Quantum and classical branching flow in space and time

TL;DR

This paper investigates the phenomenon of branching flow in quantum and classical particles within a fluctuating random potential, identifying different parameter regions and comparing quantum and classical behaviors through numerical simulations.

Contribution

It introduces a detailed analysis of quantum and classical branching flow in a 1D time-dependent potential, highlighting the transition between classical and quantum regimes.

Findings

Identification of classical and quantum regions in parameter space.

Comparison of quantum and classical branching behaviors.

Relevance of known analytical results in specific parameter regions.

Abstract

Branching flow -- a phenomenon known for steady wave propagation in two-dimensional weak 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 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 particle's kinetic energy.