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Wigner distribution function and entropy of the damped harmonic oscillator within the theory of open quantum systems

Aurelian Isar
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Abstract

The harmonic oscillator with dissipation is studied within the framework of the Lindblad theory for open quantum systems. By using the Wang-Uhlenbeck method, the Fokker-Planck equation, obtained from the master equation for the density operator, is solved for the Wigner distribution function, subject to either the Gaussian type or the $δ$-function type of initial conditions. The obtained Wigner functions are two-dimensional Gaussians with different widths. Then a closed expression for the density operator is extracted. The entropy of the system is subsequently calculated and its temporal behaviour shows that this quantity relaxes to its equilibrium value.

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Aurelian Isar. 1994-04-21. Wigner distribution function and entropy of the damped harmonic oscillator within the theory of open quantum systems. https://arxiv.org/abs/hep-th/9404129

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