Regensburg 2022 – wissenschaftliches Programm
Bereiche | Tage | Auswahl | Suche | Aktualisierungen | Downloads | Hilfe
DY: Fachverband Dynamik und Statistische Physik
DY 40: Brownian Motion and Anomalous Diffusion
DY 40.3: Vortrag
Donnerstag, 8. September 2022, 10:30–10:45, H20
Stochastic action for tubes: Connecting path probabilities to measurement — •Julian Kappler1, Jannes Gladrow2,3, Ulrich F. Keyser3, and Ronojoy Adhikari1 — 1DAMTP, Cambridge University, Cambridge, UK — 2Microsoft Research, Cambridge, UK — 3Cavendish Laboratory, University of Cambridge, Cambridge, UK
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 contribution 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]. I will furthermore relate our results to the usual path-integral formalism.
[1] J. Gladrow, U. F. Keyser, R. Adhikari, and J. Kappler. Experimental measurement of relative path probabilities and stochastic actions. Phys. Rev. X 11, 031022 (2021). 10.1103/PhysRevX.11.031022
[2] J. Kappler and R. Adhikari. Stochastic action for tubes: Connecting path probabilities to measurement. Physical Review Research 2(2), 023407 (2020). 10.1103/PhysRevResearch.2.023407