2,922 research outputs found
Quantum Hamiltonians with Quasi-Ballistic Dynamics and Point Spectrum
Consider the family of Schr\"odinger operators (and also its Dirac version)
on or where is a
transformation on (compact metric) , a real Lipschitz function and
a (sufficiently fast) power-decaying perturbation. Under certain conditions
it is shown that presents quasi-ballistic dynamics for
in a dense set. Applications include potentials generated
by rotations of the torus with analytic condition on , doubling map, Axiom A
dynamical systems and the Anderson model. If is a rank one perturbation,
examples of with quasi-ballistic dynamics and point spectrum
are also presented.Comment: 17 pages; to appear in Journal of Differential Equation
Dynamical Delocalization for the 1D Bernoulli Discrete Dirac Operator
An 1D tight-binding version of the Dirac equation is considered; after
checking that it recovers the usual discrete Schr?odinger equation in the
nonrelativistic limit, it is found that for two-valued Bernoulli potentials the
zero mass case presents absence of dynamical localization for specific values
of the energy, albeit it has no continuous spectrum. For the other energy
values (again excluding some very specific ones) the Bernoulli Dirac system is
localized, independently of the mass.Comment: 9 pages, no figures - J. Physics A: Math. Ge
Dynamical Lower Bounds for 1D Dirac Operators
Quantum dynamical lower bounds for continuous and discrete one-dimensional
Dirac operators are established in terms of transfer matrices. Then such
results are applied to various models, including the Bernoulli-Dirac one and,
in contrast to the discrete case, critical energies are also found for the
continuous Dirac case with positive mass.Comment: 18 pages; to appear in Math.
Hybrid Quasicrystals, Transport and Localization in Products of Minimal Sets
We consider convex combinations of finite-valued almost periodic sequences
(mainly substitution sequences) and put them as potentials of one-dimensional
tight-binding models. We prove that these sequences are almost periodic. We
call such combinations {\em hybrid quasicrystals} and these studies are related
to the minimality, under the shift on both coordinates, of the product space of
the respective (minimal) hulls. We observe a rich variety of behaviors on the
quantum dynamical transport ranging from localization to transport.Comment: 3 figures. To appear in Journal of Stat. Physic
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