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Journal of Physics A Mathematical and Theoretical

Wei–Norman–Kolokolov dual approach for arbitrary spin S in a time-dependent magnetic field

M. B. Kenmoe, Lukong Cornelius Fai

Published Dec 17, 2015• 0 citations
Publisher

Abstract

Abstract A comprehensive theory describing spin dynamics in a time-dependent magnetic field is constructed on the basis of a Maurer–Cartan (MC) form selected following the exponential Wei–Norman ordering technique. We demonstrate that the purely diffusive SU (2) problem described by a MC form yields the Fokker–Planck equation for the probability density function. The Fokker–Planck-like operator is observed to correspond to the Casimir operator. The case of a multichannel Coulomb model is considered for illustration.

DOI
10.1088/1751-8113/49/3/035203

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Abstract A comprehensive theory describing spin dynamics in a time-dependent magnetic field is constructed on the basis of a Maurer–Cartan (MC) form selected following the exponential Wei–Norman ordering technique. We demonstrate that the purely diffusive SU (2) problem described by a MC form yields the Fokker–Planck equation for the probability density function. The Fokker–Planck-like operator is observed to correspond to the Casimir operator. The case of a multichannel Coulomb model is considered for illustration.
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The analysis of dissipative transport equations within the framework of open quantum systems with Fokker-Planck-type scattering is carried out from the perspective of a Wigner function approach. In particular, the well-posedness of the self-consistent whole-space problem in 3D is analyzed: existence of solutions, uniqueness and asymptotic behavior in time, where we adopt the viewpoint of mild solutions in this paper. Also, the admissibility of a density matrix formulation in Lindblad form with Fokker-Planck dissipation mechanisms is discussed. We remark that our solution concept allows to carry out the analysis directly on the level of the kinetic equation instead of on the level of the density operator. AMS 1991 Subject classification: 35Q40, 35S10, 81Q99, 81V99 Key words: Open quantum system, Wigner equation, large-time behavior, self-similarity. 1. Introduction This paper is concerned with the analysis of a class of dissipative quantum models that arise when considering the motio...
The tunneling between the 2S+12S+12S+1 Zeeman multiplets of an arbitrary spin SSS using the SU(2)SU(2)SU(2) Lie group exponential ordering Wei-Norman technique is investigated. A spin subjected to a regular time-dependent magnetic field and a transverse colored noise is considered and the regimes of fast and slow noise examined.