Spin Depolarization of a Quantum Particle; Fermionic Path Integral Approach

Abstract

The spin depolarization of a quantum particle in random magnetic field is treated in terms of a path integral in the spin states as well as the translational motion. The path integral of the spin operator, represented in terms of Fermion operators, is performed in the Fermion coherent state representation. An expression for the spin depolarization is obtained for an arbitrary magnetic field distribution. A particular case, in which the magnetic field is oriented in the z-direction and the magnitude is Gaussianly distributed, is considered and the spin decays exponentially in time.