Quantum Hamiltonians with Quasi-Ballistic Dynamics and Point Spectrum

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dc.creatorde Oliveira, Cesar R.
dc.creatorPrado, Roberto A.
dc.date2007-01-04
dc.date.accessioned2026-07-07T07:39:06Z
dc.date.available2026-07-07T07:39:06Z
dc.descriptionConsider the family of Schrödinger operators (and also its Dirac version) on $\ell^2(\mathbb{Z})$ or $\ell^2(\mathbb{N})$ \[ H^W_{ω,S}=Δ+ λF(S^nω) + W, \quad ω\inΩ, \] where $S$ is a transformation on (compact metric) $Ω$, $F$ a real Lipschitz function and $W$ a (sufficiently fast) power-decaying perturbation. Under certain conditions it is shown that $H^W_{ω,S}$ presents quasi-ballistic dynamics for $ω$ in a dense $G_δ$ set. Applications include potentials generated by rotations of the torus with analytic condition on $F$, doubling map, Axiom A dynamical systems and the Anderson model. If $W$ is a rank one perturbation, examples of $H^W_{ω,S}$ with quasi-ballistic dynamics and point spectrum are also presented.
dc.description17 pages; to appear in Journal of Differential Equations
dc.identifierhttps://arxiv.org/abs/math-ph/0701010
dc.identifierhttp://arxiv.org/abs/math-ph/0701010
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/121326
dc.subjectMathematical Physics
dc.subject81Q10
dc.titleQuantum Hamiltonians with Quasi-Ballistic Dynamics and Point Spectrum
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