TY - JOUR

T1 - Stretched-exponential relaxation in weakly confined Brownian systems through large deviation theory

AU - Defaveri, Lucianno

AU - Barkai, Eli

AU - Kessler, David A.

PY - 2024/2/1

Y1 - 2024/2/1

N2 - 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 an 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 sublinear 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.

AB - 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 an 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 sublinear 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.

UR - http://www.scopus.com/inward/record.url?scp=85188045787&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.109.L022102

DO - 10.1103/PhysRevE.109.L022102

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C2 - 38491584

AN - SCOPUS:85188045787

SN - 2470-0045

VL - 109

SP - L022102

JO - Physical Review E

JF - Physical Review E

IS - 2

ER -