A Gaussian displaced thermal ansatz is shown to be form-invariant under the Lindblad dynamics of a damped, forced harmonic oscillator, yielding an explicit quantum limit cycle.
General Solution of the Quantum Damped Harmonic Oscillator II : Some Examples
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abstract
In the preceding paper (arXiv : 0710.2724 [quant-ph]) we have constructed the general solution for the master equation of quantum damped harmonic oscillator, which is given by the complicated infinite series in the operator algebra level. In this paper we give the explicit and compact forms to solutions (density operators) for some initial values. In particular, the compact one for the initial value based on a coherent state is given, which has not been given as far as we know. Moreover, some related problems are presented.
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Lindblad dynamics of the damped and forced quantum harmonic oscillator
A Gaussian displaced thermal ansatz is shown to be form-invariant under the Lindblad dynamics of a damped, forced harmonic oscillator, yielding an explicit quantum limit cycle.