1991/09/07 by D. J. Thouless, D J Thouless, Yuanzheng Paul Tan +1 · 3 citations
Physics and Astronomy · #Advanced Chemical Physics Studies #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems
paper · doi:10.1088/0305-4470/24/17/022
openalex publication_date 1991/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
Earlier work on the spectral measure for the Harper equation (discrete Mathieu equation) showed that, if there is a large common period p for the lattice and the sinusoidal potential, the spectral measure scaled as C/p, where C is a constant independent of the number of oscillations q of the potential in p lattice spacings. The corrections to this scaling law are found for q=1 and q=2. For q=1 it is shown that the corrections to scaling are logarithmic functions of p, while for q=2 the leading corrections are reduced by a factor p -2 . Analytical and numerical support is given for the assertion that this difference between odd and even values of q persists for higher values of q provided they are substantially less than p.