49,169 research outputs found
Monomial transformations of the projective space
We prove that, over any field, the dimension of the indeterminacy locus of a
rational transformation of which is defined by monomials of the same
degree with no common factors is at least , provided that the
degree of as a map is not divisible by . This implies upper bounds on
the multidegree of
Spin Orbit Coupling and Spin Waves in Ultrathin Ferromagnets: The Spin Wave Rashba Effect
We present theoretical studies of the influence of spin orbit coupling on the
spin wave excitations of the Fe monolayer and bilayer on the W(110) surface.
The Dzyaloshinskii-Moriya interaction is active in such films, by virtue of the
absence of reflection symmetry in the plane of the film. When the magnetization
is in plane, this leads to a linear term in the spin wave dispersion relation
for propagation across the magnetization. The dispersion relation thus assumes
a form similar to that of an energy band of an electron trapped on a
semiconductor surfaces with Rashba coupling active. We also show SPEELS
response functions that illustrate the role of spin orbit coupling in such
measurements. In addition to the modifications of the dispersion relations for
spin waves, the presence of spin orbit coupling in the W substrate leads to a
substantial increase in the linewidth of the spin wave modes. The formalism we
have developed applies to a wide range of systems, and the particular system
explored in the numerical calculations provides us with an illustration of
phenomena which will be present in other ultrathin ferromagnet/substrate
combinations
Scalar fields in the Lense-Thirring background with a cosmic string and Hawking radiation
We analyze the influence of the gravitational field produced by a slowly
rotating black hole with a cosmic string along the axis of symmetry on a
massive scalar field. Exact solutions of both angular and radial parts of the
Klein-Gordon equation in this spacetime are obtained, and are given in terms of
the confluent Heun functions. We emphasize the role of the presence of the
cosmic string in these solutions. We also investigate the solutions in regions
near and far from the event horizon. From the radial solution, we obtain the
exact wave solutions near the exterior horizon of the black hole, and discuss
the Hawking radiation of massive scalar particles.Comment: 6 page
- …