Continuous gated first-passage processes
Yuval Scher1, Aanjaneya Kumar2, M S Santhanam2
1School of Chemistry, Center for the Physics & Chemistry of Living Systems, Ratner Institute for Single Molecule Chemistry, and the Sackler Center for Computational Molecular & Materials Science, Tel Aviv University, 6997801 Tel Aviv, Israel.
Reports on Progress in Physics. Physical Society (Great Britain)
|August 29, 2024
Summary
This study introduces a renewal framework to solve complex gated first-passage processes, offering analytical solutions for detection times previously unknown. The findings reveal universal properties and extend to higher dimensions.
Area of Science:
- Physics
- Mathematics
- Physical Chemistry
Background:
- Gated first-passage processes are crucial in many fields but lack analytical solutions for complex targets.
- Problems like diffusion to gated intervals, disks, or spheres remain analytically intractable.
Purpose of the Study:
- To develop a unified analytical framework for continuous gated first-passage processes.
- To derive solutions for problems, including interval targets, that have previously evaded exact solutions.
Main Methods:
- A novel renewal framework is presented to analyze gated first-passage processes.
- The framework connects gated problem solutions to ungated dynamics.
- The formalism is extended to higher dimensions.
Main Results:
- The renewal framework provides unified solutions for various gated first-passage problems.
- Solutions for interval targets, previously unsolved, are now obtainable.
- The study reveals universal properties, asymptotic behaviors, and intermediate-time regimes.
Conclusions:
- The developed framework offers analytical tools for continuous gated first-passage processes.
- This work provides significant insights into the dynamics of these processes across diverse scientific domains.
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