Exact numerical methods for a many-body Wannier Stark system

We present exact methods for the numerical integration of the Wannier-Stark system in a many-body scenario including two Bloch bands. Our ab initio approaches allow for the treatment of a few-body problem with bosonic statistics and strong interparticle interaction. The numerical implementation is based on the Lanczos algorithm for the diagonalization of large, but sparse symmetric Floquet matrices. We analyze the scheme efficiency in terms of the computational time, which is shown to scale polynomially with the size of the system. The numerically computed eigensystem is applied to the analysis of the Floquet Hamiltonian describing our problem. We show that this allows, for instance, for the efficient detection and characterization of avoided crossings and their statistical analysis. We finally compare the efficiency of our Lanczos diagonalization for computing the temporal evolution of our many-body system with an explicit fourth order Runge-Kutta integration. Both implementations heavily exploit efficient matrix-vector multiplication schemes. Our results should permit an extrapolation of the applicability of exact methods to increasing sizes of generic many-body quantum problems with bosonic statistics

The prison system of Colombia and practices to transform process resocialization

Descripción actual del sistema carcelario de Colombia y practicas para mejorar el proceso de resocialización en las personas privadas de la libertad.Actual description of Colombia's prison system and practices to improve the process of rehabilitation in persons deprived of freedo

Ericson fluctuations in an open, deterministic quantum system: theory meets experiment

We provide numerically exact photoexcitation cross sections of rubidium Rydberg states in crossed, static electric and magnetic fields, in quantitative agreement with recent experimental results. Their spectral backbone underpins a clear transition towards the Ericson regime.Comment: 4 pages, 3 figures, 1 tabl

Cold atom-ion systems in radiofrequency multipole traps: event-drive molecular dynamics and stochastic simulations

We have studied the general aspects of the dynamics of an ion trapped in an ideal multipolar radiofrequency trap while interacting with a dense cold atomic gas. In particular, we have explored the dynamical stability, the energy relaxation and the characteristic harmonic motion exhibited by a trapped Yb$^{+}$ ion in different multipolar potentials and immersed in various cold atomic samples (Li, Na, Rb, Yb). For this purpose, we used two different molecular dynamics simulations; one based on a time-event drive algorithm and the other based on the stochastic Langevin equation. Relevant values for experimental realizations, such as the associated ion's lifetimes and observable distributions, are presented along with some analytical expressions which relate the ion's dynamical properties with the trap parameters.Comment: 12 pages, 11 figure

“Método perfecto” Alternativa tecnológica para el cálculo y construcción del diapasón en instrumentos de cuerda pulsada

Este proyecto trata de una alternativa que por medio de la utilización de las herramientas informáticas actúales busca facilitar el trabajo del lutier y volverlo mas exacto en el momento de calcular y construir el diapasón en instrumentos de cuerda pulsada. En esta propuesta se utiliza software como Excel para realizar el cálculo exacto de las medidas de cada espacio entre traste y traste y CorelDRAW para diseñar una plantilla la cual servirá para modificar únicamente su largo y servirá para obtener la medida que sea necesaria de manera rápida y precisa

Explicit schemes for time propagating many-body wavefunctions

Accurate theoretical data on many time-dependent processes in atomic and molecular physics and in chemistry require the direct numerical solution of the time-dependent Schr\"odinger equation, thereby motivating the development of very efficient time propagators. These usually involve the solution of very large systems of first order differential equations that are characterized by a high degree of stiffness. We analyze and compare the performance of the explicit one-step algorithms of Fatunla and Arnoldi. Both algorithms have exactly the same stability function, therefore sharing the same stability properties that turn out to be optimum. Their respective accuracy however differs significantly and depends on the physical situation involved. In order to test this accuracy, we use a predictor-corrector scheme in which the predictor is either Fatunla's or Arnoldi's algorithm and the corrector, a fully implicit four-stage Radau IIA method of order 7. We consider two physical processes. The first one is the ionization of an atomic system by a short and intense electromagnetic pulse; the atomic systems include a one-dimensional Gaussian model potential as well as atomic hydrogen and helium, both in full dimensionality. The second process is the decoherence of two-electron quantum states when a time independent perturbation is applied to a planar two-electron quantum dot where both electrons are confined in an anharmonic potential. Even though the Hamiltonian of this system is time independent the corresponding differential equation shows a striking stiffness. For the one-dimensional Gaussian potential we discuss in detail the possibility of monitoring the time step for both explicit algorithms. In the other physical situations that are much more demanding in term of computations, we show that the accuracy of both algorithms depends strongly on the degree of stiffness of the problem.Comment: 24 pages, 14 Figure