One-dimensional disordered quantum mechanics and Sinai diffusion with random absorbers

Aurélien Grabsch, Christophe Texier, Yves Tourigny

We study the one-dimensional Schrödinger equation with a disordered potential of the form $V(x)=\varphi (x{)}^2+{\varphi }^{\prime }(x)+\kappa (x)$ where $\varphi (x)$ is a Gaussian white noise with mean $\mu g$ and v…