  We numerically investigate head on collisions of isothermal visco-elastic
spheres. We find that the restitution coefficient oscillates against the impact
speed if the solid viscosity inside the sphere is small enough. We confirm that
the oscillation arises from the resonance between the duration of contact and
the eigen-frequencies of the sphere. This oscillation disappears if there
exists the strong solid viscosity in spheres. We also find that a sinusoidal
behavior of the restitution coefficient against the initial phase in the
eigenmodes for collisions between a thermally activated sphere and a flat wall.
As a result, the restitution coefficient can exceed unity if the impact speed
of the colliding sphere is nearly equal to or slower than the thermal speed. We
have confirmed the existence of the fluctuation theorem for impact processes
through our simulation.
