• DOI:10.1088/1742-5468/ac764c
• Corpus ID: 248524764

Freezing transitions of Brownian particles in confining potentials

@article{MercadoVsquez2022FreezingTO,
  title={Freezing transitions of Brownian particles in confining potentials},
  author={Gabriel Mercado-V{\'a}squez and Denis Boyer and Satya N. Majumdar},
  journal={Journal of Statistical Mechanics: Theory and Experiment},
  year={2022},
  volume={2022}
}

• Gabriel Mercado-Vásquez, D. Boyer, S. Majumdar
• Published 4 May 2022
• Mathematics
• Journal of Statistical Mechanics: Theory and Experiment

We study the mean first passage time (MFPT) to an absorbing target of a one-dimensional Brownian particle subject to an external potential v(x) in a finite domain. We focus on the cases in which the external potential is confining, of the form v(x) = k|x − x 0| n /n, and where the particle’s initial position coincides with x 0. We first consider a particle between an absorbing target at x = 0 and a reflective wall at x = c. At fixed x 0, we show that when the target distance c exceeds a critical value, there exists a nonzero optimal stiffness k opt that minimizes the MFPT to the target. However, when c lies below the critical value, the optimal stiffness k opt vanishes. Hence, for any value of n, the optimal potential stiffness undergoes a continuous ‘freezing’ transition as the domain size is varied. On the other hand, when the reflective wall is replaced by a second absorbing target, the freezing transition in k opt becomes discontinuous. The phase diagram in the (x 0, n)-plane then exhibits three dynamical phases and metastability, with a ‘triple’ point at (x 0/c ≃ 0.171 85, n ≃ 0.395 39). For harmonic or higher order potentials (n ⩾ 2), the MFPT always increases with k at small k, for any x 0 or domain size. These results are contrasted with problems of diffusion under optimal resetting in bounded domains.