Originally conceived
to describe thermal diffusion, the Langevin
equation includes both a frictional drag and a random force, the latter
representing thermal fluctuations first seen as Brownian motion. The
random force is crucial for the diffusion problem as it explains why
friction does not simply bring the system to a standstill. When using
the Langevin equation to describe ballistic motion, the importance
of the random force is less obvious and it is often omitted, for example,
in theoretical treatments of hot ions and atoms interacting with metals.
Here, friction results from electronic nonadiabaticity (electronic
friction), and the random force arises from thermal electron–hole
pairs. We show the consequences of omitting the random force in the
dynamics of H-atom scattering from metals. We compare molecular dynamics
simulations based on the Langevin equation to experimentally derived
energy loss distributions. Despite the fact that the incidence energy
is much larger than the thermal energy and the scattering time is
only about 25 fs, the energy loss distribution fails to reproduce
the experiment if the random force is neglected. Neglecting the random
force is an even more severe approximation than freezing the positions
of the metal atoms or modelling the lattice vibrations as a generalized
Langevin oscillator. This behavior can be understood by considering
analytic solutions to the Ornstein–Uhlenbeck process, where
a ballistic particle experiencing friction decelerates under the influence
of thermal fluctuations.