A time dependent Markovian master equation for adiabatic systems and its application to the Cooper pair pumping
arXiv:1108.3216 · doi:10.1103/PhysRevB.84.235140
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.
10 pages, 9 figures
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- Semiclassical Lindblad master equation for spin dynamics
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- Floquet topological phases coupled to environments and the induced photocurrent
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- Geometric quantum pumping in the presence of dissipation
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- Coherent Cooper-pair pumping by magnetic flux control
- Biexponential decay and ultralong coherence of a single qubit
- The failure of semiclassical approach in the dissipative fully-connected Ising model
- Inelastic tunneling through normal and superconducting junctions in the presence of photonic bath within Lindbladian formalism
- Quantum effect of inductance on geometric Cooper-pair transport
- Flux pumping of Cooper pairs through a Josephson Energy-Suppression Pump
- Full counting statistics applied to dissipative Cooper pair pumping