#### 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.

Done