Spin rotation for ballistic electron transmission induced by spin-orbit interaction

We study spin-dependent electron transmission through one- and two-dimensional curved waveguides and quantum dots with account of spin-orbit interaction. We prove that for a transmission through an arbitrary structure there is no spin polarization provided the electron transmits in an isolated energy subband and only two leads are attached to the structure. In particular there is no spin polarization in the one-dimensional wire, for which a spin-dependent solution is found analytically. The solution demonstrates the spin evolution as dependent on a length of wire. The numerical solution for transmission of electrons through the two-dimensional curved waveguides coincides with the solution for the one-dimensional wire if the energy of electron is within the first energy subband. In the vicinity of edges of the energy subbands there are sharp anomalies of spin flipping.