arXiv subjects

Moacir Aloisio

Publications and source records attributed to Moacir Aloisio.

8 recordsLinked to original sources

arXiv2026

Localization and eigenvalue asymptotics for long-range discrete Dirac operators with Stark potential

We study long-range discrete Dirac operators with Stark potential, extending the theory of Stark localization from scalar lattice models to systems with internal spinorial structure. We initially investigate the local setting, where two distinct localization mechanisms arise. The standard local Dirac-Stark operator yields two Stark-type spectral ladders and exponentially localized spinorial eigenfunctions. Conversely, a related pure-shift local model exhibits an invariant block structure that leads to explicitly computable eigenvalues and exact localization, with eigenfunctions compactly supported on only two spinorial sites. This extreme confinement surpasses the factorial decay characteristic of the classical scalar Stark model. For the general long-range Dirac model, we observe that the eigenvalues remain asymptotically close to the Stark ladder and prove that the corresponding eigenfunctions satisfy power-law localization estimates. Consequently, we establish power-law localization in the sense of finite moments of the position operator for the spinorial evolution. Our results demonstrate that deterministic Stark localization is robust and persists in genuinely matrix-valued lattice systems.

math.SP↗

arXiv2022

Slow dynamics for self-adjoint semigroups and unitary evolution groups

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 case of unitary evolution groups. We present an application to the quantum dynamics of purely absolutely continuous systems

math.SP↗

arXiv2021

Some generic fractal properties of bounded self-adjoint operators

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 presented. Firstly, it is shown that the set of vectors whose associated spectral measures have lower (upper) generalized fractal dimension equal to zero (one) for every $q>1$ ($0<q<1$) is either empty or generic. The second one gives sufficient conditions, for separable regular spaces of operators, for the presence of generic extreme dimensional values; in this context, we have a new proof of the celebrated Wonderland Theorem.

math.SP↗

arXiv2020

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 $0$-lower and $1/3$-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.

math-ph↗

arXiv2019

Category theorems for Schrödinger semigroups

Stimulated by the category theorems of Eisner and Serény in the setting of unitary and isometric $C_0$-semigroups on separable Hilbert spaces, we prove category theorems for Schrödinger semigroups. Specifically, we show that, to a given class of Schrödinger semigroups, Baire generically the semigroups are strongly stable but not exponentially stable. We also present a typical spectral property of the corresponding Schrödinger operators.

math.SP↗

arXiv2019

Refined scales of decaying rates of operator semigroups on Hilbert spaces: typical behaviour

We study relations between the decaying rates of operator semigroups on Hilbert spaces and some spectral properties of their respective generators; in particular, we show that the decaying rates of orbits of semigroups which are stable but not exponentially stable, typically in Baire's sense, depend on sequences of time going to infinity.

math.SP↗

arXiv2019

A note on spectrum and quantum dynamics

We show, in the same vein of Simon's Wonderland Theorem, that, typically in Baire's sense, the rates with whom the solutions of the Schrödinger equation escape, in time average, from every finite-dimensional subspace, depend on subsequences of time going to infinite.

math.SP↗

arXiv2019

Quantum quasiballistic dynamics and thick point spectrum

We obtain dynamical lower bounds for some self-adjoint operators with pure point spectrum in terms of the spacing properties of their eigenvalues. In particular, it is shown that for systems with thick point spectrum, typically in Baire's sense, the dynamics of each initial condition (with respect to some orthonormal bases of the space) presents a quasiballistic behaviour. We present explicit applications to some Schrödinger operators.

math-ph↗