Vortex dissipation in clean superconductors at ultralow temperatures

For a three-dimensional superconductor, we establish the conditions for cro ssover from quantum to classical dissipation depending on the vortex veloci ty, on the electron-phonon relaxation rate, and on the impurity mean free p ath in the regime of ultralow temperatures. The crossover occurs for such a vortex velocity that the dissipated power is large enough to heat electron s in the core above the temperature of the order of the distance omega(0) b etween localized levels in the vortex core [C. Caroli, P. G. de Gennes, and J. Matricon, Phys. Lett. 9, 307 (1964)]. The electronic temperature T* com es into play in the superclean limit omega(0) tau(imp) much greater than 1 and takes the part of the heat bath temperature T. The electronic temperatu re can be essentially higher than T due to a very slow inelastic relaxation for T similar to omega(0). [S0163-1829(99)07025-3].