Quantum and classical branching flow in space and time

Branching flow, a phenomenon known for steady wave propagation in two-dimensional weakly correlated random potential, is also present in the time-dependent Schr\"odinger equation for a single particle in one dimension, moving in a fluctuating random potential. We explore the two-dimensional parameter space of this model using numerical simulations and identify its classical regions, where just one classical parameter is sufficient for its specification, and its quantum region, where such a simplification is not possible. We also identify the region of the parameter space where known analytical results of a classical white noise model are relevant. Qualitative behavior of quantum and classical particle dynamics is discussed in terms of branching time scale and a new time scale related to a particle's kinetic energy.