Survival probability in the Rosenzweig-Porter random matrix ensemble
We consider the survival probability R(t) in Rosenzweig-Porter Random Matrix ensemble in all three phases: ergodic extended (EE), localized (L) and non-ergodic extended (NEE). We show that R(t) decays exponentially in the NEE phase with the rate equal to the width of a mini-band that is self-organized in the NEE phase and that encodes the fractal dimension of wave functions. The ergodic transition between the NEE and EE phase manifests itself in oscillations in R(t) that survive the thermodynamic limit in EE phase and die in this limit in the NEE phase. In the localized phase R(t→∞)=R(t=0) in the themodynamic limit.