96-458 Jaksic V., Molchanov S.

Localization for one dimensional long range random Hamiltonians (213K, postscript) Oct 1, 96

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Abstract. We study spectral properties of random Schrodinger operators $h_\omega = h_0 + v_\omega(n)$ on $l^2({\bf Z})$ whose free part $h_0$ is long range. We prove that the spectrum of $h_\omega$ is pure point for typical $\omega$ if the random variables $v_\omega(n)$ have sufficently long tails and if off-diagonal terms of $h_0$ decay as $\vert i-j \vert^{-\gamma}$ for some $\gamma >8$.

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