1999/10/21 by Fréderic Faure, Frederic Faure
Mathematics · Physics and Astronomy · #Chern class #Combinatorics #Computer science #Floquet theory #Geometry #Homotopy #Mathematics #Nonlinear system #Phase space #Physics #Pure mathematics #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum many-body systems #Quantum mechanics #Semiclassical physics #Simple (philosophy) #Space (punctuation) #Topological Materials and Phenomena #Topological quantum number #Topology (electrical circuits) #Torus #cond-mat.mes-hall #quant-ph
paper · pdf · doi:10.1088/0305-4470/33/3/308
published as J.Phys.A:Math. Gen. 33 (2000) 531-555 · 27 pages, 14 figures
arxiv created 1999/10/21 · openalex publication_date 2000/01/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 semiclassical approach with the 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 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.