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Transfer matrices and transport for Schrödinger operators. (English) Zbl 1074.81019
Summary: 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.

MSC:
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
47N50 Applications of operator theory in the physical sciences
82C70 Transport processes in time-dependent statistical mechanics
35J10 Schrödinger operator, Schrödinger equation
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