Optimal potentials for diffusive search strategies

Abstract

We consider one dimensional diffusive search strategies subjected to external potentials. The location of a single target is drawn from a given probability density function (PDF) $f_G(x)$ and is fixed for each stochastic realization of the process. We optimize the quality of the search strategy as measured by the mean first passage time (MFPT) to the position of the target. For a symmetric but otherwise arbitrary distribution $f_G(x)$ we find the optimal potential that minimizes the MFPT. The minimal MFPT is given by a nonstandard measure of the dispersion, which can be related to the cumulative Rényi entropy. We compare optimal times in this model with optimal times obtained for the model of diffusion with stochastic resetting, in which the diffusive motion is interrupted by intermittent jumps (resets) to the initial position. Additionally, we discuss an analogy between our results and a so-called square-root principle.

16 pages, 2 figures, 1 table

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Cited by in corpus (9)

• Stochastic Resetting and Applications
• On subdiffusive continuous time random walks with stochastic resetting
• Driving rapidly while remaining in control: classical shortcuts from Hamiltonian to stochastic dynamics
• Diffusion with Resetting Inside a Circle
• Comparison of two models of tethered motion
• Robust random search with scale-free stochastic resetting
• Freezing transitions of Brownian particles in confining potentials
• Stochastic resetting prevails over sharp restart for broad target distributions
• How target distributions shape optimal stochastic resetting