Stochastic resetting in underdamped Brownian motion

Abstract

We consider a single Brownian particle in one dimension in a medium at a constant temperature in the underdamped regime. We stochastically reset the position of the Brownian particle to a fixed point in the space with a constant rate $r$ whereas its velocity evolves irrespective of the position of the particle and stochastic resetting mechanism. The nonequilibrium steady state of the position distribution is studied for this model system. Further, we study the distribution of the position of the particle in the finite time and the approach to the nonequilibrium steady state distribution with time. Numerical simulations are done to verify the analytical results.

References in corpus (35)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Diffusion with Stochastic Resetting
• Intermittent search strategies
• Stochastic thermodynamics: Principles and perspectives
• Diffusion with Optimal Resetting
• First Passage Under Restart
• First order transition for the optimal search time of Lévy flights with resetting
• Optimal stochastic restart renders fluctuations in first passage times universal
• Run and tumble particle under resetting: a renewal approach
• Diffusion in a potential landscape with stochastic resetting
• Stochastic resetting in backtrack recovery by RNA polymerases
• Dynamical transition in the temporal relaxation of stochastic processes under resetting
• Diffusion with stochastic resetting at power-law times
• Random walks with preferential relocations to places visited in the past and their application to biology
• Fluctuating interfaces subject to stochastic resetting
• Optimal diffusive search: nonequilibrium resetting versus equilibrium dynamics
• Boosting search by rare events
• Stochastic thermodynamics of resetting
• Stochastic Search with Poisson and Deterministic Resetting
• Stochastic multiplicative processes with reset events
• Monotonous continuous-time random walks with drift and stochastic reset events
• Large deviations for Markov processes with resetting
• Effects of refractory period on stochastic resetting
• Quantum dynamics with stochastic reset
• Robustness of optimal intermittent search strategies in dimension 1, 2 and 3
• Integral Fluctuation Theorems for Stochastic Resetting Systems
• Random walk with random resetting to the maximum
• Switching and growth for microbial populations in catastrophic responsive environments
• Path-integral formalism for stochastic resetting: Exactly solved examples and shortcuts to confinement
• Spectral properties of simple classical and quantum reset processes
• Efficient search by optimized intermittent random walks
• Interacting Brownian Motion with Resetting
• Diffusion with Resetting Inside a Circle
• Resetting of fluctuating interfaces at power-law times
• Transcription factor search for a DNA promoter in a three-states model

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• Extremal statistics for stochastic resetting systems
• Local time of diffusion with stochastic resetting
• Entropy production in systems with unidirectional transitions
• Random acceleration process under stochastic resetting
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• Stochastic resetting on comb-like structures
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• Diffusion with Partial Resetting
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• Thermodynamic cost of finite-time stochastic resetting
• Work fluctuations for diffusion dynamics submitted to stochastic return
• Condensation transition in large deviations of self-similar Gaussian processes with stochastic resetting
• Non-equilibrium thermodynamics of diffusion in fluctuating potentials
• Anomalous diffusion in random-walks with memory-induced relocations
• Unusual stationary state in Brownian systems with Lorentz force
• First passage time and information of a one-dimensional Brownian particle with stochastic resetting to random positions
• Zero-current Nonequilibrium State in Symmetric Exclusion Process with Dichotomous Stochastic Resetting
• Effect of tax dynamics on linearly growing processes under stochastic resetting: a possible economic model
• Non-linear diffusion with stochastic resetting
• Aggregation with constant kernel under stochastic resetting
• Stochastic resetting and first arrival subjected to Gaussian noise and Poisson white noise
• Effect of stochastic resetting on Brownian motion with stochastic diffusion coefficient
• Optimal Measurement Protocols in Quantum Zeno Effect
• Stochastic resetting with refractory periods: pathway formulation and exact results
• Comparing the roles of time overhead and spatial dimensions on optimal resetting rate vanishing transitions, in Brownian processes with potential bias and stochastic resetting
• Stochastic resetting prevails over sharp restart for broad target distributions
• Stochastic resetting of a population of random walks with resetting-rate-dependent diffusivity
• Symmetric Exclusion Process under Stochastic Power-law Resetting
• Emerging cost-time Pareto front for diffusion with stochastic return
• Active Brownian particle under stochastic position and orientation resetting in a harmonic trap
• Crossover from Anomalous to Normal Diffusion: Ising Model with Stochastic Resetting
• Stochastic resetting in a networked multiparticle system with correlated transitions
• Stochastic Resetting Mitigates Latent Gradient Bias of SGD from Label Noise
• Winding number of a Brownian particle on a ring under stochastic resetting
• The one-dimensional telegraphic process with noninstantaneous stochastic resetting
• Exact fluctuation and long-range correlations in a single-file model under resetting
• Bounding energy growth in friction-less stochastic oscillators
• Inducing and optimizing Markovian Mpemba effect with stochastic reset