Schroedinger equations with potentials generated by shifts and skew-shifts

4:00 pm Thursday, October 29, 2009
Michael Goldstein (University of Toronto)


In this talk we give an exposition of the ideas, methods and techn ological tools developed in last ten years for the analysis of one-dimensional d ifference Schroedinger equations with potentials generated by shift and sk ew-shift H(x, ω)ϕ (n) ≡ −ϕ(n − 1) − ϕ ;(n + 1) + V (Tω^n(x))ϕ(n) = Eϕ(n) , n ∈ Z. Here Tω is a shift Tω (x) = x + ω, x, ω ∈ Tν , or a skew-shift, Tω (x, y) = (x + ω, y + x), (x, y) ∈ T^2 , ω ∈ T, and T^nω , n ∈ Z, stands for the n-th iteration of T . We state also the central open problems in this field.

 

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