Transient aging in fractional Brownian and Langevin-equation motion
Stochastic processes driven by stationary fractional Gaussian noise, that is, fractional Brownian motion and fractional Langevin-equation motion, are usually considered to be ergodic in the sense that, after an algebraic relaxation, time and ensemble averages of physical observables coincide. Recent...
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| Format: | Journal article |
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American Physical Society
2013
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| _version_ | 1826289814692954112 |
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| author | Kursawe, J Schulz, J Metzler, R |
| author_facet | Kursawe, J Schulz, J Metzler, R |
| author_sort | Kursawe, J |
| collection | OXFORD |
| description | Stochastic processes driven by stationary fractional Gaussian noise, that is, fractional Brownian motion and fractional Langevin-equation motion, are usually considered to be ergodic in the sense that, after an algebraic relaxation, time and ensemble averages of physical observables coincide. Recently it was demonstrated that fractional Brownian motion and fractional Langevin-equation motion under external confinement are transiently nonergodic—time and ensemble averages behave differently—from the moment when the particle starts to sense the confinement. Here we show that these processes also exhibit transient aging, that is, physical observables such as the time-averaged mean-squared displacement depend on the time lag between the initiation of the system at time t=0 and the start of the measurement at the aging time ta. In particular, it turns out that for fractional Langevin-equation motion the aging dependence on ta is different between the cases of free and confined motion. We obtain explicit analytical expressions for the aged moments of the particle position as well as the time-averaged mean-squared displacement and present a numerical analysis of this transient aging phenomenon. |
| first_indexed | 2024-03-07T02:34:39Z |
| format | Journal article |
| id | oxford-uuid:a8602af3-c96e-4e5f-b97b-7afa654e6c74 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T02:34:39Z |
| publishDate | 2013 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | oxford-uuid:a8602af3-c96e-4e5f-b97b-7afa654e6c742022-03-27T03:01:10ZTransient aging in fractional Brownian and Langevin-equation motionJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:a8602af3-c96e-4e5f-b97b-7afa654e6c74Mathematical Institute - ePrintsAmerican Physical Society2013Kursawe, JSchulz, JMetzler, RStochastic processes driven by stationary fractional Gaussian noise, that is, fractional Brownian motion and fractional Langevin-equation motion, are usually considered to be ergodic in the sense that, after an algebraic relaxation, time and ensemble averages of physical observables coincide. Recently it was demonstrated that fractional Brownian motion and fractional Langevin-equation motion under external confinement are transiently nonergodic—time and ensemble averages behave differently—from the moment when the particle starts to sense the confinement. Here we show that these processes also exhibit transient aging, that is, physical observables such as the time-averaged mean-squared displacement depend on the time lag between the initiation of the system at time t=0 and the start of the measurement at the aging time ta. In particular, it turns out that for fractional Langevin-equation motion the aging dependence on ta is different between the cases of free and confined motion. We obtain explicit analytical expressions for the aged moments of the particle position as well as the time-averaged mean-squared displacement and present a numerical analysis of this transient aging phenomenon. |
| spellingShingle | Kursawe, J Schulz, J Metzler, R Transient aging in fractional Brownian and Langevin-equation motion |
| title | Transient aging in fractional Brownian and Langevin-equation motion |
| title_full | Transient aging in fractional Brownian and Langevin-equation motion |
| title_fullStr | Transient aging in fractional Brownian and Langevin-equation motion |
| title_full_unstemmed | Transient aging in fractional Brownian and Langevin-equation motion |
| title_short | Transient aging in fractional Brownian and Langevin-equation motion |
| title_sort | transient aging in fractional brownian and langevin equation motion |
| work_keys_str_mv | AT kursawej transientaginginfractionalbrownianandlangevinequationmotion AT schulzj transientaginginfractionalbrownianandlangevinequationmotion AT metzlerr transientaginginfractionalbrownianandlangevinequationmotion |