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CATEGORIES:DAMTP Statistical Physics and Soft Matter Seminar
SUMMARY:Diffusion processes in tubular neighborhoods of sm
ooth paths - Julian Kappler\, DAMTP
DTSTART;TZID=Europe/London:20200121T130000
DTEND;TZID=Europe/London:20200121T140000
UID:TALK136435AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/136435
DESCRIPTION:A fundamental question associated with stochastic
dynamics is to meaningfully quantify the probabili
ty of individual trajectories. Since the probabili
ty of a single trajectory is zero\, theoretical re
sults only quantify relative likelihoods of pairs
of trajectories. This diminishes their practical a
pplicability as it is not possible to evaluate\, e
xperimentally\, a ratio of two vanishingly small q
uantities. We overcome this limitation by consider
ing\, instead\, the probability of stochastic traj
ectories to remain within a tube of small but fini
te radius R around a smooth path. In the limit of
vanishing radius\, the ratio of probabilities for
pairs of tubes approaches the stochastic action fo
r the relative likelihood of pairs of trajectories
. This provides\, for the first time\, a direct me
thod of relating the stochastic action to experime
nt. We subsequently characterize the stochastic dy
namics within the tubular ensemble\, by calculatin
g the spatial probability density and the entropy
production. In the limit of vanishing radius both
reduce to the established single-trajectory result
s.
LOCATION:MR11\, CMS
CONTACT:Etienne Fodor
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