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Article overview
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Heavy tails and one-dimensional localization | Michael Cranston
; Stanislav Molchanov
; Nicola Squartini
; | Date: |
4 Nov 2015 | Abstract: | We 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 | Services: | Forum | Review | PDF | Favorites |
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