  The damping of vortex cyclotron modes is investigated within a generalized
quantum theory of vortex waves. Similarly to the case of Kelvin modes, the
friction coefficient turns out to be essentially unchanged under such
oscillations, but it is shown to be affected by appreciable memory corrections.
On the other hand, the nonequilibrium energetics of the vortex, which is
investigated within the framework of linear response theory, shows that its
memory corrections are negligible. The vortex response is found to be of the
Debye type, with a relaxation frequency whose dependence on temperature and
impurity concentration reflects the complexity of the heat bath and its
interaction with the vortex.
