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Physica A Statistical Mechanics and its Applications

Steady state for the combined system of a periodically driven oscillator and a bath in quantum statistics

Yumei Zhang, G�nter Sauermann

Published Mar 1, 1991• 4 citations
Publisher
DOI
10.1016/0378-4371(91)90303-t

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We study probability distribution of a steady state of a periodically driven system coupled to a thermal bath by using a quantum master equation in the weak-coupling limit. It is proved that, even when the external field is strong, the probability distribution is independent of the detailed nature of the thermal bath under the following conditions: (i) the Hamiltonian of the relevant system is bounded and the period of the driving field is short, (ii) the Hamiltonians for the driving field at different times commute, and (iii) the Hamiltonians of the driving field and of the interaction between the relevant system and the thermal bath commute. It is shown that the steady state is described by the Gibbs distribution of the Floquet states of the relevant system at the temperature of the thermal bath.
The Redfield quantum master equation is widely used to study the dynamics of interacting sub-systems that are weakly coupled to baths. Redfield dynamics under secular approximation preserves positivity of the reduced density operator and thermalizes the system into a Gibbs state at equilibrium. Long-time effects arising from non-secular terms are often neglected, but depending on the system spectrum and relative bath couplings, non-secular contributions are shown here to drive the system into a non-Gibbs state. For two strongly interacting quantum oscillators with independent baths at equal temperature, we analyze the microscopic origin of the deviations from Gibbs statistics. Provided that the oscillators are unequally damped by their baths, we show that steady state occupation numbers can significantly deviate from a Boltzmann distribution due to an excitation flux driven by bath-induced coherences between nearly-degenerate oscillator levels. Conditions for the recovery of thermal Gibbs statistics are discussed and experimental signatures suggested.