Electron beams of cylindrically symmetric spin polarization

Cylindrically symmetric electron beams in spin polarization are reported for the first time. They are shown to be the eigen states of total angular momentum in the $z$ direction. But they are neither the eigen states of spin nor the eigen states of orbital angular momentum in that direction.Comment: 10 pages and 2 figure

A Non-Mainstream Viewpoint on Apparent Superluminal Phenomena in AGN Jet

The group velocity of light in material around the AGN jet is acquiescently one (c as a unit), but this is only a hypothesis. Here, we re-derive apparent superluminal and Doppler formulas for the general case (it is assumed that the group velocity of light in the uniform and isotropic medium around a jet (a beaming model) is not necessarily equal to one, e.g., Araudo et al. (2010) thought that there may be dense clouds around AGN jet base), and show that the group velocity of light close to one could seriously affect apparent superluminal phenomena and Doppler effect in the AGN jet (when the viewing angle and Lorentz factor take some appropriate values).Comment: 4 pages, 2 figures, new version accepted for publication in Journal of Astrophysics and Astronom

Controllable Goos-H\"{a}nchen shifts and spin beam splitter for ballistic electrons in a parabolic quantum well under a uniform magnetic field

The quantum Goos-H\"{a}nchen shift for ballistic electrons is investigated in a parabolic potential well under a uniform vertical magnetic field. It is found that the Goos-H\"{a}nchen shift can be negative as well as positive, and becomes zero at transmission resonances. The beam shift depends not only on the incident energy and incidence angle, but also on the magnetic field and Landau quantum number. Based on these phenomena, we propose an alternative way to realize the spin beam splitter in the proposed spintronic device, which can completely separate spin-up and spin-down electron beams by negative and positive Goos-H\"{a}nchen shifts.Comment: 6 pages, 6 figure