Heavy tails and one-dimensional localization

الأصل · EN

We address the fundamental questions concerning the operator eqnarray* Hθ⁰ψ(x)=-ψ"(x)+V(x,ω)ψ(x),ψ(0)θ₀-ψ'(0)θ₀=0. eqnarray* where the random potential V has a variety of forms. In one example, it is composed of width one bumps of random heights where the square root of the heights are in the domain of attraction of a stable law with index α∈(0,1) or in another it is composed of width one bumps of height one where the distance between bumps is in the domain of attraction of a stable law with index α∈(0,1). We consider the existence of Lyapunov exponents, integrated density of states and the nature of the spectrum of the operator.