Dynamics of superfluid films

A theory of the dynamical properties of a helium film near its superfluid transition is presented. Details are given of previously published results on the linear response of the film to a substrate oscillation. A key role is played by the diffusive motion of quantized vortices, which become free above the thermodynamic Kosterlitz-Thouless temperature $T_c$ but which only exist as bound pairs below $T_c$. An analogy with a two-dimensional plasma is presented and used. Contact is made with experiments involving oscillating substrates. The nucleation of single vortices from pairs is calculated, and this process is balanced against pair recombination to calculate the rate of decay of superflow below $T_c$. Formulas are worked out for the propagation and damping of third sound, and a discussion is given of hydrodynamic modes. An analogy between the dynamical equations for the film and Maxwell's equations is exploited.