Transport in disordered systems: The single big jump approach
In a growing number of strongly disordered and dense systems, the dynamics of a particle pulled by an external force field exhibits superdiffusion. In the context of glass-forming systems, supercooled glasses, and contamination spreading in porous media, it was suggested that this behavior be modele...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2019-12-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.1.033172 |
| _version_ | 1797211626623991808 |
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| author | Wanli Wang Alessandro Vezzani Raffaella Burioni Eli Barkai |
| author_facet | Wanli Wang Alessandro Vezzani Raffaella Burioni Eli Barkai |
| author_sort | Wanli Wang |
| collection | DOAJ |
| description | In a growing number of strongly disordered and dense systems, the dynamics of a particle pulled by an external force field exhibits superdiffusion. In the context of glass-forming systems, supercooled glasses, and contamination spreading in porous media, it was suggested that this behavior be modeled with a biased continuous-time random walk. Here we analyze the plume of particles lagging far behind the mean, with the single big jump principle. Revealing the mechanism of the anomaly, we show how a single trapping time, the largest one, is responsible for the rare fluctuations in the system. These nontypical fluctuations still control the behavior of the mean square displacement, which is the most basic quantifier of the dynamics in many experimental setups. We show how the initial conditions, describing either the stationary state or nonequilibrium case, persist forever in the sense that the rare fluctuations are sensitive to the initial preparation. To describe the fluctuations of the largest trapping time, we modify Fréchet's law from extreme value statistics, taking into consideration the fact that the large fluctuations are very different from those observed for independent and identically distributed random variables. |
| first_indexed | 2024-04-24T10:29:29Z |
| format | Article |
| id | doaj.art-bbc7a7ddf28f4d01a615b76a7757b3ef |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:29:29Z |
| publishDate | 2019-12-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-bbc7a7ddf28f4d01a615b76a7757b3ef2024-04-12T16:47:38ZengAmerican Physical SocietyPhysical Review Research2643-15642019-12-011303317210.1103/PhysRevResearch.1.033172Transport in disordered systems: The single big jump approachWanli WangAlessandro VezzaniRaffaella BurioniEli BarkaiIn a growing number of strongly disordered and dense systems, the dynamics of a particle pulled by an external force field exhibits superdiffusion. In the context of glass-forming systems, supercooled glasses, and contamination spreading in porous media, it was suggested that this behavior be modeled with a biased continuous-time random walk. Here we analyze the plume of particles lagging far behind the mean, with the single big jump principle. Revealing the mechanism of the anomaly, we show how a single trapping time, the largest one, is responsible for the rare fluctuations in the system. These nontypical fluctuations still control the behavior of the mean square displacement, which is the most basic quantifier of the dynamics in many experimental setups. We show how the initial conditions, describing either the stationary state or nonequilibrium case, persist forever in the sense that the rare fluctuations are sensitive to the initial preparation. To describe the fluctuations of the largest trapping time, we modify Fréchet's law from extreme value statistics, taking into consideration the fact that the large fluctuations are very different from those observed for independent and identically distributed random variables.http://doi.org/10.1103/PhysRevResearch.1.033172 |
| spellingShingle | Wanli Wang Alessandro Vezzani Raffaella Burioni Eli Barkai Transport in disordered systems: The single big jump approach Physical Review Research |
| title | Transport in disordered systems: The single big jump approach |
| title_full | Transport in disordered systems: The single big jump approach |
| title_fullStr | Transport in disordered systems: The single big jump approach |
| title_full_unstemmed | Transport in disordered systems: The single big jump approach |
| title_short | Transport in disordered systems: The single big jump approach |
| title_sort | transport in disordered systems the single big jump approach |
| url | http://doi.org/10.1103/PhysRevResearch.1.033172 |
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