Anomalous heating dynamics in the stochastically driven system.

Driven interacting classical and quantum systems exhibit exotic novel dynamical phases characterised by non-trivial crossover in diffusion properties of these phases.

Imperfect driving has been of interest recently. Such driving can give novel mechanisms to control the dynamical phases in a many-body system. An interesting effect is that transition between a metastable phase to that of a fully chaotic heating phase which is controlled by the drive frequency of the system is controlled by the randomness. We discuss these anomalous diffusive phases in classical incoherently driven kicked many-body rotor and quantum kicked top. En route we also study interaction with the environment through non-Hermitian dynamics.