Grand Ensembles of deterministic operators. II. Localization for generic `haarsh' potentials

Details Grand Ensembles of deterministic operators. II. Localization for generic `haarsh' potentials Grand Ensembles of deterministic operators. II. Localization for generic `haarsh' potentials

2009-07-09

arxiv.org/abs/0907.1494v2

Physics

Mathematical Physics

Scientific paper

We consider a particular class of lattice Schr\"odinger operators with deterministic potentials depending upon an infinite number of parameters in an auxiliary measurable space. We prove exponential dynamical localization for generic families in the strong disorder regime, using a variant of the Multi-Scale Analysis. In our model, the potential is generated by a function on a torus which is discontinuous (`haarsh') and constructed with the help of an expansion which reminds Haar's wavelet expansions.

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