Collective modes in quantum lattice or three-dimensional XY model, 2

An external field is applied to the XY model which was studied in a previous paper. With the help of Mori's memory function formalism, two types of collective modes are obtained. One of those, which was previously pointed out to correspond to the first sound in superfluid helium, survives at the critical temperature T sub(c). The other is a new mode, which disappears as a result of symmetry restored above T sub(c). This mode comes about owing to the coupling between the Goldstone mode and the energy fluctuation due to an external field, and is regarded to correspond to the second sound in superfluid helium. The linearized two-fluid hydrodynamic equations for superfluid helium are obtained in the context of the XY model, in which the detailed correspondence to the superfluid helium is clarified. (author)