Master Equation in Phase Space for a Spin in an Arbitrarily Directed Uniform External Field |
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Authors: | Yuri P Kalmykov Bernard P J Mulligan Serguey V Titov and William T Coffey |
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Institution: | (1) Theory Group, School of Physics and Astronomy, University of Manchester, Manchester, UK; |
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Abstract: | 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 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 Yu.P. Kalmykov
et al., J. Stat. Phys. 131:969, 2008]. The properties of this equation, resembling the corresponding Fokker-Planck equation, are investigated. In particular,
in the large spin limit, S→∞, the master equation becomes the classical Fokker-Planck equation describing the magnetization dynamics of a classical
paramagnet in an arbitrarily directed uniform external field. |
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