Section: New Results

Reactive trajectories for molecular dynamics

Participants : Frédéric Cérou, Arnaud Guyader, Florent Malrieu.

See  3.3 and  4.2 .

This is a collaboration with Tony Lelièvre (CERMICS, Ecole des Ponts ParisTech).

Consider a one-dimensional Brownian motion in a double well potential. It is known that, as its variance goes to zero, the Brownian particle has to wait for a longer and longer time to jump from a well to the other. This metastable behavior is described by the Freidlin–Wentzell theory. We are investigating the length of the paths between the last passage time in the bottom of a well and the hitting time of the other one (reactive trajectory). In the case of an Ornstein–Uhlenbeck process between the wells, we obtained the remarkable result that the time length of the reactive trajectories converges in distribution when the noise intensity goes to zero, to a Gumbel random variable shifted by a deterministic term growing like minus the logarithm of the noise intensity. Our numerical simulations are also in good accordance with this theoretical result. We are also very close to extend this result to more general one dimensional diffusion processes.