Quantum occupation time

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 Polya number, and weak occupation time plateau.