Dynamical phases in a ``multifractal'' Rosenzweig-Porter model

We consider the static and dynamic phases in a Rosenzweig-Porter (RP) random matrix ensemble with tailed distribution of off-diagonal elements form large-deviation ansatz. present general theory survival probability such random-matrix model show that {\it averaged} may decay time as simple exponent, stretch-exponent power-law or slower. Correspondingly, we identify exponential, stretch-exponential frozen-dynamics phases. As an example, mapping Anderson on Random Regular Graph (RRG) onto "multifractal" RP find exact values $\kappa$ depending box-distributed disorder thermodynamic limit. another example logarithmically-normal (LN-RP) analytically its phase diagram exponent $\kappa$. In addition, our allows to compute shift apparent transition lines at finite system size case associated RRG LN-RP same symmetry function hopping, finite-size multifractal "phase" emerges near tricritical point which is also localization transition.