after a short transition period the pumped electric charge exhibits fluctuations that grow much faster than predicted by the adiabatic theory. We also derive the exact expressions for the average propagator (in the co-moving basis representation) for the diffusive and ballistic types of motion considered.