Thermal excitation of waves on quantized vortices

We consider the problem of the thermal excitation of vortex waves on quantized vortex lines and rings. We discover that this problem, which has been largely neglected in the past, apparently presents a ‘‘free energy catastrophe’’ above about 1.85 K; that is, if one naively proceeds to compute the thermally induced vortex waves on rings or lines, the entropy of the waves becomes so large that the free energy of vortices is driven negative, and superfluidity could not exist. Various mechanisms for eliminating this problem are considered; it appears to be necessary to consider the relevant system to be the vortex plus the bath in order to avoid double counting of states. We comment on the relevance of this calculation to the problem of thermally induced nucleation of vortices.