Berlin 2018 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 10: Statistical Physics I (General)

DY 10.5: Vortrag

Montag, 12. März 2018, 11:00–11:15, BH-N 333

Duality between relaxation and first passage in reversible Markov dynamics — •David Hartich and Aljaz Godec — Mathematical Biophysics Group, Max-Planck-Institute for Biophysical Chemistry (Göttingen)

The first passage time characterizes the time until a stochastic process reaches a given threshold for the first time, e.g. the first instance a molecule reaches its target, or the first crossing of an energetic barrier. Complementary to first passage time statistics are well known relaxation processes. Until now an explicit connection between a first passage process and a relaxation process, albeit sought for, remained elusive.

Here, we prove a duality between them in the form of a spectral interlacing enabling us to explicitly determine the full first passage time distribution in terms of a simple relaxation process. To illustrate our theory we analyze diffusion in a triple-well potential, and express the first passage time statistics in terms of relaxation eigenmodes. Finally, we highlight the relevance of our theory by studying first passage kinetics in the so-called few-encounter limit dominated by the fastest reactive trajectories. Our results are relevant for gene regulation processes and the triggering of certain neurodegenerative diseases.