Semiclassical path integral approach for spin relaxations in narrow wires

The semiclassical path integral (SPI) method has been applied for studying spin relaxation in a narrow two-dimensional strip with the Rashba spin-orbit interaction. Our numerical calculations show good agreement with the experimental data, although some features of experimental results are not clear yet. We also calculated the relaxation of a uniform spin-density distribution in the ballistic regime of very narrow wires. With the decreasing wire width, the spin polarization exhibits a transition from the exponential decay to the oscillatory Bessel-type relaxation. The SPI method has also been employed to calculate the relaxation of the particularly long-lived helix mode. Good agreement has been found with calculations based on the diffusion theory.