Damping of vortex waves in a superfluid

Abstract

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.

Mutual friction in helium II: a microscopic approach

“…We are only able to mention a couple of papers [18,19], that long ago reached the conclusion that the damping of vortex oscillations due to phonon scattering, should not modify appreciably the value of the friction coefficient calculated for a rigid vortex. The same conclusion was recently obtained for a high-frequency branch of helical waves, within a wider temperature range, including a roton-dominated regime [20].…”

“…[20], which has been shown to lead to a very good agreement with the experimental determinations of the longitudinal friction coefficient D for temperatures below 1 K [18]. From (15) we may see that B consists of two terms arising from the frequencies w w i = 0 and w i = W. Such contributions, however, are weighted by respective factors […”

“…Since the vortex core parameter is assumed to be much less than the wavelength, we have w k << W, being w k the Kelvin wave frequency and W = / r k s v m the cyclotron frequency, with m v the vortex mass per unit length and k the quantum of circulation [1]. This in turn ensures that cyclotron and Kelvin modes become decoupled [15], yielding a Hamiltonian of oscillatory modes given by…”

“…On the other hand, for temperatures above 0.6 K, only the portion of the dispersion curve around the roton minimum makes a significant contribution to the integrand in (15), then making use of the usual approximations in roton calculations [20], we obtain …”

Vortex pseudomomentum and dissipation in a superfluid vortex lattice

“…Moreover, there are different theories [15,16,17] that yield several orders of magnitude higher values for the vortex mass, casting doubt on models based on massless vortices §. On the other hand, it has been recently suggested that an unambiguous vortex mass may not exist, and that ‡ Vortex bending in the form of thermal excitation of vortex oscillation modes, or collective excitations as Tkachenko waves are not expected to be relevant to this discussion [1,12,13]. § There have also been conflicting results for the vortex mass in superconductors [18].…”