The effect of time resolution on the observed first passage times in diffusive dynamics

Abstract

Single-molecule and single-particle tracking experiments are typically unable to resolve fine details of thermal motion at short timescales where trajectories are continuous. We show that, when a diffusive trajectory [Formula: see text] is sampled at finite time intervals δt, the resulting error in measuring the first passage time to a given domain can exceed the time resolution of the measurement by more than an order of magnitude. Such surprisingly large errors originate from the fact that the trajectory may enter and exit the domain while being unobserved, thereby lengthening the apparent first passage time by an amount that is larger than δt. Such systematic errors are particularly important in single-molecule studies of barrier crossing dynamics. We show that the correct first passage times, as well as other properties of the trajectories such as splitting probabilities, can be recovered via a stochastic algorithm that reintroduces unobserved first passage events probabilistically.

Study the delay time influence on the R6G dye attenuation coefficient utilizing laser probe technology

“…Various natural processes, such as atomic motion in chemical processes, vibrating molecules, the absorption and emission of photons, and scattering events, occur rapidly. Some of these events occur on tiny time scales, such as picoseconds (10 − 12 sec) or femtoseconds (10 − 15 sec) (1). Studying these rapid processes is crucial for comprehending the dynamics of different excitations in materials, leading to signi cant improvements in the precision of time-resolved measurements over the last several decades.…”