The Rosenzweig-Porter random matrix ensemble serves as a qualitative phenomenological model for the level statistics and fractality of eigenstates across many-body localization transition in static systems. We propose unitary (circular) analogue this ensemble, which similarly captures phenomenology periodically driven (Floquet) define outcome Dyson Brownian motion process. show numerical eviden...

In this paper, we consider an extension of the Rosenzweig-Porter model, L\'evy-RP (L-RP) in which off-diagonal matrix elements are broadly distributed, providing a more realistic benchmark to develop effective description nonergodic extended (NEE) states interacting many-body disordered systems. We put forward simple, general, and intuitive argument that allows one unveil multifractal structure...

We investigate the spectra of adjacency matrices multiplex networks under random matrix theory (RMT) framework. Through extensive numerical experiments, we demonstrate that upon multiplexing two networks, combined network exhibit superposition Gaussian orthogonal ensemble (GOE)s for very small strength followed by a smooth transition to GOE statistics with an increase in strength. Interestingly...