Alladi Ramakrishnan Hall

First-passage functionals for Ornstein Uhlenbeck process with stochastic resetting and Non-uniqueness of quantum first detection time

Ashutosh Dubey

IMSc

In this talk, I will discuss about the statistical
properties of first passage Brownian functionals of an
Ornstein-Uhlenbeck process in the presence of stochastic resetting. We
consider a one dimensional set-up where the diffusing particle sets
off from some initial location and resets to the same initial location
at a certain rate. The particle diffuses in a harmonic potential which
is centered around the origin and the center also serves as an
absorbing boundary for the particle. In this set-up, we investigate
the first moment of local time density, residence or occupation time
and the first passage time. In particular, we find that resetting can
either prolong or shorten the mean residence and first passage time
depending on the system parameters. The transition between these two
behaviors or phases can be characterized precisely in terms of optimal
resetting rates, which interestingly undergo a continuous transition
as we vary the trap stiffness. We characterize this transition and
identify the critical -parameter \& -coefficient for both cases. In
the later part, I will talk about the quantum first passage detection
problem. The model consists of a quantum particle moving on a discrete
lattice sites and its dynamics is described by tight binding type
Hamiltonian. Here, we show that by placing an onsite potential
outside the region between the initial position of the particle and
the detector, one can change the asymptotic behaviour of the first
detection time and equivalently of the survival probability of the
particle.