Displaying similar documents to “Quantum energy expectation in periodic time-dependent Hamiltonians via Green functions.”

Quantum Dynamics and generalized fractal dimensions: an introduction

François Germinet (2002-2003)

Séminaire Équations aux dérivées partielles

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We review some recent results on quantum motion analysis, and in particular lower bounds for moments in quantum dynamics. The goal of the present exposition is to stress the role played by quantities we shall call and by the so called of the spectral measure in the analysis of quantum motion. We start with very simple derivations that illustrate how these quantities naturally enter the game. Then, gradually, we present successive improvements, up to most recent result.

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...