Symmetry-adapted liouville space

F.P. Temme

Physica A: Statistical Mechanics and its Applications, 1990, vol. 166, issue 3, 676-684

Abstract: In examining nuclear spin dynamics of NMR spin clusters in density operator/generalized torque formalisms over |kqv〉〉 operator bases of Liouville space, it is necessary to consider the symmetry mappings and carrier spaces under a specialized group for such (ki = 1) nuclear spin clusters. The SU2 × Ln group provides the essential mappings and the form of H̃ carrier space, which allows one to: (a) draw comparisons with Hilbert space duality, and (b) outline the form of the Coleman-Kotani genealogical hierarchy under induced Ln-symmetry. The simple-reducibility of the tensor space of ki = 1 recoupled tensors depends on a consideration of the v forms under SU2 ≈ SO(3) of these Tkq(v) bases, where v spans all {K̃…}(k1-kn) forms. The use of Ln-combinatorial aspects, from the study of scalar invariants, and generalized word-length formalisms provide insight into the structure of explicit Ln/SU2 bases. The value of such Tkq(v:[λ~]) comes from the way in which they allow the partitioning of the density operator σ(Ln) for multispin NMR problems and their φkq(v: [λ~])[t] polarizations.

Date: 1990
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:166:y:1990:i:3:p:676-684

DOI: 10.1016/0378-4371(90)90079-8

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