8,109 research outputs found
Quantum Intermittency in Almost-Periodic Lattice Systems Derived from their Spectral Properties
Hamiltonian tridiagonal matrices characterized by multi-fractal spectral
measures in the family of Iterated Function Systems can be constructed by a
recursive technique here described. We prove that these Hamiltonians are
almost-periodic. They are suited to describe quantum lattice systems with
nearest neighbours coupling, as well as chains of linear classical oscillators,
and electrical transmission lines.
We investigate numerically and theoretically the time dynamics of the systems
so constructed. We derive a relation linking the long-time, power-law behaviour
of the moments of the position operator, expressed by a scaling function
of the moment order , and spectral multi-fractal dimensions,
D_q, via . We show cases in which this relation
is exact, and cases where it is only approximate, unveiling the reasons for the
discrepancies.Comment: 13 pages, Latex, 6 postscript figures. Accepted for publication in
Physica
Some asymptotic properties of the spectrum of the Jacobi ensemble
For the random eigenvalues with density corresponding to the Jacobi ensemble
a strong uniform approximation by the roots of the Jacobi polynomials is
derived if the parameters depend on and .
Roughly speaking, the eigenvalues can be uniformly approximated by roots of
Jacobi polynomials with parameters , where
the error is of order . These results are used to
investigate the asymptotic properties of the corresponding spectral
distribution if and the parameters and vary with
. We also discuss further applications in the context of multivariate random
-matrices.Comment: 20 pages, 2 figure
Right limits and reflectionless measures for CMV matrices
We study CMV matrices by focusing on their right-limit sets. We prove a CMV
version of a recent result of Remling dealing with the implications of the
existence of absolutely continuous spectrum, and we study some of its
consequences. We further demonstrate the usefulness of right limits in the
study of weak asymptotic convergence of spectral measures and ratio asymptotics
for orthogonal polynomials by extending and refining earlier results of
Khrushchev. To demonstrate the analogy with the Jacobi case, we recover
corresponding previous results of Simon using the same approach
Spectral analysis of a class of hermitian Jacobi matrices in a critical (double root) hyperbolic case
We consider a class of Jacobi matrices with periodically modulated diagonal
in a critical hyperbolic ("double root") situation. For the model with
"non-smooth" matrix entries we obtain the asymptotics of generalized
eigenvectors and analyze the spectrum. In addition, we reformulate a very
helpful theorem from a paper of Janas and Moszynski in its full generality in
order to serve the needs of our method
From Random Matrices to Quasiperiodic Jacobi Matrices via Orthogonal Polynomials
We present an informal review of results on asymptotics of orthogonal
polynomials, stressing their spectral aspects and similarity in two cases
considered. They are polynomials orthonormal on a finite union of disjoint
intervals with respect to the Szego weight and polynomials orthonormal on R
with respect to varying weights and having the same union of intervals as the
set of oscillations of asymptotics. In both cases we construct double infinite
Jacobi matrices with generically quasiperiodic coefficients and show that each
of them is an isospectral deformation of another. Related results on asymptotic
eigenvalue distribution of a class of random matrices of large size are also
shortly discussed
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