Correlation effects in a discrete quantum random walk

TL;DR

This paper introduces new models of quantum random walks with memory effects, analyzes their correlation properties, and proposes a correlation exponent as a tool to study non-Markovian dynamics in quantum systems.

Contribution

The paper presents novel history-dependent quantum random walk models and introduces a correlation exponent to quantify memory effects in these systems.

Findings

Correlation effects are significant in the models studied.

The correlation exponent effectively characterizes non-Markovian behavior.

Models can be extended to more complex physical scenarios.

Abstract

We introduce history-dependent discrete-time quantum random walk models by adding uncorrelated memory terms and also by modifying Hamiltonian of the walker to include couplings with memory-keeping agents. We next numerically study the correlation effects in these models. We also propose a correlation exponent as a relevant and promising tool for investigation of correlation or memory (hence non-Markovian) effects. Our analysis can easily be applied to more realistic models in which different regimes may emerge because of competition between different underlying physical mechanisms.