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  • Open Access

Resetting of underdamped Brownian motion

Hanna Franke and Igor M. Sokolov*

  • *Contact author: igor.sokolov@physik.hu-berlin.de
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Phys. Rev. E 113, 064125 – Published 11 June, 2026

DOI: https://doi.org/10.1103/qyl8-6q9h

Abstract

We study underdamped Brownian motion under Poissonian resetting, where we apply two different full resetting procedures. The first one resets both position and velocity to zero, while the second one resets the displacement to zero but takes the velocity after resetting to follow a Maxwell distribution. In both cases, the marginal probability density function (PDF) of the displacement in the stationary state shows exponential tails for large displacements, but the singularities at the mode of the PDF are very different and specific for the corresponding resetting prescription: in the first case, one has p(x)∼|x|−1/3, while in the second one, one gets p(x)∼−ln|x|. The convergence of the PDF to a stationary one is investigated by examining its excess kurtosis as a function of time. Applying two sets of initial conditions for the second resetting procedure, we show that the behavior of the excess kurtosis for short times is highly sensitive to these.

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Phys. Rev. E 113, 064125– Published 11 June, 2026
  • Received 18 December 2025
  • Accepted 26 May 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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