$x$-$p$ Representation

We now can write

$$D = \frac{1}{\sqrt{2}}\left(\left(c_-+c_+\right)x + i \left(c_--c_+\r... ...ega)}{\sqrt{2}} \left(x \coth \left(\frac{\beta\Omega}{2}\right) + i p \right),$$

where we again used $\coth \left({\beta\Omega}/{2}\right) = 1+2n_B(\Omega).$ Using $E=D^{\dagger}$, one obtains the Master equation from the Non-RWA Model in secular approximation,

$$\fbox{$ \begin{array}{rcl} \displaystyle \frac{d}{dt}\rho&=& -i[H... ...rho(\Omega)}{2} \left(xp\rho -\rho px -p\rho x+ x\rho p\right). \end{array}$\ }$$ (67)