Quasiprobability distributions for open quantum systems within the Lindblad theory
Аурелиан Исар, W. Scheid, Aurel Sǎndulescu · Journal of Mathematical Physics · 1991
The Lindblad master equation for the damped quantum harmonic oscillator is transformed into Fokker–Planck equations for quasiprobability distributions. A comparative study is made for the Glauber P representation, the antinormal-ordering Q representation and the Wigner W representation. It will be proven that the variances for the damped harmonic oscillator found with these representations are the same. By solving the Fokker–Planck equations in the steady state, it will be shown that the quasiprobability distributions are two-dimensional Gaussians with widths determined by the diffusion coefficients.