Abstract
We investigate ergodic time scales in single-particle tracking by introducing a covariance measure Ω(Δ;t) for the time-averaged relative square displacement recorded in lag-time Δ at elapsed time t. The present model is established in the generalized Langevin equation with a power-law memory function. The ratio Ω(Δ;Δ)/Ω(Δ;t) is shown to obey a universal scaling law for long but finite times and is used to extract the effective ergodic time. We derive a finite-time-averaged Green-Kubo relation and find that, to control the deviations in measurement results from ensemble averages, the ratio Δ/t must be neither too small nor close to unity. Our paper connects the experimental self-averaging property of a tracer with the theoretic velocity autocorrelation function and sheds light on the transition to ergodicity.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.