Semiclassical mechanics of rotons
The roton elementary excitations in superfluid liquid 4He have an unusual dispersion curve. The energy is an approximately quadratic function of (p - p0), the difference between the magnitude of the momentum p and a characteristic value p0. As a result, while for p > p0 a roton has its (group) velocity parallel to its momentum, when p < p0 the velocity and momentum are antiparallel. When p = p0, the roton has non-zero momentum but zero velocity. These kinematic properties lead to unusual trajectories when rotons scatter or experience external forces. This paper examines this behaviour in the classical (ray optics) limit, where the roton wavelength is small compared with all other dimensions. Several experiments illustrate these effects. The examples are interesting in themselves, and also offer unconventional pedagogical possibilities.