Dresden 2011 – wissenschaftliches Programm
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MA: Fachverband Magnetismus
MA 45: Micromagnetism/ Computational Magnetics
MA 45.5: Vortrag
Mittwoch, 16. März 2011, 18:30–18:45, HSZ 403
Master equation in phase space for a spin in an arbitrarily directed uniform external field — Yuri Kalmykov1, •Bernard Mulligan2, Serguey Titov3, and William Coffey4 — 1Laboratoire de Mathématiques, Physique et Systèmes, Université de Perpignan, 52, Avenue de Paul Alduy, 66860 Perpignan Cedex, France. — 2Dresden — 3Institute of Radio Engineering and Electronics, Russian Acad. Sci., Vvedenskii Square 1,Fryazino 141190, Russia. — 4Department of Electronic and Electrical Engineering, Trinity College, Dublin 2, Ireland.
The time evolution equation for the probability density function of spin orientations in the phase space representation of the polar and azimuthal angles is derived [1] for the nonaxially symmetric problem of a quantum paramagnet subjected to a uniform magnetic field of arbitrary direction. This is accomplished by first rotating the coordinate system into one in which the polar axis is collinear with the field vector, then writing the reduced density matrix equation in the new coordinate system as an explicit inverse Wigner-Stratonovich transformation so that the phase space master equation may be derived just as in the axially symmetric case [2]. The properties of this equation, resembling the corresponding Fokker-Planck equation, are investigated. In particular, in the large spin limit, the master equation becomes the classical Fokker-Planck equation describing the magnetization dynamics of a classical paramagnet in an arbitrarily directed uniform external field.
1. Yu.P. Kalmykov et al., J. Stat. Phys., 141, 589 (2010).
2. Yu. P. Kalmykov et al., J. Stat. Phys. 131, 969 (2008).