Rotation Numbers, Boundary Forces and Gap labelling

Details Rotation Numbers, Boundary Forces and Gap labelling Rotation Numbers, Boundary Forces and Gap labelling

2005-06-07

arxiv.org/abs/math-ph/0506016v1

J. Phys. A: Math. Gen. 38 (2005) 3937-3946

Physics

Mathematical Physics

10 pages, version accepted for publication

Scientific paper

10.1088/0305-4470/38/18/005

We review the Johnson-Moser rotation number and the $K_0$-theoretical gap labelling of Bellissard for one-dimensional Schr\"odinger operators. We compare them with two further gap-labels, one being related to the motion of Dirichlet eigenvalues, the other being a $K_1$-theoretical gap label. We argue that the latter provides a natural generalisation of the Johnson-Moser rotation number to higher dimensions.

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