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DY: Fachverband Dynamik und Statistische Physik
DY 45: Brownian Motion and Anomalous Transport - organized by Ralf Metzler (Potsdam)
DY 45.4: Talk
Wednesday, March 24, 2021, 15:10–15:30, DYc
Stochastic action for tubes: Connecting path probabilities to measurement — •Julian Kappler1, Jannes Gladrow2, Ulrich F. Keyser2, and Ronojoy Adhikari1 — 1Department of Applied Mathematics and Theoretical Physics, Cambridge University, Cambridge, United Kingdom — 2Cavendish Laboratory, University of Cambridge
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 probability of diffusive trajectories to remain within a tube of small but finite radius around a smooth path. This probability can be measured in experiment, via the rate at which trajectories exit the tube for the first time, thereby establishing a link between path probabilities and physical observables. In my talk I will show how this link can be used to both measure ratios of path probabilities [1], and to extend the theoretical stochastic action from individual paths to tubes [2].
[1] J. Gladrow, U. F. Keyser, R. Adhikari, and J. Kappler. Direct experimental measurement of relative path probabilities and stochastic actions. arXiv:2006.16820
[2] J. Kappler and R. Adhikari. Stochastic action for tubes: Connecting path probabilities to measurement. Physical Review Research, 2(2), June 2020.