Open quantum random walks: bi-stability on pure states and ballistically induced diffusion

TL;DR

This paper studies open quantum random walks and discovers a transition from simple oscillations to bistable pure states, leading to a change from normal diffusion to ballistic diffusion, with implications for quantum systems and potential experiments.

Contribution

It reveals a transition in internal quantum states affecting orbital motion, introducing a new understanding of diffusion behaviors in open quantum systems.

Findings

Transition from simple oscillations to bistable pure states

Induction of ballistic diffusion with large mean free path

Conversion of mixed states into random pure states

Abstract

Open quantum random walks (OQRWs) deal with quantum random motions on the line for systems with internal and orbital degrees of freedom. The internal system behaves as a quantum random gyroscope coding for the direction of the orbital moves. We reveal the existence of a transition, depending on OQRW moduli, in the internal system behaviors from simple oscillations to random flips between two unstable pure states. This induces a transition in the orbital motions from usual diffusion to ballistically induced diffusion with large mean free path and large effective diffusion constant at large time. We also show that mixed states of the internal system are converted into random pure states during the process. We touch upon possible experimental realizations.