Decoherence and Quantum Walks: anomalous diffusion and ballistic tails

TL;DR

This paper presents a quantum walk model where strong environmental coupling leads to anomalous diffusion with ballistic tails, challenging the typical expectation of classical diffusive behavior in open quantum systems.

Contribution

It introduces a novel quantum walk model with strong system-environment coupling resulting in unusual long-time dynamics, including ballistic spreading and weak localization effects.

Findings

Mean square displacement shows ballistic behavior at long times

Presence of weak localization near the origin

Counter-example to the expectation of diffusive behavior in open quantum systems

Abstract

The common perception is that strong coupling to the environment will always render the evolution of the system density matrix quasi-classical (in fact, diffusive) in the long time limit. We present here a counter-example, in which a particle makes quantum transitions between the sites of a d-dimensional hypercubic lattice whilst strongly coupled to a bath of two-level systems which 'record' the transitions. The long-time evolution of an initial wave packet is found to be most unusual: the mean square displacement of the particle density matrix shows long-range ballitic behaviour, but simultaneously a kind of weakly-localised behaviour near the origin. This result may have important implications for the design of quantum computing algorithms, since it describes a class of quantum walks.