19 citations · 86 across the 15 of their papers we have counts for
18 papers
Quantitative spectral stability and sharp Fourier estimates for periodic CMV matrices with decaying perturbations
Moacir Aloisio, César R. de Oliveira, Mariane Pigossi
We study half-line CMV matrices whose Verblunsky coefficients are decaying perturbations of periodic sequences. We quantify the stability of fine properties of the absolutely conti…
Eigenfunction correlators under power-law SULE and localization for lattice operators
M. Aloisio, C. R. de Oliveira, R. Matos +2
We develop a deterministic framework showing that a power-law form of semi-uniform localization of eigenfunctions (SULE) imposes strong structural constraints on lattice operators,…
On spectral measures and convergence rates in von Neumann's Ergodic Theorem
M. Aloisio, S. L. Carvalho, C. R. de Oliveira +1
We show that the power-law decay exponents in von Neumann's Ergodic Theorem (for discrete systems) are the pointwise scaling exponents of a spectral measure at the spectral value~$…
Spectral Hausdorff dimensions for a class of Schrödinger operators in bounded intervals
Vanderléa R. Bazao, Túlio O. Carvalho, César R. de Oliveira
Exact Hausdorff dimensions are computed for singular continuous components of the spectral measures of a class of Schrödinger operators in bounded intervals.
Slow dynamics for self-adjoint semigroups and unitary evolution groups
Moacir Aloisio, Silas L. Carvalho, César R. de Oliveira +1
We obtain slow dynamics for self-adjoint semigroups and unitary evolution groups. For semigroups, the slow dynamics is for orbits, and for the average return probability in the cas…
Dirac cones for bi- and trilayer Bernal-stacked graphene in a quantum graph model
Cesar R. de Oliveira, Vinicius L. Rocha
A quantum graph model for a single sheet of graphene is extended to bilayer and trilayer Bernal-stacked graphene; the spectra are characterized and the dispersion relations explici…
All self-adjoint extensions of the magnetic Laplacian in nonsmooth domains and gauge transformations
Cesar R. de Oliveira, Wagner Monteiro
We use boundary triples to find a parametrization of all self-adjoint extensions of the magnetic Schrödinger operator, in a quasi-convex domain~ with compact boundary, and magne…
Lower bounds for fractal dimensions of spectral measures of the period doubling Schrödinger operator
Vanderlea R. Bazao, Tulio O. Carvalho, Cesar R. de Oliveira
It is shown that there exits a lower bound to the Hausdorff dimension of the spectral measures of the one-dimensional period doubling substitution Schrödinger operator, and,…
Some generic fractal properties of bounded self-adjoint operators
Moacir Aloisio, Silas L. Carvalho, César R. de Oliveira
We study generic fractal properties of bounded self-adjoint operators through lower and upper generalized fractal dimensions of their spectral measures. Two groups of results are p…
Hydrogen atom bound states whose spectral measures have positive upper fractal dimensions
Moacir Aloisio, Silas L. Carvalho, César R. de Oliveira
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 dimens…
A new version of the Aharonov-Bohm effect
Cesar R. de Oliveira, Renan G. Romano
We propose a simple situation in which the magnetic Aharonov-Bohm potential influences the values of the deficiency indices of the initial Schrödinger operator, so determining whet…
On the spectral Hausdorff dimension of 1D discrete Schrödinger operators under power decaying perturbations
Vanderlea R. Bazao, Silas L. Carvalho, César R. de Oliveira
We show that spectral Hausdorff dimensional properties of discrete Schröodinger operators with (1) Sturmian potentials of bounded density and (2) a class of sparse potentials are p…
Complex -convergence and magnetic Dirichlet Laplacian in bounded thin tubes
R. Bedoya, C. R. de Oliveira, A. A. Verri
The resolvent convergence of self-adjoint operators via the technique of -convergence of quadratic forms is adapted to incorporate complex Hilbert spaces. As an application, we…
Mathematical predominance of Dirichlet condition for the one-dimensional Coulomb potential
Cesar R. de Oliveira, Alessandra A. Verri
We restrict a quantum particle under a coulombian potential (i.e., the Schrödinger operator with inverse of the distance potential) to three dimensional tubes along the x-axis and…
Quantum singular operator limits of thin Dirichlet tubes via -convergence
Cesar R. de Oliveira
The -convergence of lower bounded quadratic forms is used to study the singular operator limit of thin tubes (i.e., the vanishing of the cross section diameter) of the Laplace o…
Scattering and self-adjoint extensions of the Aharonov-Bohm hamiltonian
Cesar R. de Oliveira, Marciano Pereira
We consider the hamiltonian operator associated with planar sec- tions of infinitely long cylindrical solenoids and with a homogeneous magnetic field in their interior. First, in t…
(De)Localization in the Prime Schrodinger Operator
Cesar R. de Oliveira, Giancarlo Q. Pellegrino
It is reported a combined numerical approach to study the localization properties of the one-dimensional tight-binding model with potential modulated along the prime numbers. A loc…
Quantum Return Probability for Substitution Potentials
Cesar R. de Oliveira, Giancarlo Q. Pellegrino
We propose an effective exponent ruling the algebraic decay of the average quantum return probability for discrete Schrodinger operators. We compute it for some non-periodic substi…