Diffusion in periodic, correlated random forcing landscapes
| hal.structure.identifier | Laboratoire Ondes et Matière d'Aquitaine [LOMA] | |
| dc.contributor.author | DEAN, David S | |
| hal.structure.identifier | Laboratoire de Physique Théorique et Modèles Statistiques [LPTMS] | |
| dc.contributor.author | GUPTA, Shamik | |
| hal.structure.identifier | Laboratoire de Physique Théorique de la Matière Condensée [LPTMC] | |
| dc.contributor.author | OSHANIN, Gleb | |
| hal.structure.identifier | Laboratoire de Physique Théorique et Modèles Statistiques [LPTMS] | |
| dc.contributor.author | ROSSO, Alberto | |
| hal.structure.identifier | Laboratoire de Physique Théorique et Modèles Statistiques [LPTMS] | |
| dc.contributor.author | SCHEHR, Grégory | |
| dc.date.created | 2014-07-15 | |
| dc.date.issued | 2014 | |
| dc.identifier.issn | 1751-8113 | |
| dc.description.abstractEn | We study the dynamics of a Brownian particle in a strongly correlated quenched random potential defined as a periodically-extended (with period $L$) finite trajectory of a fractional Brownian motion with arbitrary Hurst exponent $H \in (0,1)$. While the periodicity ensures that the ultimate long-time behavior is diffusive, the generalised Sinai potential considered here leads to a strong logarithmic confinement of particle trajectories at intermediate times. These two competing trends lead to dynamical frustration and result in a rich statistical behavior of the diffusion coefficient $D_L$: Although one has the typical value $D^{\rm typ}_L \sim \exp(-\beta L^H)$, we show via an exact analytical approach that the positive moments ($k>0$) scale like $\langle D^k_L \rangle \sim \exp{[-c' (k \beta L^{H})^{1/(1+H)}]}$, and the negative ones as $\langle D^{-k}_L \rangle \sim \exp(a' (k \beta L^{H})^2)$, $c'$ and $a'$ being numerical constants and $\beta$ the inverse temperature. These results demonstrate that $D_L$ is strongly non-self-averaging. We further show that the probability distribution of $D_L$ has a log-normal left tail and a highly singular, one-sided log-stable right tail reminiscent of a Lifshitz singularity. | |
| dc.description.sponsorship | Marcheurs Browniens répulsifs et matrices aléatoires - ANR-11-BS04-0013 | |
| dc.language.iso | en | |
| dc.publisher | IOP Publishing | |
| dc.rights.uri | http://creativecommons.org/licenses/by-sa/ | |
| dc.subject.en | Brownian motion | |
| dc.subject.en | quenched disorder | |
| dc.subject.en | anomalous dynamics | |
| dc.title.en | Diffusion in periodic, correlated random forcing landscapes | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1088/1751-8113/47/37/372001 | |
| dc.subject.hal | Physique [physics]/Matière Condensée [cond-mat]/Mécanique statistique [cond-mat.stat-mech] | |
| dc.identifier.arxiv | 1406.2612 | |
| bordeaux.journal | Journal of Physics A: Mathematical and Theoretical | |
| bordeaux.page | 372001 | |
| bordeaux.volume | 47 | |
| bordeaux.issue | 37 | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01069753 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01069753v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20of%20Physics%20A:%20Mathematical%20and%20Theoretical&rft.date=2014&rft.volume=47&rft.issue=37&rft.spage=372001&rft.epage=372001&rft.eissn=1751-8113&rft.issn=1751-8113&rft.au=DEAN,%20David%20S&GUPTA,%20Shamik&OSHANIN,%20Gleb&ROSSO,%20Alberto&SCHEHR,%20Gr%C3%A9gory&rft.genre=article |
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