Mechanical analogues of spin Hamiltonians and dynamics

Bloch et al. mapped the precession of the spin-half in a magnetic field of variable magnitude and direction to the rotations of a rigid sphere rolling on a curved surface utilizing SU(2)-SO(3) isomorphism. This formalism is extended to study the behaviour of spin-orbit interactions and the mechanical analogy for Rashba-Dresselhauss spin-orbit interaction in two dimensions is presented by making its spin states isomorphic to the rotations of a rigid sphere rolling on a ring. The change in phase of spin is represented by the angle of rotation of sphere after a complete revolution. In order to develop the mechanical analogy for the spin filter, we find that perfect spin filtration of down spin makes the sphere to rotate at some unique angles and the perfect spin filtration of up spin causes the rotations with certain discrete frequencies.