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We consider resonant tunneling between disorder localized states in a potential energy displaying perfect correlations over large distances. The phenomenon described here may be of relevance to models exhibiting many-body localization. Furthermore, in the context of single particle operators, our examples demonstrate that exponential resolvent localization does not imply exponential dynamical localization for random Schrodinger operators with correlated potentials.
We briefly review the diffraction of quasicrystals and then give an elementary alternative proof of the diffraction formula for regular cut-and-project sets, which is based on Bochners theorem from Fourier analysis. This clarifies a common view that
We consider a three-dimensional chaotic system consisting of the suspension of Arnolds cat map coupled with a clock via a weak dissipative interaction. We show that the coupled system displays a synchronization phenomenon, in the sense that the relat
We derive the leading order radiation through tunneling of an oscillating soliton in a well. We use the hydrodynamic formulation with a rigorous control of the errors for finite times.
We decorate the one-dimensional conic oscillator $frac{1}{2} left[-frac{d^{2} }{dx^{2} } + left|x right| right]$ with a point impurity of either $delta$-type, or local $delta$-type or even nonlocal $delta$-type. All the three cases are exactly solvab
In this paper, we construct a Spectrum Generating Algebra (SGA) for a quantum system with purely continuous spectrum: the quantum free particle in a Lobachevski space with constant negative curvature. The SGA contains the geometrical symmetry algebra