New representations for (max,+) automata with applications to performance evaluation and control of discrete event systems

A large class of timed discrete event systems can be modeled by means of (max,+) automata, that is automata with weights in the so-called (max,+) algebra. In this contribution, specific recursive equations over (max,+) and (min,+) algebras are shown to be suitable for describing extremal behaviors of (max,+) automata. Several pertinent performance indicators can be easily derived or approximated from these representations with a low computation complexity. It is also shown how to define inputs which model exogenous influences on their dynamic evolution, and a new approach for the control of (max,+) automata is proposed

Eléments d'évaluation de performances pour les systèmes à événements discrets à travers de nouvelles représentations pour les automates (max,+)

Dans ce papier, on étudie les performances des systèmes à événements discrets modélisés à l\u27aide d\u27automates (max,+). Pour cela, nous proposons des représentations qui permettent aisément d\u27obtenir le temps d\u27exécution maximum ainsi qu\u27un minorant du temps d\u27exécution minimum pour les séquences de longueur n. Une comparaison avec les résultats de la littérature vise à mettre en avant les avantages de l\u27approche proposée à partir de ces représentations

Localization of a dipolar Bose-Einstein condensate in a bichromatic optical lattice

By numerical simulation and variational analysis of the Gross-Pitaevskii equation we study the localization, with an exponential tail, of a dipolar Bose-Einstein condensate (DBEC) of $^{52}$Cr atoms in a three-dimensional bichromatic optical-lattice (OL) generated by two monochromatic OL of incommensurate wavelengths along three orthogonal directions. For a fixed dipole-dipole interaction, a localized state of a small number of atoms ($\sim 1000$) could be obtained when the short-range interaction is not too attractive or not too repulsive. A phase diagram showing the region of stability of a DBEC with short-range interaction and dipole-dipole interaction is given

Zeeman slowers made simple with permanent magnets in a Halbach configuration

We describe a simple Zeeman slower design using permanent magnets. Contrary to common wire-wound setups no electric power and water cooling are required. In addition, the whole system can be assembled and disassembled at will. The magnetic field is however transverse to the atomic motion and an extra repumper laser is necessary. A Halbach configuration of the magnets produces a high quality magnetic field and no further adjustment is needed. After optimization of the laser parameters, the apparatus produces an intense beam of slow and cold 87Rb atoms. With a typical flux of 1 - 5 \times 10^10 atoms/s at 30 ms^-1, our apparatus efficiently loads a large magneto-optical trap with more than 10^10 atoms in one second, which is an ideal starting point for degenerate quantum gases experiments.Comment: 8+6 pages (article + appendices: calculation details, probe and oven description, pictures), 18 figures, supplementary material (movie, Mathematica programs and technical drawings

New representations for (max,+)-automata with applications to the performance evaluation of discrete event systems

A large class of timed discrete event systems can be modeled thanks to (max,+)-automata, that is automata with weights in the so-called (max,+) algebra. In this contribution, new representations are proposed for (max,+)-automata. Indeed, specific recursive equations over (max,+) and (min,+) algebras are shown to be suitable for describing extremal behaviors of (max,+)-automata. It is underlined that several performance evaluation elements, such as maximum and minimum string execution times, can be easily derived from these representations

A Dielectric Superfluid of Polar Molecules

We show that, under achievable experimental conditions, a Bose-Einstein condensate (BEC) of polar molecules can exhibit dielectric character. In particular, we derive a set of self-consistent mean-field equations that couple the condensate density to its electric dipole field, leading to the emergence of polarization modes that are coupled to the rich quasiparticle spectrum of the condensate. While the usual roton instability is suppressed in this system, the coupling can give rise to a phonon-like instability that is characteristic of a dielectric material with a negative static dielectric function.Comment: Version published in New Journal of Physics, 11+ pages, 4 figure

Complete devil's staircase and crystal--superfluid transitions in a dipolar XXZ spin chain: A trapped ion quantum simulation

Systems with long-range interactions show a variety of intriguing properties: they typically accommodate many meta-stable states, they can give rise to spontaneous formation of supersolids, and they can lead to counterintuitive thermodynamic behavior. However, the increased complexity that comes with long-range interactions strongly hinders theoretical studies. This makes a quantum simulator for long-range models highly desirable. Here, we show that a chain of trapped ions can be used to quantum simulate a one-dimensional model of hard-core bosons with dipolar off-site interaction and tunneling, equivalent to a dipolar XXZ spin-1/2 chain. We explore the rich phase diagram of this model in detail, employing perturbative mean-field theory, exact diagonalization, and quasiexact numerical techniques (density-matrix renormalization group and infinite time evolving block decimation). We find that the complete devil's staircase -- an infinite sequence of crystal states existing at vanishing tunneling -- spreads to a succession of lobes similar to the Mott-lobes found in Bose--Hubbard models. Investigating the melting of these crystal states at increased tunneling, we do not find (contrary to similar two-dimensional models) clear indications of supersolid behavior in the region around the melting transition. However, we find that inside the insulating lobes there are quasi-long range (algebraic) correlations, opposed to models with nearest-neighbor tunneling which show exponential decay of correlations

Dynamical electron transport through a nanoelectromechanical wire in a magnetic field

We investigate dynamical transport properties of interacting electrons moving in a vibrating nanoelectromechanical wire in a magnetic field. We have built an exactly solvable model in which electric current and mechanical oscillation are treated fully quantum mechanically on an equal footing. Quantum mechanically fluctuating Aharonov-Bohm phases obtained by the electrons cause nontrivial contribution to mechanical vibration and electrical conduction of the wire. We demonstrate our theory by calculating the admittance of the wire which are influenced by the multiple interplay between the mechanical and the electrical energy scales, magnetic field strength, and the electron-electron interaction