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}
}
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… 
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References

SHOWING 1-10 OF 61 REFERENCES

Resetting with stochastic return through linear confining potential

We consider motion of an overdamped Brownian particle subject to stochastic resetting in one dimension. In contrast to the usual setting where the particle is instantaneously reset to a preferred

Intermittent resetting potentials

We study the non-equilibrium steady states (NESS) and first passage properties of a Brownian particle with position X subject to an external confining potential of the form V(X) = μ|X|, and that is

First passage of a particle in a potential under stochastic resetting: A vanishing transition of optimal resetting rate.

Interestingly, it is found that for a sufficiently strong external potential, the advantageous optimal resetting rate r_{*} vanishes with a deviation from the critical strength of the potential as a power law with an exponent β which appears to be universal.

Freezing Transition in the Barrier Crossing Rate of a Diffusing Particle.

It is shown that the freezing transition occurs when in the associated quantum problem, the gap between the ground state (bound) and the continuum of scattering states vanishes.

Resetting dynamics in a confining potential

We study Brownian motion in a confining potential under a constant-rate resetting to a reset position x 0. The relaxation of this system to the steady-state exhibits a dynamic phase transition, and

Diffusion with optimal resetting

We consider the mean time to absorption by an absorbing target of a diffusive particle with the addition of a process whereby the particle is reset to its initial position with rate r. We consider

Dynamical phase transition in the first-passage probability of a Brownian motion.

A very good agreement is found between theoretical predictions and experimental results obtained with a Brownian bead whose diffusion is initialized by an optical trap which determines the initial distribution g(x_{0}/σ), and this transition is robust.

First passage under stochastic resetting in an interval.

A comprehensive study of the first-passage properties of the Brownian particle diffusing in a one-dimensional interval with absorbing end points and shows how this set-up is a manifestation of a success-failure problem.

Optimal mean first-passage time for a Brownian searcher subjected to resetting: Experimental and theoretical results

The optimal mean first-passage time as a function of the resetting period/rate for different values of the ratio b = L/$\sigma$ is studied and an interesting phase transtion at a critical value b = bc is found.

Random acceleration process under stochastic resetting

  • Prashant Singh
  • Mathematics
    Journal of Physics A: Mathematical and Theoretical
  • 2020
We consider the motion of a randomly accelerated particle in one dimension under stochastic resetting mechanism. Denoting the position and velocity by x and v respectively, we consider two different
...