  Biomolecular folding, at least in simple systems, can be described as a two
state transition in a free energy landscape with two deep wells separated by a
high barrier. Transition paths are the short part of the trajectories that
cross the barrier. Average transition path times and, recently, their full
probability distribution have been measured for several biomolecular systems,
e.g. in the folding of nucleic acids or proteins. Motivated by these
experiments, we have calculated the full transition path time distribution for
a single stochastic particle crossing a parabolic barrier, focusing on the
underdamped regime. Our analysis thus includes inertial terms, which were
neglected in previous studies. These terms influence the short time scale
dynamics of a stochastic system, and can be of experimental relevance in view
of the short duration of transition paths. We derive the full transition path
time distribution in the underdamped case and discuss the similarities and
differences with the high friction (overdamped) limit.
