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Master equation for an oscillator coupled to the electromagnetic field. (English) Zbl 0890.35116
Summary: The macroscopic description of a quantum oscillator with linear passive dissipation is formulated in terms of a master equation for the reduced density matrix. The procedure used is based on the asymptotic methods of nonlinear dynamics, which enables one to obtain an expression for the general term in the weak coupling expansion. For the special example of a charged oscillator interacting with the electromagnetic field, an explicit form of the master equation through third-order in this expansion is obtained. This form differs from that generally obtained using the rotating wave approximation in that there is no electromagnetic (Lamb) shift and that an explicit expression is given for the decay rate.

35Q40PDEs in connection with quantum mechanics
81V80Applications of quantum theory to quantum optics
82B31Stochastic methods in equilibrium statistical mechanics
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