Survival probability in a one-dimensional quantum walk on a trapped lattice

TL;DR

This paper investigates the survival probability of quantum walkers on a one-dimensional lattice with traps, revealing a piecewise stretched exponential decay and a crossover between classical-like behaviors.

Contribution

It provides the first detailed analysis of quantum survival probabilities on trapped lattices, identifying a crossover between different decay regimes both numerically and analytically.

Findings

Quantum walkers exhibit a piecewise stretched exponential survival probability.

A crossover between Rosenstock and Donsker-Varadhan behaviors is observed.

Analytical and numerical methods confirm the decay dynamics.

Abstract

The dynamics of the survival probability of quantum walkers on a one-dimensional lattice with random distribution of absorbing immobile traps are investigated. The survival probability of quantum walkers is compared with that of classical walkers. It is shown that the time dependence of survival probability of quantum walkers has a piecewise stretched exponential character depending on the density of traps in numerical and analytical observations. The crossover between the quantum analogs of the Rosenstock and Donsker-Varadhan behaviors is identified.