Rotation Numbers, Boundary Forces and Gap labelling

Abstract

We review the Johnson-Moser rotation number and the $K_0$-theoretical gap labelling of Bellissard for one-dimensional Schrödinger 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.

10 pages, version accepted for publication

References in corpus (1)

• Topological quantization of boundary forces and the integrated density of states

Cited by in corpus (4)

• Virtual Topological Insulators with Real Quantized Physics
• Local symmetry theory of resonator structures for the real-space control of edge states in binary aperiodic chains
• Bulk-boundary correspondance for Sturmian Kohmoto like models
• Quantum Metrology: Towards an alternative definition for the meter