Abstract
We discuss the semiclassical behavior of an arbitrary bivariate polynomial, evaluated on certain spectral projections of spin operators, and contrast it with the behavior of the polynomial when evaluated on random pairs of projections. The discrepancy is closely related to a type of Slepian concentration problem, which is also addressed. This is a survey article.
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Notes
- 1.
\(\mu _{k,n}\) is the unique probability measure invariant under the action of the unitary group on \(\mathrm G_k(n)\).
- 2.
Throughout, all Hilbert spaces are assumed to be separable and complex.
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Shabtai, O. (2022). Pairs of Spectral Projections of Spin Operators. In: Dobrev, V. (eds) Lie Theory and Its Applications in Physics. LT 2021. Springer Proceedings in Mathematics & Statistics, vol 396. Springer, Singapore. https://doi.org/10.1007/978-981-19-4751-3_25
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DOI: https://doi.org/10.1007/978-981-19-4751-3_25
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