Aubin Archambault, Caroline Crauste-Thibierge, Alberto Imparato, Sergio Ciliberto, Ludovic Bellon, submitted to Phys. Rev. Lett.
arXiv: 2607.01405
The distribution of the first passage time tfp for the position x to overcome a threshold xB is calculated in an underdamped harmonic oscillator. The proof combines several approaches based on the determination of the eigenvalues of the Kramers differential operator for the intermediate and long time regimes and on a Hamiltonian approximation for the short times. The theoretical predictions are in excellent agreement with the results of an experiment on an underdamped micro-cantilever. The knowledge of the tfp distribution opens the way to several applications, among them the precise estimation of the power of information engines, which we have also experimentally checked.