Space-dependent diffusion with stochastic resetting: A first-passage study

Abstract

We explore the effect of stochastic resetting on the first-passage properties of space-dependent diffusion in presence of a constant bias. In our analytically tractable model system, a particle diffusing in a linear potential $U(x)\propto \mu |x|$ with a spatially varying diffusion coefficient $D(x)=D_0|x|$ undergoes stochastic resetting, i.e., returns to its initial position $x_0$ at random intervals of time, with a constant rate $r$. Considering an absorbing boundary placed at $x_a<x_0$, we first derive an exact expression of the survival probability of the diffusing particle in the Laplace space and then explore its first-passage to the origin as a limiting case of that general result. In the limit $x_a\to 0$, we derive an exact analytic expression for the first-passage time distribution of the underlying process. Once resetting is introduced, the system is observed to exhibit a series of dynamical transitions in terms of a sole parameter, $\nu =(1+\mu D_0^{-1})$, that captures the interplay of the drift and the diffusion. Constructing a full phase diagram in terms of $\nu$, we show that for $\nu <0$, i.e., when the potential is strongly repulsive, the particle can never reach the origin. In contrast, for weakly repulsive or attractive potential ($\nu >0$), it eventually reaches the origin. Resetting accelerates such first-passage when $\nu <3$, but hinders its completion for $\nu >3$. A resetting transition is therefore observed at $\nu =3$, and we provide a comprehensive analysis of the same. The present study paves the way for an array of theoretical and experimental works that combine stochastic resetting with inhomogeneous diffusion in a conservative force-field.

11 pages, 5 figures

References in corpus (42)

• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Diffusion with Stochastic Resetting
• Stochastic Resetting and Applications
• Persistence and First-Passage Properties in Non-equilibrium Systems
• Diffusion with Optimal Resetting
• First Passage Under Restart
• State-dependent diffusion: thermodynamic consistency and its path integral formulation
• Critical Market Crashes
• First order transition for the optimal search time of Lévy flights with resetting
• Entropic transport: Kinetics, scaling and control mechanisms
• Optimal stochastic restart renders fluctuations in first passage times universal
• Experimental realization of diffusion with stochastic resetting
• Diffusion under time-dependent resetting
• Diffusion in a potential landscape with stochastic resetting
• Optimal mean first-passage time for a Brownian searcher subjected to resetting: experimental and theoretical results
• Diffusion with resetting in arbitrary spatial dimension
• Stochastic resetting in backtrack recovery by RNA polymerases
• Diffusion with stochastic resetting at power-law times
• The Michaelis-Menten reaction scheme as a unified approach towards the optimal restart problem
• Optimal first arrival times in Lévy flights with resetting
• Boosting search by rare events
• Influence of Noise on Force Measurements
• Hard Spheres in Vesicles: Curvature-Induced Forces and Particle-Induced Curvature
• Drift without flux: Brownian walker with a space dependent diffusion coefficient
• Stochastic Search with Poisson and Deterministic Resetting
• Brownian Dynamics of a Sphere Between Parallel Walls
• Search with home returns provides advantage under high uncertainty
• Effects of refractory period on stochastic resetting
• First passage of a particle in a potential under stochastic resetting: a vanishing transition of optimal resetting rate
• Péclet number governs transition to acceleratory restart in drift-diffusion
• Single-molecule theory of enzymatic inhibition predicts the emergence of inhibitor-activator duality
• Infinite Ergodic Theory for Heterogeneous Diffusion Processes
• Diffusion with resetting in a logarithmic potential
• Landau theory of restart transitions
• Switching and growth for microbial populations in catastrophic responsive environments
• Disordering effects of color in nonequilibrium phase transitions induced by multiplicative noise
• Path-integral formalism for stochastic resetting: Exactly solved examples and shortcuts to confinement
• Diffusion with stochastic resetting is invariant to return speed
• Invariants of motion with stochastic resetting and space-time coupled returns
• Magnetization dynamics: path-integral formalism for the stochastic Landau-Lifshitz-Gilbert equation
• Heavy tails in the distribution of time-to-solution for classical and quantum annealing
• Noise correlation-induced splitting of Kramers' escape rate from a metastable state

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• Fick-Jacobs description and first passage dynamics for diffusion in a channel under stochastic resetting
• First passage of a diffusing particle under stochastic resetting in bounded domains with spherical symmetry
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• Rate enhancement of gated drift-diffusion process by optimal resetting
• First-passage functionals for Ornstein Uhlenbeck process with stochastic resetting
• Non-linear diffusion with stochastic resetting
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• Efficiency of random search with space-dependent diffusivity
• Random acceleration process on finite intervals under stochastic restarting
• Dichotomous flow with thermal diffusion and stochastic resetting
• Stochastic resetting prevails over sharp restart for broad target distributions
• Random resetting in search problems
• Random search with resetting in heterogeneous environments
• Random-search efficiency in a bounded interval with spatially heterogeneous diffusion coefficient
• Drift-diffusive resetting search process with stochastic returns: speed-up beyond optimal instantaneous return
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