Curvature of quantum rings

E. Jonckheere, F. C. Langbein, S. G. Schirmer. Curvature of quantum rings. In: Proc. 5th Int Symp Communications Control and Signal Processing (ISCCSP), pp. 1-6, 2012. [DOI:10.1109/ISCCSP.2012.6217863] [arXiv:1202.2556] [PDF]



We develop a geometric approach to spin networks with Heisenberg or XX coupling. Geometry is acquired by defining a distance on the discrete set of spins. The key feature of the geometry of such networks is their Gauss curvature κ, viewed here as the ability to isometrically embed the chain in the standard Riemannian manifold of curvature κ. Here we focus on spin rings. Even though their visual geometry is trivial, it turns out that the geometry they acquire from the quantum mechanical distance is far from trivial.

Cite this page as 'Frank C Langbein, "Curvature of quantum rings," Ex Tenebris Scientia, 4th November 2012, [accessed 7th May 2021]'.

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