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Localization for quasi-periodic Schrodinger operators with dynamics defined by the skew-shift and potential in a Gevrey-class
Mathematical Physics Spectral Theory dynamics quasi-periodic Schrodinger operators
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2012/4/16
We consider the discrete one-dimensional Schr\"{o}dinger operator with quasi-periodic potential $v_n := \lambda v (\shift^n \, \xx)$, where $\shift : \T^2 \rightarrow \T^2, \, \shift \xx := (x_1+x_2, ...
On the spectrum of skew-shift Schrödinger operators
spectrum ergodic Schrodinger operators skew-shift
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2010/11/30
I prove that the spectrum of a skew-shift Schrodinger operator contains larges interval in the semi-classical regime. In the semi-classical limit,these intervals approach the range of the potential.