Stretched-exponential relaxation in weakly-confined Brownian systems through large deviation theory

2023/09/22 by Defaveri, Lucianno, Barkai, Eli, Kessler, David A.
#FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech)

paper · doi:10.48550/arxiv.2309.13126

Abstract

Stretched-exponential relaxation is a widely observed phenomenon found in ordered ferromagnets as well as glassy systems. One modeling approach connects this behavior to a droplet dynamics described by an effective Langevin equation for the droplet radius with a r^2/3 potential. Here, we study a Brownian particle under the influence of a general confining, albeit weak, potential field that grows with distance as a sub-linear power law. We find that for this memoryless model, observables display stretched-exponential relaxation. The probability density function of the system is studied using a rate function ansatz. We obtain analytically the stretched-exponential exponent along with an anomalous power-law scaling of length with time. The rate function exhibits a point of nonanalyticity, indicating a dynamical phase transition. In particular, the rate function is double-valued both to the left and right of this point, leading to four different rate functions, depending on the choice of initial conditions and symmetry.

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