Time-dependent Markovian master equation for adiabatic systems and its application to Cooper-pair pumping

I. Kamleitner and A. Shnirman
Phys. Rev. B 84, 235140 – Published 22 December 2011; Erratum Phys. Rev. B 87, 039903 (2013)

Abstract

For adiabatically and periodically manipulated dissipative quantum systems, we derive, using Floquet theory, a simple Markovian master equation. Contrary to some previous works, we explicitly take into account the time dependence of the Hamiltonian and, therefore, obtain a master equation with a time-dependent dissipative part. We illustrate our theory with two examples and compare our results with the previously proposed master equations. In particular, we consider the problem of Cooper-pair pumping and demonstrate the inadequacy of the secular (rotating-wave) approximation when calculating the pumped charge. The secular approximation producing a master equation of the Lindblad-type approximates well the quantum state (density matrix) of the system, while to determine the pumped charge, a non-Lindblad master equation beyond the rotating-wave approximation is necessary.

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  • Received 23 August 2011

DOI:https://doi.org/10.1103/PhysRevB.84.235140

©2011 American Physical Society

Erratum

Authors & Affiliations

I. Kamleitner1 and A. Shnirman1,2

  • 1Institut für Theory der Kondensierten Materie, Karlsruher Institut für Technologie, DE-76128 Karlsruhe, Germany
  • 2DFG-Center for Functional Nanostructures (CFN), DE-76128 Karlsruhe, Germany

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Issue

Vol. 84, Iss. 23 — 15 December 2011

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