DEAN, David S; GUPTA, Shamik; OSHANIN, Gleb; ROSSO, Alberto; SCHEHR, Grégory

doi:10.1088/1751-8113/47/37/372001

Métadonnées

Afficher la notice complète

Licence d’utilisation du document

http://creativecommons.org/licenses/by-sa/

DEAN, David S
Laboratoire Ondes et Matière d'Aquitaine [LOMA]

GUPTA, Shamik
Laboratoire de Physique Théorique et Modèles Statistiques [LPTMS]

OSHANIN, Gleb
Laboratoire de Physique Théorique de la Matière Condensée [LPTMC]

Langue

Article de revue

Ce document a été publié dans

Journal of Physics A: Mathematical and Theoretical. 2014, vol. 47, n° 37, p. 372001

IOP Publishing

Résumé en anglais

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.< Réduire

Mots clés en anglais

Brownian motion

quenched disorder

anomalous dynamics

DOI

http://dx.doi.org/10.1088/1751-8113/47/37/372001

Project ANR

Marcheurs Browniens répulsifs et matrices aléatoires - ANR-11-BS04-0013

Origine

Importé de hal

Unités de recherche

Laboratoire Ondes et Matière d'Aquitaine (LOMA) - UMR 5798