Hypergroups and Hypergroup Algebras

The survey contains a brief description of the ideas, constructions, results, and prospects of the theory of hypergroups and generalized translation operators. Representations of hypergroups are considered, being treated as continuous representations of topological hypergroup algebras.Comment: 52 page

Polarization-induced Rashba spin-orbit coupling in structurally symmetric III-Nitride quantum wells

The effective linear coupling coefficient and the total spin-splitting are calculated in Ga- and N- face InGaN quantum wells. Alloy content, geometry, and gate voltage affect an internal field and an electron density distribution in the growth direction that has direct effect on a spin-splitting. The sign of structural inversion asymmetry (SIA) spin-orbit coupling coefficient depends on an internal electric field in the well that results in different signs for Ga-face and N-face III-Nitride structures. The effective linear coupling coefficient is always positive because of the Dresselhaus-type contribution that is a major one in quantum wells under consideration. The magnitude of the spin-splitting is comparable with that experimentally observed in III-Nitrides and III-V zinc-blende structures.Comment: 17 pages, 8 figure