Spin relaxation in phase space
Abstract
We have treated numerous illustrative examples of spin relaxation problems using Wigner's phase-space formulation of quantum mechanics of particles and spins. The merit of the phase space formalism as applied to spin relaxation problems is that only master equations for the phase-space distributions akin to Fokker-Planck equations for the evolution of classical phase-space distributions in configuration space are involved so that operators are unnecessary. The explicit solution of these equations can be expanded for an arbitrary spin Hamiltonian in a finite series of spherical harmonics like in the classical case. The expansion coefficients (statistical moments or averages of the spherical harmonics which are obviously by virtue of the Wigner-Stratonovich map the averages of the polarization operators) may be determined from differential-recurrence relations in a manner similar to the classical case. Furthermore, the phase space representation via the Weyl symbols of the relevant spin operators suggests how powerful computation techniques developed for Fokker-Planck equations (matrix continued fractions, mean first passage time, etc.) may be transparently extended to the quantum domain.
Cite
@article{arxiv.1603.00377,
title = {Spin relaxation in phase space},
author = {Yu. P. Kalmykov and W. T. Coffey and S. V. Titov},
journal= {arXiv preprint arXiv:1603.00377},
year = {2017}
}