  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.
