Status | Confirmed |
Seminar Series | SEM-LPTMC |
Subjects | cond-mat.mes-hall |
Date | Thursday 23 January 2020 |
Time | 14:00 |
Institute | LPTMC |
Seminar Room | Jussieu tower 13-12 5th floor room 5-23 |
Speaker's Last Name | Meerson |
Speaker's First Name | Baruch |
Speaker's Email Address | |
Speaker's Institution | Racah institue of physics, Hebrew university of Jerusalem, Israël |
Title | Geometrical optics of constrained Brownian motion: three short stories |
Abstract | 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 FerrariSpohn 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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