Topological properties of quantum periodic Hamiltonians

Abstract

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 (θ) 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.

27 pages, 14 figures

References in corpus (2)

• Hall conductance of Bloch electrons in a magnetic field
• Semi-classical study of the Quantum Hall conductivity

Cited by in corpus (7)

• Topological Chern indices in molecular spectra
• Localization by bichromatic potentials versus Anderson localization
• Topologically coupled energy bands in molecules
• General Approach to the Quantum Kicked Particle in a Magnetic Field: Quantum-Antiresonance Transition
• Topologically Universal Spectral Hierarchies of Quasiperiodic Systems
• Topological Phase Transitions from Harper to Fibonacci Crystals
• On semiclassical dispersion relations of Harper-like operators