Pantheon SEMPARIS Le serveur des séminaires parisiens Paris

Statut Confirmé
Domaines cond-mat.mes-hall
Date Jeudi 23 Janvier 2020
Heure 14:00
Institut LPTMC
Salle Jussieu tower 13-12 5th floor room 5-23
Nom de l'orateur Meerson
Prenom de l'orateur Baruch
Addresse email de l'orateur
Institution de l'orateur Racah institue of physics, Hebrew university of Jerusalem, Israël
Titre Geometrical optics of constrained Brownian motion: three short stories
Résumé The optimal fluctuation method — essentially geometrical optics — gives a deep insight into large deviations of Brownian motion, and it achieves this purpose by simple means. Here we illustrate these points by telling three short stories about Brownian motions, ``pushed" into a large-deviation regime by constraints. Story 1 deals with a long-time survival of a Brownian particle in 1 + 1 dimension against absorption by a wall which advances according to a power law $x_w (t)  \sim t^{\gamma}$, where  $\gamma> 1/2$. We also calculate the large deviation function (LDF) of the particle position at an earlier time, conditional on the survival by a later time. Story 2 addresses a stretched Brownian motion above an absorbing obstacle in the plane. We compute the short-time LDF of the position of the surviving Brownian particle at an intermediate point. In story 3 we compute the short-time LDF of the winding angle of a Brownian particle wandering around a reflecting disk in the plane. In all three stories we uncover singularities of the LDFs which can be interpreted as dynamical phase transitions and which have a simple geometric origin. We also use the small-deviation limit of the geometrical optics to reconstruct the distribution of typical fluctuations. We argue that, in stories 1 and 2, this is the Ferrari–Spohn distribution. The talk is based on a recent paper by B. Meerson and N. R. Smith, J. Phys. A: Math. Theor. 52, 415001 (2019) .
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