Regensburg 2010 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 4: Statistical Physics (general) II
DY 4.6: Talk
Monday, March 22, 2010, 15:15–15:30, H47
Phase space master equations for the Lipkin-Meshkov Hamiltonian — •Bernard P.J. Mulligan1, William T. Coffey2, Yuri P. Kalmykov3, and Serguey V. Titov4 — 1Max Planck Institute for the Physics of Complex Systems, Dresden, Germany — 2Trinity College Dublin, Ireland — 3Universite de Perpignan, France — 4Russian Academy of Sciences, Russia
The spin system with the Lipkin-Meshkov Hamiltonian
| β ĤS =−ξ ŜX −σ ŜZ2 |
(ξ and σ are external and internal field parameters) is treated as a nonaxially symmetric example of the phase space description of spin dynamics using a master equation for the quasiprobability distribution function of spin orientations in the representation (phase) space of the polar angles (analogous to the Wigner phase space distribution for translational motion). The master equation yields (via the Wigner-Stratonovich transformation of the density matrix) the solution as a Fourier series in the spherical harmonics with Fourier coefficients given by the statistical moments in a manner analogous to the classical distribution. In particular we take the values of S = 1/2,1.