Abstract
Abstract
We present a possible quantum analogue of occupation time, a random variable studied in random processes, using a quasi-probability distribution over the sample space of quantum particle paths defined by a generalized weak measurement scheme. Taking this approach, a broad range of statistical properties of quantum occupation time can be studied. We illustrate the theory on a discrete-time quantum walk on a line, where we derive two novel results. We introduce the notions of weak recurrence, weak Pólya number, and weak occupation time plateau.
Funder
Grantová Agentura České Republiky
Centrum pokročilých aplikovaných přírodních věd
Subject
Condensed Matter Physics,Mathematical Physics,Atomic and Molecular Physics, and Optics
Reference34 articles.
1. Theory of local times;Kitada;Il Nuovo Cimento B,1994
2. Occupation times for countable Markov chains. I. Chains with discrete time;Vallander;J. Math. Sci.,1984
3. Occupation times in Markov processes;Sericola;Communications in Statistics. Stochastic Models,2000