Quantum Persistence: A Random Walk Scenario

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.

6 pages, 6 figures, revtex4. To be published in PRE

References in corpus (2)

• Recurrence properties of unbiased coined quantum walks on infinite $d$-dimensional lattices
• Dynamics of unvisited sites in presence of mutually repulsive random walkers

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• The spectral dimension controls the decay of the quantum first detection probability
• Quantum random walk : effect of quenching
• Persistence of unvisited sites in quantum walks on a line
• Multi-player conflict avoidance through entangled quantum walks
• Transition in Splitting Probabilities of Quantum Walks
• Fluctuations and Persistence in Quantum Diffusion on Regular Lattices