  Helium diffusion in metals is the basic requirement of nucleation and growth
of bubble, which gives rise to adverse degradation effects on mechanical
properties of structural materials in reactors under irradiation. Multi-scale
modeling scheme has been developed to study effects of helium on the long-term
microstructural evolution. However, the implementation of Arrhenius law based
on the quasi-equilibrium reaction process is not appropriate to predict the
migration behavior of helium in metals due to low-energy barrier. A
coarse-grained formula is required to incorporate the non-equilibrium nature,
e.g., the dissipative friction coefficient $\gamma$. In this paper, we derive
an analytical expression for $\gamma$ based on a coarse-grained model of
Brownian motion upon a periodic potential, in terms of dissipative feature of
the thermal excitations in the many-body dynamical system by constructing an
adiabatic relaxation process, which is then confirmed by a numerical example of
vacancy migration in BCC W. Then the many-body dynamics simulations are
performed for helium migration in BCC W and Fe, where the classical mobility
are obtained and in good agreement with the data from experiments and other
calculations. Finally, we propose a coarse-grained formula for the helium
migration in BCC W and Fe, i.e., Eq.(47) in the context, using the calculated
parameters from the adiabatic relaxation simulations. This work would help to
develop a new multi-scale modeling scheme for effects of helium in metals, as
well as the atomistic reactions with low-energy pathways in materials science.
