Severe slowing-down and universality of the dynamics in disordered interacting many-body systems: ageing and ultraslow diffusion
- Low-dimensional, many-body systems are often characterized by ultraslow dynamics. We study a labelled particle in a generic system of identical particles with hard-core interactions in a strongly disordered environment. The disorder is manifested through intermittent motion with scale-free sticking times at the single particle level. While for a non-interacting particle we find anomalous diffusion of the power-law form < x(2)(t)> similar or equal to t(alpha) of the mean squared displacement with 0 < alpha < 1, we demonstrate here that the combination of the disordered environment with the many-body interactions leads to an ultraslow, logarithmic dynamics < x(2)(t)> similar or equal to log(1/2)t with a universal 1/2 exponent. Even when a characteristic sticking time exists but the fluctuations of sticking times diverge we observe the mean squared displacement < x(2)(t)> similar or equal to t(gamma) with 0 < gamma < 1/2, that is slower than the famed Harris law < x(2)(t)> similar or equal to t(1/2) without disorder. We rationalize theLow-dimensional, many-body systems are often characterized by ultraslow dynamics. We study a labelled particle in a generic system of identical particles with hard-core interactions in a strongly disordered environment. The disorder is manifested through intermittent motion with scale-free sticking times at the single particle level. While for a non-interacting particle we find anomalous diffusion of the power-law form < x(2)(t)> similar or equal to t(alpha) of the mean squared displacement with 0 < alpha < 1, we demonstrate here that the combination of the disordered environment with the many-body interactions leads to an ultraslow, logarithmic dynamics < x(2)(t)> similar or equal to log(1/2)t with a universal 1/2 exponent. Even when a characteristic sticking time exists but the fluctuations of sticking times diverge we observe the mean squared displacement < x(2)(t)> similar or equal to t(gamma) with 0 < gamma < 1/2, that is slower than the famed Harris law < x(2)(t)> similar or equal to t(1/2) without disorder. We rationalize the results in terms of a subordination to a counting process, in which each transition is dominated by the forward waiting time of an ageing continuous time process.…
Verfasserangaben: | Lloyd P. Sanders, Michael A. Lomholt, Ludvig Lizana, Karl Fogelmark, Ralf MetzlerORCiDGND, Tobias Ambjoernsson |
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DOI: | https://doi.org/10.1088/1367-2630/16/11/113050 |
ISSN: | 1367-2630 |
Titel des übergeordneten Werks (Englisch): | New journal of physics : the open-access journal for physics |
Verlag: | IOP Publ. Ltd. |
Verlagsort: | Bristol |
Publikationstyp: | Wissenschaftlicher Artikel |
Sprache: | Englisch |
Jahr der Erstveröffentlichung: | 2014 |
Erscheinungsjahr: | 2014 |
Datum der Freischaltung: | 27.03.2017 |
Freies Schlagwort / Tag: | ageing; continuous time random walks; single-file diffusion |
Band: | 16 |
Seitenanzahl: | 14 |
Fördernde Institution: | Swedish Research Council [2009-2924, 2012-4526]; Academy of Finland (FiDiPro scheme) |
Organisationseinheiten: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
Peer Review: | Referiert |
Publikationsweg: | Open Access |