Stretched-exponential relaxation in weakly-confined Brownian systems through large deviation theory
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866916132162633728 |
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| author | Defaveri, Lucianno Barkai, Eli Kessler, David A. |
| author_facet | Defaveri, Lucianno Barkai, Eli Kessler, David A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_13126 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Stretched-exponential relaxation in weakly-confined Brownian systems through large deviation theory Defaveri, Lucianno Barkai, Eli Kessler, David A. Statistical Mechanics 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. |
| title | Stretched-exponential relaxation in weakly-confined Brownian systems through large deviation theory |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2309.13126 |