I am looking for a reference to the fundamental solution\Greens function of the two dimensional Kramers PDE
$$\partial_t \rho(t,x,v) = -v\frac{\partial}{dx}\rho(t,x,v)+\gamma\frac{\partial}{\partial v}(v\rho(t,x,v)) +\frac{\partial^2}{dv^2}\rho(t,x,v) $$
with $x,v\in\mathbb{R}$ and some constant $\gamma>0$. I have really looked hard and am confused why this is not readily available on the net. I found it in this book but Elements of 'Nonequilibrium Statistical Mechanics' by V. Balakrishnan but there are typos in this work. Does anyone have a correct reference?