Topological properties of quantum periodic Hamiltonians

Details Topological properties of quantum periodic Hamiltonians Topological properties of quantum periodic Hamiltonians

1999-10-21

arxiv.org/abs/cond-mat/9910325v1

J.Phys.A:Math. Gen. 33 (2000) 531-555

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

27 pages, 14 figures

Scientific paper

10.1088/0305-4470/33/3/308

We consider periodic quantum Hamiltonians on the torus phase space (Harper-like Hamiltonians). We calculate the topological Chern index which characterizes each spectral band in the generic case. This calculation is made by a semi-classical approach with use of quasi-modes. As a result, the Chern index is equal to the homotopy of the path of these quasi-modes on phase space as the Floquet parameter (\theta) of the band is varied. It is quite interesting that the Chern indices, defined as topological quantum numbers, can be expressed from simple properties of the classical trajectories.

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