1,117 research outputs found
Almost periodic Schrödinger operators along interval exchange transformations
AbstractIt is shown that Schrödinger operators, with potentials along the shift embedding of irreducible interval exchange transformations in a dense set, have pure singular continuous spectrum for Lebesgue almost all points of the interval. Such potentials are natural generalizations of the Sturmian case
Quantum Energy Expectation in Periodic Time-Dependent hamiltonians via Green Functions
Let be the Floquet operator of a time periodic hamiltonian .
For each positive and discrete observable (which we call a {\em probe
energy}), we derive a formula for the Laplace time average of its expectation
value up to time in terms of its eigenvalues and Green functions at the
circle of radius . Some simple applications are provided which support
its usefulness.Comment: 31 page
Hydrogen atom bound states whose spectral measures have positive upper fractal dimensions
It is shown that, Baire generically, the bound states of the Hamiltonian of
the Hydrogen atom have spectral measures with exact -lower and -upper
generalized fractal dimensions; the relation to (a weak form of) dynamical
delocalization along orthonormal bases is also discussed. Such result is a
consequence of the distribution of the Hamiltonian eigenvalues
On the spectrum and weakly effective operator for Dirichlet Laplacian in thin deformed tubes
We study the Laplacian in deformed thin (bounded or unbounded) tubes in
?, i.e., tubular regions along a curve whose cross sections are
multiplied by an appropriate deformation function . One the main
requirements on is that it has a single point of global maximum. We find
the asymptotic behaviors of the eigenvalues and weakly effective operators as
the diameters of the tubes tend to zero. It is shown that such behaviors are
not influenced by some geometric features of the tube, such as curvature,
torsion and twisting, and so a huge amount of different deformed tubes are
asymptotically described by the same weakly effective operator
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