SKM 2023 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 32: Focus Session: Physics of Fluctuating Paths (joint session DY/CPP)
DY 32.11: Vortrag
Mittwoch, 29. März 2023, 17:45–18:00, ZEU 160
Sojourn probabilities for diffusive dynamics with state-dependent friction: Theory and experiment — Alice Thorneywork1, 2, Jannes Gladrow2, 3, Ulrich F. Keyser2, Ronojoy Adhikari4, and •Julian Kappler4, 5 — 1Department of Chemistry, University of Oxford, Oxford, United Kingdom — 2Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom — 3Microsoft Research, Cambridge, United Kingdom — 4Department of Applied Mathematics and Theoretical Physics, Cambridge University, Cambridge, United Kingdom — 5Fakultät für Physik, Ludwig-Maximilians-Universität, München, Germany
The trajectories of diffusion processes are continuous but nondifferentiable, and each occurs with vanishing probability. This introduces a gap between theory, where path probabilities are used in many contexts, and experiment, where only events with nonzero probability are measurable. We bridge this gap by considering the sojourn probability, i.e. the probability for diffusive trajectories to remain within a tube of small but finite radius around a smooth path. For systems with state-dependent diffusivity, we show that the sojourn probability is characterized by a functional that is different from all previously reported multiplicative-noise stochastic actions. We corroborate our theoretical results by comparison to experimentally measured sojourn probabilities for a colloidal particle in a corrugated microchannel. Our work directly connects the discussion of path probabilities for diffusive dynamics with state-dependent friction to physical observables.