Abstract
We study the first-passage time distribution (FPTD) for a freely diffusing particle starting at in one dimension, to a target located at , averaged over the initial position drawn from a normalized distribution of finite width . We show the averaged FPTD undergoes a sharp dynamical phase transition from a two-peak structure for to a single-peak structure for . This transition is generated by the competition of two characteristic timescales and , where is the diffusion coefficient. A very good agreement is found between theoretical predictions and experimental results obtained with a Brownian bead whose diffusion is initialized by an optical trap which determines the initial distribution . We show that this transition is robust: It is present for all initial conditions with a finite , in all dimensions, and also exists for more general stochastic processes going beyond free diffusion.
- Received 14 February 2021
- Revised 20 April 2021
- Accepted 22 June 2021
DOI:https://doi.org/10.1103/PhysRevE.104.L012102
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