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CPP: Fachverband Chemische Physik und Polymerphysik

CPP 39: Focus Session: Physics of Fluctuating Paths (joint session DY/CPP)

CPP 39.11: Talk

Wednesday, March 29, 2023, 17:45–18:00, ZEU 160

Sojourn probabilities for diffusive dynamics with state-dependent friction: Theory and experiment — Alice Thorneywork^{1, 2}, Jannes Gladrow^{2, 3}, Ulrich F. Keyser², Ronojoy Adhikari⁴, and •Julian Kappler^{4, 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.