Phase space Langevin equation for spin relaxation in a dc magnetic fieldYu. P. Kalmykov1, W. T. Coffey2 and S. V. Titov3
1 Laboratoire de Mathématiques, Physique et Systèmes, Université de Perpignan - 52, Avenue de Paul Alduy, 66860 Perpignan Cedex, France, EU
2 Department of Electronic and Electrical Engineering, Trinity College - Dublin 2, Ireland, EU
3 Institute of Radio Engineering and Electronics, Russian Academy of Sciences - Vvedenskii Square 1, Fryazino, 141190, Russia
received 13 May 2009; accepted in final form 16 September 2009; published October 2009
published online 16 October 2009
A Langevin equation for the quantum Brownian motion of a spin of arbitrary size in a uniform external dc magnetic field is derived from the phase space master equation in the weak coupling and narrowing limits, for the quasiprobability distribution (Wigner) function of spin orientations in the configuration space of polar and azimuthal angles following methods long familiar in quantum optics. The closed system of differential-recurrence equations for the statistical moments describing magnetic relaxation of the spin is obtained as an example of applications of this equation.
76.20.+q - General theory of resonances and relaxations.
05.10.Gg - Stochastic analysis methods (Fokker-Planck, Langevin, etc.).
05.40.Jc - Brownian motion.
© EPLA 2009