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Transfer matrices and transport for Schrödinger operators

François Germinet[1]; Alexander Kiselev; Serguei Tcheremchantsev

  • [1] Université de Cergy-Pontoise, laboratoire AGM, CNRS-UMR 8088, Dépt. de Mathématiques, 95302 Cergy-Pontoise Cédex, (France), University of Wisconsin, Department of Mathematics, Madison, WI 53706, (USA), Université d'Orléans, Laboratoire MAPMO, CNRS-UMR 6628, B.P. 6759, 45067 Orléans Cédex, (France)

Annales de l’institut Fourier (2004)

  • Volume: 54, Issue: 3, page 787-830
  • ISSN: 0373-0956

Abstract

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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 are provided. We also develop some general analysis of wave- packets that enables one to characterize transports exponents at low and large moments.

How to cite

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Germinet, François, Kiselev, Alexander, and Tcheremchantsev, Serguei. "Transfer matrices and transport for Schrödinger operators." Annales de l’institut Fourier 54.3 (2004): 787-830. <http://eudml.org/doc/116127>.

@article{Germinet2004,
abstract = {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 are provided. We also develop some general analysis of wave- packets that enables one to characterize transports exponents at low and large moments.},
affiliation = {Université de Cergy-Pontoise, laboratoire AGM, CNRS-UMR 8088, Dépt. de Mathématiques, 95302 Cergy-Pontoise Cédex, (France), University of Wisconsin, Department of Mathematics, Madison, WI 53706, (USA), Université d'Orléans, Laboratoire MAPMO, CNRS-UMR 6628, B.P. 6759, 45067 Orléans Cédex, (France)},
author = {Germinet, François, Kiselev, Alexander, Tcheremchantsev, Serguei},
journal = {Annales de l’institut Fourier},
keywords = {Schrödinger operators; transfer matrices; transport exponents},
language = {eng},
number = {3},
pages = {787-830},
publisher = {Association des Annales de l'Institut Fourier},
title = {Transfer matrices and transport for Schrödinger operators},
url = {http://eudml.org/doc/116127},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Germinet, François
AU - Kiselev, Alexander
AU - Tcheremchantsev, Serguei
TI - Transfer matrices and transport for Schrödinger operators
JO - Annales de l’institut Fourier
PY - 2004
PB - Association des Annales de l'Institut Fourier
VL - 54
IS - 3
SP - 787
EP - 830
AB - 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 are provided. We also develop some general analysis of wave- packets that enables one to characterize transports exponents at low and large moments.
LA - eng
KW - Schrödinger operators; transfer matrices; transport exponents
UR - http://eudml.org/doc/116127
ER -

References

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