20 research outputs found
A generalization of the Heine--Stieltjes theorem
We extend the Heine-Stieltjes Theorem to concern all (non-degenerate)
differential operators preserving the property of having only real zeros. This
solves a conjecture of B. Shapiro. The new methods developed are used to
describe intricate interlacing relations between the zeros of different pairs
of solutions. This extends recent results of Bourget, McMillen and Vargas for
the Heun equation and answers their question on how to generalize their results
to higher degrees. Many of the results are new even for the classical case.Comment: 12 pages, typos corrected and refined the interlacing theorem
Influence of a Uniform Current on Collective Magnetization Dynamics in a Ferromagnetic Metal
We discuss the influence of a uniform current, , on the
magnetization dynamics of a ferromagnetic metal. We find that the magnon energy
has a current-induced contribution proportional to
, where is the spin-current, and
predict that collective dynamics will be more strongly damped at finite . We obtain similar results for models with and without local moment
participation in the magnetic order. For transition metal ferromagnets, we
estimate that the uniform magnetic state will be destabilized for . We discuss the relationship of this effect to
the spin-torque effects that alter magnetization dynamics in inhomogeneous
magnetic systems.Comment: 12 pages, 2 figure