Quantum Persistence: A Random Walk Scenario

TL;DR

This paper extends the classical concept of persistence to quantum dynamics using quantum random walks, revealing power-law scaling and new exponents, and compares quantum and classical walk behaviors.

Contribution

It introduces a quantum version of persistence, defines related quantities like first-passage time, and analyzes their scaling behavior in quantum random walks.

Findings

Power law scaling of persistence-related quantities

Introduction of a new succession probability measure

Comparison between quantum and classical walk behaviors

Abstract

In this paper we extend the concept of persistence, well defined for classical stochastic dynamics, to the context of quantum dynamics. We demonstrate the idea via quantum random walk and a successive measurement scheme, where persistence is defined as the time during which a given site remains unvisited by the walker. We also investigated the behavior of related quantities, e.g., the first-passage time and the succession probability (newly defined), etc. The study reveals power law scaling behavior of these quantities with new exponents. Comparable features of the classical and the quantum walks are discussed.