Strong resonant tunneling, level repulsion and spectral type for one-dimensional adiabatic quasi-periodic Schrödinger operators
Alexander Fedotov, Frédéric Klopp (2005)
Annales scientifiques de l'École Normale Supérieure
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Alexander Fedotov, Frédéric Klopp (2005)
Annales scientifiques de l'École Normale Supérieure
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Arne Jensen (1989)
Journées équations aux dérivées partielles
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Kauffman, Robert M. (1993)
International Journal of Mathematics and Mathematical Sciences
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François Germinet, Alexander Kiselev, Serguei Tcheremchantsev (2004)
Annales de l’institut Fourier
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We provide a general lower bound on the dynamics of one dimensional Schrödinger operators in terms of transfer matrices. In particular it yields a non trivial lower bound on the transport exponents as soon as the norm of transfer matrices does not grow faster than polynomially on a set of energies of full Lebesgue measure, and regardless of the nature of the spectrum. Applications to Hamiltonians with a) sparse, b) quasi-periodic, c) random decaying potential...
W.O. Amrein, A. M. Boutet de Monvel-Berthier, V. Georgescu (1987)
Bulletin de la Société Mathématique de France
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Niels Joergen Kokholm (1989)
Journées équations aux dérivées partielles
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