Abstract
The investigation of the dynamical universality classes of quantum systems is an important, and rather less explored, aspect of non-equilibrium physics. In this work, considering the out-of-equilibrium dynamics of spinless fermions in a one-dimensional quasiperiodic model with and without a periodic driving, we report the existence of the dynamical one-parameter based Family-Vicsek (FV) scaling of the "quantum surface-roughness" associated with the particle-number fluctuations. In absence of periodic driving, the model is interestingly shown to host a subdiffusive critical phase separated by two subdiffusive critical lines and a triple point from other phases. An analysis of the fate of critical phase in the presence of (inter-phase) driving indicates that the critical phase is quite fragile and has a tendency to get absorbed into the delocalized or localized regime depending on the driving parameters. Furthermore, periodic driving can conspire to show quantum Kardar-Parisi-Zhang (KPZ)-like superdiffusive dynamical behavior, which seems to have no classical counterpart. We further construct an effective Floquet Hamiltonian, which qualitatively captures this feature occurring in the driven model