Next seminar : Séminaire du LPTMS: Baruch Meerson

Tuesday, January 21 2020 at 11:00:00

Geometrical optics of constrained Brownian motion: three short stories

Baruch Meerson (Racah Institute of Physics, Hebrew University of Jerusalem)

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 xw(t)~ tγ, where γ > 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).

Last Highlight : Comment une barrière peut être plus haute et plus facile à franchir

Que ce soit en physique, en chimie ou en biologie, les vitesses de réaction sont très souvent limitées par des barrières énergétiques à franchir grâce à l'activation thermique. Des travaux menés par le LPTMS et le LPS d'Orsay en collaboration avec l'Université de Cambridge,  démontrent que l'on peut jouer sur le profil d'une barrière pour en accélérer le franchissement par un objet Brownien : l'optimisation des profils conduit aux barrières les plus élevées.

https://inp.cnrs.fr/fr/cnrsinfo/comment-une-barriere-peut-etre-plus-haute-et-plus-facile-franchir


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