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29 March 2024
 
  » arxiv » 1511.1394

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Heavy tails and one-dimensional localization
Michael Cranston ; Stanislav Molchanov ; Nicola Squartini ;
Date 4 Nov 2015
AbstractWe address the fundamental questions concerning the operator egin{eqnarray*} H^{ heta_0}psi(x)=-psi"(x)+V(x,omega)psi(x),,psi(0)cos heta_0-psi’(0)sin heta_0=0. end{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 $alphain(0,1)$ 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 $alphain(0,1).$ We consider the existence of Lyapunov exponents, integrated density of states and the nature of the spectrum of the operator.
Source arXiv, 1511.1394
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