Semiclassical Mechanics of Rotons

Abstract

The elementary excitations in superfluid liquid He-4 named rotons have an unusual dispersion curve. The energy is an approximately quadratic function of (p-p_0), the difference between the magnitude of the momentum p and a characteristic value p_0. As a result, while for p>p_0 a roton has its (group) velocity parallel to its momentum, when p<p_0 the velocity and momentum are antiparallel. When p=p_0, 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 behavior 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.