On the Spinning Motion of the Hovering Magnetic Top

In this paper we analyze the spinning motion of the hovering magnetic top. We have observed that its motion looks different from that of a classical top. A classical top rotates about its own axis which precesses around a vertical fixed external axis. The hovering magnetic top, on the other hand, has its axis slightly tilted and moves rigidly as a whole about the vertical axis. We call this motion synchronous, because in a stroboscopic experiment we see that a point at the rim of the top moves synchronously with the top axis. We show that the synchronous motion may be attributed to a small deviation of the magnetic moment from the symmetry axis of the top. We calculate the minimum angular velocity required for stability in terms of the moments of inertia and magnetic field and show that it is different from that of a classical top. We also give experimental results that were taken with a top whose moment of inertia can be changed. These results show very good agreement with our calculations.Comment: 19 pages (including 3 figures named fig1.eps-fig3.eps), uses amssymb, epsf and amsbsy (AMSLaTeX

Velocity dependent interactions and a new sum rule in bcc He

Recent neutron scattering experiments [PRL,{\bf 88},p.195301 (2002)] on solid $^4$He, discovered a new optic-like mode in the bcc phase. This excitation was predicted by a recently proposed model that describes the correlated atomic zero-point motion in bcc Helium in terms of dynamic electric dipole moments. Modulations of the relative phase of these dipoles between different atoms describes the anomalously soft T$_1$(110) phonon and two new optic-like modes, one of which was recently found in the neutron scattering experiments. In this work we show that the correlated dipolar interactions can be written as a velocity dependent interaction. This then results in a modified f-sum rule for the T$_1$(110) phonon, in good agreement with the recent experimental data.Comment: 5 pages, 3 figure