Longitudinal and transverse forces on a vortex in superfluid⁴He

Abstract

We examine the transverse and longitudinal components of the drag force upon a straight vortex line due to the scattering of liquid 4 He excitations. For this purpose, we consider a recently proposed Hamiltonian that describes the dissipative motion of a vortex, giving an explicit expression for the vortex-quasiparticle interaction. The involved dissipative coefficients are obtained in terms of the reservoir correlation function. Most of our explicit calculations are concerned to the range of temperatures below 0.4 K, at which the reservoir is composed by phonon quasiparticle excitations. We also discuss some important implications in the determination of possible scattering processes leading to dissipation, according to the values of vortex mass found in the literature.

Friction force on a vortex due to the scattering of superfluid excitations in helium II

“…2(c-d) must not have an appreciable weight in the integrand of Eq. (19). On the other hand, we have found that the weight of roton R + ↔ R − transitions is important.…”

“…Most of such transitions are of course between R ± rotons since, if we neglect from D 0 in Eq. (19) only phonon-roton transitions, we obtain that the solid curve in Fig. 4 would be decreased less than 8 %.…”

“…The above description shows that for temperatures up to 0.4 K, only the phonon part of the dispersion curve is significant in evaluating the expression (19), consequently if we set q 1 = k and ω k = c s k in Eq. (19), we obtain the result (13) as expected. 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 Eq.…”

“…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 Eq. (19), then one can safely make use of the usual approximations in roton calculations. 24 In fact, the Landau parabolic approximation, ω k = ∆/h +h(k − k 0 ) 2 /2µ, leads to two values for q j , q 1 = k and q 2 = 2k 0 − k; in addition the Bose distribution in Eq.…”

“…24 In fact, the Landau parabolic approximation, ω k = ∆/h +h(k − k 0 ) 2 /2µ, leads to two values for q j , q 1 = k and q 2 = 2k 0 − k; in addition the Bose distribution in Eq. (19) can be well approximated by the Boltzmann distribution, and the range of integration can be extended in such an equation from −∞ to +∞ with negligible error. Under such approximations we have in the roton dominated regime,…”