Non-adiabatic quantum pumping by a randomly moving quantum dot

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 → ∞, 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.

Scattering of accelerated wave packets

“…Floquet scattering is at the heart of some important physical effects, such as photon-assisted tunneling [14,32,33], quantum pumps [34][35][36][37], chaos-assisted tunneling [28,[38][39][40][41], coherent destruction of tunneling [8,42], quantum interference [43], Floquet-Fano resonances [17,31], field-induced barrier transparency [44,45], etc. Scattering from arbitrary time-periodic potentials or from stationary potentials with external non-periodic driving fields has received less attention so far [46][47][48][49][50][51][52][53][54]. The main reason is that the lack of time periodicity makes the scattering dynamics more involved, and in very few special cases an analytical treatment is available [47,50,51].…”