TY  - JOUR
A1  - Singh, Rishu Kumar
A1  - Górska, Katarzyna
A1  - Sandev, Trifce
T1  - General approach to stochastic resetting
JF  - Physical review : E, Statistical, nonlinear and soft matter physics
N2  - We address the effect of stochastic resetting on diffusion and subdiffusion process. For diffusion we find that mean square displacement relaxes to a constant only when the distribution of reset times possess finite mean and variance. In this case, the leading order contribution to the probability density function (PDF) of a Gaussian propagator under resetting exhibits a cusp independent of the specific details of the reset time distribution. For subdiffusion we derive the PDF in Laplace space for arbitrary resetting protocol. Resetting at constant rate allows evaluation of the PDF in terms of H function. We analyze the steady state and derive the rate function governing the relaxation behavior. For a subdiffusive process the steady state could exist even if the distribution of reset times possesses only finite mean.
Y1  - 2022
U6  - https://doi.org/10.1103/PhysRevE.105.064133
SN  - 2470-0045
SN  - 2470-0053
VL  - 105
IS  - 6
PB  - American Physical Society
CY  - College Park
ER  - 
TY  - JOUR
A1  - Singh, Rishu Kumar
A1  - Metzler, Ralf
A1  - Sandev, Trifce
T1  - Resetting dynamics in a confining potential
JF  - Journal of physics : A, Mathematical and theoretical
N2  - We study Brownian motion in a confining potential under a constant-rate resetting to a reset position x(0). The relaxation of this system to the steady-state exhibits a dynamic phase transition, and is achieved in a light cone region which grows linearly with time. When an absorbing boundary is introduced, effecting a symmetry breaking of the system, we find that resetting aids the barrier escape only when the particle starts on the same side as the barrier with respect to the origin. We find that the optimal resetting rate exhibits a continuous phase transition with critical exponent of unity. Exact expressions are derived for the mean escape time, the second moment, and the coefficient of variation (CV).
KW  - diffusion
KW  - resetting
KW  - barrier escape
KW  - first-passage
Y1  - 2020
U6  - https://doi.org/10.1088/1751-8121/abc83a
SN  - 1751-8113
SN  - 1751-8121
VL  - 53
IS  - 50
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  -