Memory Effects in Superfluid Vortex Dynamics

Abstract

The dissipative dynamics of a vortex line in a superfluid is investigated within the frame of a non-Markovian quantal Brownian motion model. Our starting point is a recently proposed interaction Hamiltonian between the vortex and the superfluid quasiparticle excitations, which is generalized to incorporate the effect of scattering from fermion impurities ( 3 He atoms). Thus, a non-Markovian equation of motion for the mean value of the vortex position operator is derived within a weakcoupling approximation. Such an equation is shown to yield, in the Markovian and elastic scattering limits, a 3 He contribution to the longitudinal friction coefficient equivalent to that arising from the Rayfield-Reif formula. Simultaneous Markov and elastic scattering limits are found, however, to be incompatible, since an unexpected breakdown of the Markovian approximation is detected at low cyclotron frequencies. Then, a non-Markovian expression for the longitudinal friction coefficient is derived and computed as a function of temperature and 3 He concentration. Such calculations show that cyclotron frequencies within the range 0.01−0.03 ps −1 yield a very good agreement to the longitudinal friction figures computed from the Iordanskii and Rayfield-Reif formulas for pure 4 He, up to temperatures near 1 K. A similar performance is found for nonvanishing 3 He concentrations, where the comparison is also shown to be very favorable with respect to the available experimental data. Memory effects are shown to be weak and increasing with temperature and concentration.

Damping of vortex waves in a superfluid

“…Such an interaction is modelled through a generic momentum-conserving scattering Hamiltonian, which is used to study the dissipative dynamics of the cyclotron modes. Thus, we shall show that the friction turns out to be essentially unaffected by such oscillations, allowing us to extend our previous conclusions on the memory effects on straight vortex lines [11]. A similar behaviour was long ago reported by Fetter [10] and Sonin [12] for the lowfrequency Kelvin modes, showing that the dissipation of such modes remains essentially equal to that of strictly rectilinear vortices.…”

“…(iii) The drag force on vortices that has been experimentally detected arise from scattering, thus we leave aside from our study the phonon radiation damping [2,11]. We note that such a scattering interaction Hamiltonian is also unusual since it must be nonlinear in the heat bath operators.…”

Mutual friction in helium II: a microscopic approach

“…[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 […”

“…This of course does not mean that vortices would remain straight against the quasiparticle scattering; on the contrary, thermal excitation of Kelvin waves is undoubtedly expected to occur, although details of this process are not evident from expressions (20) and (21). However, some features about such a process may be deduced from our results (17) and (18). First it is convenient to discuss the physical meaning of the frequency w 0 .…”

“…Then, following the methodology of Ref. 18, we have derived a system of non-Markovian equations ruling the time evolution of the quasiparticle populations n q [19], which leads to the following equation of motion for the quasiparticle pseudomomentum: …”