Search, Reset, Capture!

The concept of “first passage time”, the moment a process first reaches a specific threshold, is a cornerstone of modern science. However, in many real-world scenarios, the target is not a static object; it is "blinking," spontaneously switching between active and inactive states where it can only be detected during brief windows of opportunity. The Statistical Physics and Nonlinear Dynamics Group (Igor Sokolov) established a new mathematical framework for understanding search dynamics in environments where the target intermittently disappears. While traditional models focus on static goals, they investigated "blinking" targets that switch between active and inactive states. By integrating stochastic resetting, the group demonstrated that even complex, gated targets can be captured efficiently. Their work reveals that these systems retain a unique form of memory, as the target’s state remains independent of the searcher’s reset. This research provides essential tools for optimizing processes ranging from molecular binding in cells to signal detection in electronic networks, offering a vital roadmap for navigating search kinetics in a world of intermittent opportunities. If you want to learn more about blinking targets, read the full article.

Abstract

The first hitting times of a stochastic process, i.e., the first time a process reaches a particular level, are of significant interest across various scientific disciplines, including biology, chemistry, and economics. We modify the standard setup by allowing the target to spontaneously switch between two states, either active or inactive, and investigate the distribution of first hitting times accrued while the target is active. For this setup, we provide closed formulas for the distribution of the first hitting time. Additionally, we can introduce stochastic resetting to the underlying process and, utilizing our results, derive the formulas for the first time the active target is hit by the process under stochastic resetting. Interestingly, we show that resetting in this setup still leaves some memory; the system is no longer Markovian, which prevents a straightforward application of standard techniques. The analytical results are accompanied by computer simulations of Langevin dynamics.