Curvature of quantum rings

Author

Jonckheere, E. ; Langbein, Frank C. ; Schirmer, Sophie G.

Author_Institution

USC Center for Quantum Inf. Sci. & Technol., Los Angeles, CA, USA

fYear

2012

fDate

2-4 May 2012

Firstpage

1

Lastpage

6

Abstract

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.

Keywords

Gaussian distribution; Heisenberg model; geometry; quantum theory; Gauss curvature; Heisenberg coupling; XX coupling; geometric approach; quantum mechanical distance; quantum ring curvature; spin chain; spin networks; spin rings; standard Riemannian curvature manifold; Couplings; Eigenvalues and eigenfunctions; Extraterrestrial measurements; Geometry; Manifolds; Quantum mechanics; Feynman path integral; Riemannian spaces; Spin chains; coarse geometry; curvature;

fLanguage

English

Publisher

ieee

Conference_Titel

Communications Control and Signal Processing (ISCCSP), 2012 5th International Symposium on

Conference_Location

Rome

Print_ISBN

978-1-4673-0274-6

Type

conf

DOI

10.1109/ISCCSP.2012.6217863

Filename

6217863