Abstract
The quantum problem of a nonlinear oscillator interacting with the field of harmonic oscillators with continuously distributed frequencies is examined. The Heisenberg representation is used. It is demonstrated that after elimination of field variables from the equation, the oscillator dynamics is described by an integro-differential operator equation. It is proved that in the general nonlinear case, an exact solution for the quantum oscillator demonstrates dissipative behavior under certain limitations on the relaxation kernel.
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Dinariev, O.Y. Dynamics of a Quantum Damped Oscillator with Relaxation. Russian Physics Journal 46, 449–456 (2003). https://doi.org/10.1023/A:1026265705498
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DOI: https://doi.org/10.1023/A:1026265705498