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Zbl 0861.60097
Isar, A.
The harmonic oscillator with dissipation within the theory of open quantum systems.
(English)
[J] Helv. Phys. Acta 67, No.4, 436-449 (1994). ISSN 0018-0238

Summary: Time evolution of the expectation values of various dynamical operators of the harmonic oscillator with dissipation is analytically obtained within the framework of the Lindblad theory for open quantum systems. We deduce the density matrix of the damped harmonic oscillator from the solution of the Fokker-Planck equation for the coherent state representation, obtained from the master equation for the density operator. The Fokker-Planck equation for the Wigner distribution function, subject to either the Gaussian type or the $\delta$-function type of initial conditions, is also solved by using the Wang-Uhlenbeck method. The obtained Wigner functions are two-dimensional Gaussians with different widths.
MSC 2000:
*60K40 Physical appl. of random processes
82C31 Stochastic methods in time-dependent statistical mechanics

Keywords: harmonic oscillator; open quantum systems; Fokker-Planck equation; Wigner distribution; Wang-Uhlenbeck method

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