Dresden 2011 – wissenschaftliches Programm
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KR: Fachgruppe Kristallographie
KR 5: Poster Multiferroics (Joint Session of MA, DF, DS, KR, TT)
KR 5.84: Poster
Dienstag, 15. März 2011, 10:45–13:00, P2
Spin dynamics in phase space — 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 dynamics of a quantum spin is presented in the representation (phase) space of polar and azimuthal angles via a master equation for the quasiprobability distribution of spin orientations, allowing the averages of quantum mechanical spin operators to be calculated just as the classical case from the Weyl Symbol of the operator. The phase space master equation (see for e.g. [1,2]) has essentially the same form as the classical Fokker-Planck equation, allowing existing solution methods (matrix continued fractions, integral relaxation times, etc.) to be used. For illustration [1], the time behavior of the longitudinal component of the magnetization and its characteristic relaxation times are evaluated for a uniaxial paramagnet of arbitrary spin S in an external constant magnetic field applied along the axis of symmetry. In the large spin limit, the quantum solutions reduce to those of the Fokker-Planck equation for a classical uniaxial superparamagnet. For linear response, the results entirely agree with existing solutions.
1. Kalmykov et al., J. Stat. Phys., 141, 589 (2010).
2. Kalmykov et al., Phys. Rev. B 81, 094432 (2010).