The structure of eigenfunctions of one-dimensional unordered structures
Izvestiya. Mathematics , Tome 12 (1978) no. 1, pp. 69-101
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In this work it is shown that all the eigenfunctions of the one-dimensional random Schröger operator $H=-d^2/dt^2+q(t,\omega)$, $t\in R^1$, with random potential $q(t,\omega)$, $\omega\in\Omega$, of Markov type decrease exponentially with probability 1. This confirms an old conjecture of N. F. Mott which has been discussed many times in the physics literature.
Bibliography: 14 titles.
@article{IM2_1978_12_1_a3,
author = {S. A. Molchanov},
title = {The structure of eigenfunctions of one-dimensional unordered structures},
journal = {Izvestiya. Mathematics },
pages = {69--101},
publisher = {mathdoc},
volume = {12},
number = {1},
year = {1978},
language = {en},
url = {http://geodesic.mathdoc.fr/item/IM2_1978_12_1_a3/}
}
S. A. Molchanov. The structure of eigenfunctions of one-dimensional unordered structures. Izvestiya. Mathematics , Tome 12 (1978) no. 1, pp. 69-101. http://geodesic.mathdoc.fr/item/IM2_1978_12_1_a3/