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The Langevin equation includes a random force to maintain equilibrium andprevent friction from bringing motion to a standstill; but for ballisticmotion, the random force is often neglected. Here, we use the Langevin equationfor molecular dynamics simulations of 2.76 eV H-atoms experiencing electronicfriction in collisions with 300 K metals, where a random force arises fromthermal electron-hole pairs. Simulations without the random force faildramatically to reproduce experiment, although the incidence energy is muchlarger than $k_\text{B}T$. We analyze the Ornstein-Uhlenbeck process to showthat this is a general property of ballistic particles experiencing frictionunder the influence of thermal fluctuations.

The random force in molecular dynamics with electronic friction