Dynamical phases in a "multifractal" Rosenzweig-Porter model

Understand

We consider the static and dynamic phases in a Rosenzweig-Porter (RP) random matrix ensemble with the tailed distribution of off-diagonal matrix elements of the form of the large-deviation ansatz.

• We present a general theory of survival probability in such a random-matrix model and show that the {\it averaged} survival probability may decay with time as the simple exponent, as the stretch-exponent and as a power-law or slower.
• Correspondingly, we identify the exponential, the stretch-exponential and the frozen-dynamics phases.
• As an example, we consider the mapping of the Anderson model on Random Regular Graph (RRG) onto the "multifractal" RP model and find exact values of the stretch-exponent $\kappa$ depending on box-distributed disorder in the thermodynamic limit.