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.
Quantum Damped Harmonic Oscillator
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abstract
In this chapter we treat the quantum damped harmonic oscillator, and study mathematical structure of the model, and construct general solution with any initial condition, and give a quantum counterpart in the case of taking coherent state as an initial condition. This is a simple and good model of Quantum Mechanics with dissipation which is important to understand real world, and readers will get a powerful weapon for Quantum Physics.
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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.