  A general form of the Hamiltonian for electrons confined to a curved
one-dimensional (1D) channel with spin-orbit coupling (SOC) linear in momentum
is rederived and is applied to a U-shaped channel. Discretizing the derived
continuous 1D Hamiltonian to a tight-binding version, the Landauer-Keldysh
formalism (LKF) for nonequilibrium transport can be applied. Spin transport
through the U-channel based on the LKF is compared with previous quantum
mechanical approaches. The role of a curvature-induced geometric potential
which was previously neglected in the literature of the ring issue is also
revisited. Transport regimes between nonadiabatic, corresponding to weak SOC or
sharp turn, and adiabatic, corresponding to strong SOC or smooth turn, is
discussed. Based on the LKF, interesting charge and spin transport properties
are further revealed. For the charge transport, the interplay between the
Rashba and the linear Dresselhaus (001) SOCs leads to an additional modulation
to the local charge density in the half-ring part of the U-channel, which is
shown to originate from the angle-dependent spin-orbit potential. For the spin
transport, theoretically predicted eigenstates of the Rashba rings, Dresselhaus
rings, and the persistent spin-helix state are numerically tested by the
present quantum transport calculation.
