Master Equation IV: Phase Space Solution Methods

We discuss these methods here only for the Master equation of the damped harmonic oscillator in RWA,

$$\frac{d}{dt}\rho(t) = -i\bar{\Omega}[a^{\dagger}a,{\rho}] - \kappa \Big\{ a^{\dagger} a {\rho} + \rho a^{\dagger} a - 2 a \rho a^{\dagger} \Big\}$$

$$- 2\kappa n_B(\Omega) \Big\{ a^{\dagger} a {\rho} +\rho a a^{\dagger} - a \rho a^{\dagger} -a^{\dagger} \rho a \Big\}.$$ (68)