Transfer matrices and transport for Schrödinger operators
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...