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L. Alonso

Publications and source records attributed to L. Alonso.

6 recordsLinked to original sources
arXiv2021

Probing ultracold gases using photoionization fine structure

Photoionization of atoms immersed in an environment such as an ultracold gas is investigated. We show that the interference of two ionization pathways, one passing directly to the continuum and one accounting for scattering processes between the photoelectron and a neighboring atom, produces a fine structure in the photoionization cross-section over an energy range less than 1 eV above threshold. This fine structure includes all the details of the corresponding three-body system, e.g. the interatomic distance or the scattering information of the electron-atom subsystem; therefore, photoelectrons produced in a multi-particle environment can be utilized as structural probes. As an illustration, for experimentally relevant parameters, we propose a scheme based on the photoionization of a Rydberg molecule where the low-energy electron-atom phase shifts are extracted from the fine structure spectra using neural networks.

physics.atom-ph↗
arXiv2019

Geometrical and spectral study of $\beta$-skeleton graphs

We perform an extensive numerical analysis of $\beta$-skeleton graphs, a particular type of proximity graphs. In a $\beta$-skeleton graph (BSG) two vertices are connected if a proximity rule, that depends of the parameter $\beta\in(0,\infty)$, is satisfied. Moreover, for $\beta>1$ there exist two different proximity rules, leading to lune-based and circle-based BSGs. First, by computing the average degree of large ensembles of BSGs we detect differences, which increase with the increase of $\beta$, between lune-based and circle-based BSGs. Then, within a random matrix theory (RMT) approach, we explore spectral and eigenvector properties of randomly weighted BSGs by the use of the nearest-neighbor energy-level spacing distribution and the entropic eigenvector localization length, respectively. The RMT analysis allows us to conclude that a localization transition occurs at $\beta=1$.

physics.soc-ph↗
arXiv2017

Weighted random--geometric and random--rectangular graphs: Spectral and eigenfunction properties of the adjacency matrix

Within a random-matrix-theory approach, we use the nearest-neighbor energy level spacing distribution $P(s)$ and the entropic eigenfunction localization length $\ell$ to study spectral and eigenfunction properties (of adjacency matrices) of weighted random--geometric and random--rectangular graphs. A random--geometric graph (RGG) considers a set of vertices uniformly and independently distributed on the unit square, while for a random--rectangular graph (RRG) the embedding geometry is a rectangle. The RRG model depends on three parameters: The rectangle side lengths $a$ and $1/a$, the connection radius $r$, and the number of vertices $N$. We then study in detail the case $a=1$ which corresponds to weighted RGGs and explore weighted RRGs characterized by $a\sim 1$, i.e.~two-dimensional geometries, but also approach the limit of quasi-one-dimensional wires when $a\gg1$. In general we look for the scaling properties of $P(s)$ and $\ell$ as a function of $a$, $r$ and $N$. We find that the ratio $r/N^\gamma$, with $\gamma(a)\approx -1/2$, fixes the properties of both RGGs and RRGs. Moreover, when $a\ge 10$ we show that spectral and eigenfunction properties of weighted RRGs are universal for the fixed ratio $r/{\cal C}N^\gamma$, with ${\cal C}\approx a$.

physics.soc-ph↗
arXiv2015

Joint probability distributions for projection probabilities of random orthonormal states

A finite dimensional quantum system for which the quantum chaos conjecture applies has eigenstates, which show the same statistical properties than the column vectors of random orthogonal or unitary matrices. Here, we consider the different probabilities for obtaining a specific outcome in a projective measurement, provided the system is in one of its eigenstates. We then give analytic expressions for the joint probability density for these probabilities, with respect to the ensemble of random matrices. In the case of the unitary group, our results can be applied, also, to the phenomenon of universal conductance fluctuations, where the same mathematical quantities describe partial conductances in a two-terminal mesoscopic scattering problem with a finite number of modes in each terminal.

math-ph↗
arXiv2001

Correction to the paper "Duality and Flat Base Change on Formal Schemes"

In section 8.3 of our paper "Duality and Flat Base Change on Formal Schemes" (http://arXiv.org/abs/alg-geom/9708006) some important results concerning localization of, and preservation of coherence by, basic duality functors, were based on the false statement that any closed formal subscheme of an open subscheme of the completion P of a relative projective space is an open subscheme of a closed formal subscheme of P. In this note, the said results are provided with solid foundations.

math.AG↗