Non-equilibrium transition from dissipative quantum walk to classical random walk

TL;DR

This paper analytically investigates the non-equilibrium transition of a quantum walk to a classical random walk due to dissipation from a phonon bath, highlighting decoherence, entropy, and quantum correlations.

Contribution

It provides a theoretical analysis of how dissipation causes a quantum walk to transition into a classical random walk, including the dynamics of quantum entanglement and decoherence.

Findings

Suppression of ballistic peaks due to dissipation

Quantitative analysis of von Neumann entropy and quantum purity

Transition from quantum to classical behavior with increasing dissipation

Abstract

We have investigated the time-evolution of a free particle in interaction with a phonon thermal bath, using the tight-binding approach. A dissipative quantum walk can be defined and many important non-equilibrium decoherence properties can be investigated analytically. The non-equilibrium statistics of a pure initial state have been studied. Our theoretical results indicate that the evolving wave-packet shows the suppression of Anderson's boundaries (ballistic peaks) by the presence of dissipation. Many important relaxation properties can be studied quantitatively, such as von Neumann's entropy and quantum purity. In addition, we have studied Wigner's function. The time-dependent behavior of the quantum entanglement between a free particle -in the lattice- and the phonon bath has been characterized analytically. This result strongly suggests the non-trivial time-dependence of the off-diagonal elements of the reduced density matrix of the system. We have established a connection between the quantum decoherence and the dissipative parameter arising from interaction with the phonon bath. The time-dependent behavior of quantum correlations has also been pointed out, showing continuous transition from quantum random walk to classical random walk, when dissipation increases.