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.
2 More- Received 23 August 2011
DOI:https://doi.org/10.1103/PhysRevB.84.235140
©2011 American Physical Society