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SUMMARY:Diffusion processes in tubular neighborhoods of smooth paths - Jul
 ian Kappler\, DAMTP
DTSTART:20200121T130000Z
DTEND:20200121T140000Z
UID:TALK136435@talks.cam.ac.uk
CONTACT:Etienne Fodor
DESCRIPTION:A fundamental question associated with stochastic dynamics is 
 to meaningfully quantify the probability of individual trajectories. Since
  the probability of a single trajectory is zero\, theoretical results only
  quantify relative likelihoods of pairs of trajectories. This diminishes t
 heir practical applicability as it is not possible to evaluate\, experimen
 tally\, a ratio of two vanishingly small quantities. We overcome this limi
 tation by considering\, instead\, the probability of stochastic trajectori
 es to remain within a tube of small but finite radius R around a smooth pa
 th. In the limit of vanishing radius\, the ratio of probabilities for pair
 s of tubes approaches the stochastic action for the relative likelihood of
  pairs of trajectories. This provides\, for the first time\, a direct meth
 od of relating the stochastic action to experiment. We subsequently charac
 terize the stochastic dynamics 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 resu
 lts.
LOCATION:MR11\, CMS
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