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Stretched-exponential relaxation in weakly confined Brownian systems through large deviation theory
Lucianno Defaveri1, Eli Barkai2, David A Kessler1
1Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel.
Physical Review. E
|March 16, 2024
Summary
This study reveals stretched-exponential relaxation in a Brownian particle model with a sublinear potential. The findings indicate a dynamical phase transition and anomalous scaling, offering insights into complex system dynamics.
Area of Science:
- Statistical Mechanics
- Condensed Matter Physics
- Complex Systems
Background:
- Stretched-exponential relaxation is observed in diverse systems like ferromagnets and glasses.
- Existing models link this to droplet dynamics and specific potentials.
Purpose of the Study:
- To investigate stretched-exponential relaxation in a Brownian particle model with a general sublinear power-law confining potential.
- To analyze the probability density function and identify phase transitions.
Main Methods:
- Modeling a Brownian particle under a weak, sublinear power-law potential.
- Employing a rate-function ansatz to study the probability density function.
- Analytical derivation of the stretched-exponential exponent and scaling laws.
Main Results:
- Demonstrated stretched-exponential relaxation for a memoryless model.
- Derived the stretched-exponential exponent and anomalous length-time scaling.
- Identified a dynamical phase transition via a nonanalytic rate function.
Conclusions:
- The model successfully reproduces stretched-exponential relaxation under a general sublinear potential.
- The rate function's nonanalyticity signifies a dynamical phase transition.
- The double-valued nature of the rate function suggests complex behavior dependent on initial conditions.
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