Rashba effect in two-dimensional mesoscopic systems with transverse magnetic field

We present semiclassical and quantum mechanical results for the effects of a strong magnetic field in quantum wires in the presence of Rashba spin-orbit coupling. Analytical and numerical results show how the perturbation acts in the presence of a transverse magnetic field in the ballistic regime and we assume a strong reduction of the backward scattering interaction which could have some consequences for the Tomonaga-Luttinger transport. We analyze the spin texture due to the action of spin-orbit coupling and magnetic field, often referring to the semiclassical solutions that magnify the singular spin polarization: results are obtained for free electrons in a two-dimensional electron gas and for electrons in a quantum wire. We propose the systems as possible devices for the spin filtering at various regimes.