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Resonance tongues and spectral gaps in quasi-periodic Schrödinger operators with one or more frequencies. A numerical exploration

Author
Puig, J.; Simó, C.
Type of activity
Report
Date
2010-07
Code
[prepr201007PuiS]
Repository
http://hdl.handle.net/2117/8946 Open in new window
URL
http://www.ma1.upc.edu/~jpuig/preprints/puig-simo_10_1.pdf Open in new window
Abstract
Abstract. In this paper we investigate numerically the spectrum of some representative examples of discrete one-dimensional Schr¨odinger operators with quasi-periodic potential in terms of a perturbative constant b and the spectral parameter a. Our examples include the well-known Almost Mathieu model, other trigonometric potentials with a single quasi-periodic frequency and generalisations with two and three frequencies. We computed numerically the rotation number and the Lyapunov exponent to d...
Keywords
Lyapunov exponent, Numerical explorations, Quasi-Periodic Cocycles and Skew-products, Quasi-Periodic Schr\"odinger operators, Resonance Tongues, Rotation number, Spectral Gaps
Group of research
SD - UPC Dynamical Systems

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