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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
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, ...
Asymptotics of spectral quantities of Schrodinger operators
Asymptotics spectral quantities Schrodinger operators
2011/9/19
Abstract: In this paper we provide new asymptotic estimates of the Floquet exponents of Schr\"odinger operators on the circle. By the same techniques, known asymptotic estimates of various others spec...
Discrete Schrodinger operators with random alloy-type potential
multiscale analysis fractional moment method Cartan’s Theorem localization discrete alloy-type model non-monotone
2011/9/6
Abstract: We review recent results on localization for discrete alloy-type models based on the multiscale analysis and the fractional moment method, respectively. The discrete alloy-type model is a fa...
A Short Course on One-Dimensional Random Schrodinger Operators
One-Dimensional Random Schrodinger Operators Spectral Theory Mathematical Physics
2011/8/26
Abstract: We discuss various approaches to localization results for one-dimensional random Schr\"odinger operators, both discrete and continuum. We focus in particular on the approach based on F\"urst...
Absolutely continuous spectrum of a one-paramentric family of Schrodinger operators
one-paramentric family Schrodinger operators Spectral Theory
2011/7/27
Abstract: We consider a family of operators $-\Delta+ t V$ with a slowly decaying and oscillating potential $V$. We prove that the absolutely continuous spectrum of this operator is essentially suppor...
Ballistic Behavior for Random Schrodinger Operators on the Bethe Strip
Random Schrodinger operators Anderson model spreading of wave packets ballistic behavior Bethe strip
2011/7/26
Ballistic Behavior for Random Schrodinger Operators on the Bethe Strip.