Non-adiabatic quantum pumping by a randomly moving quantum dot

Stanislav Derevyanko, Daniel Waltner

Research output: Contribution to journalArticlepeer-review


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 (BP) 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 BP 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.

Original languageAmerican English
Article number305302
Number of pages25
JournalJournal of Physics A: Mathematical and Theoretical
Issue number30
StatePublished - 31 Jul 2015


  • Brownian motion
  • Levy walks
  • delta potential
  • nonadiabatic quantum pumping
  • phases
  • scattering theory

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • General Physics and Astronomy
  • Statistics and Probability
  • Mathematical Physics
  • Modelling and Simulation


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