Influence of the extent of the eigenstates of a system on the resonances formed through its coupling to a field

We examine resonances for two systems consisting of a particle coupled to a massless boson's field. The field is the free field in the whole space. In the first system, the particle is confined inside a ball. We show that besides the usual energy levels of the particle, which have become complex through the coupling to the field, other resonances are to be taken into account if the ball's radius is comparable to the particle's Compton wavelength. In the second system, the particle is in a finite-depth square-well potential. We study the way the resonances' width depends on the extent of the uncoupled particle's wave functions. In both cases, we limit ourselves to considering two levels of the particle only

On hybrid states of two and three level atoms

We calculate atom-photon resonances in the Wigner-Weisskopf model, admitting two photons and choosing a particular coupling function. We also present a rough description of the set of resonances in a model for a three-level atom coupled to the photon field. We give a general picture of matter-field resonances these results fit into.Comment: 33 pages, 12 figure

Using a conic bundle method to accelerate both phases of a quadratic convex reformulation

We present algorithm MIQCR-CB that is an advancement of method MIQCR~(Billionnet, Elloumi and Lambert, 2012). MIQCR is a method for solving mixed-integer quadratic programs and works in two phases: the first phase determines an equivalent quadratic formulation with a convex objective function by solving a semidefinite problem $(SDP)$, and, in the second phase, the equivalent formulation is solved by a standard solver. As the reformulation relies on the solution of a large-scale semidefinite program, it is not tractable by existing semidefinite solvers, already for medium sized problems. To surmount this difficulty, we present in MIQCR-CB a subgradient algorithm within a Lagrangian duality framework for solving $(SDP)$ that substantially speeds up the first phase. Moreover, this algorithm leads to a reformulated problem of smaller size than the one obtained by the original MIQCR method which results in a shorter time for solving the second phase. We present extensive computational results to show the efficiency of our algorithm

Puzzle Game about Connectivity and Biological Corridors

Biodiversity puzzle gameLandscape fragmentation prevents some species from moving as they should. This fragmentation, mainly due to urbanization, agriculture and forest exploitation, is a major cause of biodiversity loss. One of the options commonly envisaged to remedy this fragmentation - restore some connectivity - is the development of biological corridors. These corridors are natural spaces, usually linear. They allow species to move between different areas that are natural habitats for them.The aim of this game is to raise awareness among different audiences about issues related to biodiversity conservation, and more specifically the notion of landscape connectivity. The question is approached in a playful way: to determine, in a hypothetical landscape, the network of biological corridors, at the lowest cost, that would connect a fragmented set of natural habitats. The costs associated with sites that could be protected to form a corridor include monetary costs, ecological costs and social costs. This game also makes it possible to evoke human activities likely to develop in unprotected sites and have a negative impact on the preservation of biodiversity. It is a very simple game that cannot, of course, take into account all the complexity inherent in connectivity problems

On the consequences of the fact that atomic levels have a certain width

This note presents two ideas. The first one is that quantum theory has a fundamentally perturbative basis but leads to nonperturbative states which it would seem natural to take into account in the foundation of a theory of quantum phenomena. The second one consists in questioning the validity of the present notion of time. Both matters are related to the fact that atomic levels have a certain width. This note is presented qualitatively so as to evidence its main points, independently of the models on which these have been tested.Comment: 8 page

Exact Solution Methods for the kk-item Quadratic Knapsack Problem

The purpose of this paper is to solve the 0-1 $k$-item quadratic knapsack problem $(kQKP)$, a problem of maximizing a quadratic function subject to two linear constraints. We propose an exact method based on semidefinite optimization. The semidefinite relaxation used in our approach includes simple rank one constraints, which can be handled efficiently by interior point methods. Furthermore, we strengthen the relaxation by polyhedral constraints and obtain approximate solutions to this semidefinite problem by applying a bundle method. We review other exact solution methods and compare all these approaches by experimenting with instances of various sizes and densities.Comment: 12 page

Solving a general mixed-integer quadratic problem through convex reformulation : a computational study

International audienceLet (QP) be a mixed integer quadratic program that consists of minimizing a qua-dratic function subject to linear constraints. In this paper, we present a convex reformulation of (QP), i.e. we reformulate (QP) into an equivalent program, with a convex objective function. Such a reformulation can be solved by a standard solver that uses a branch and bound algorithm. This reformulation, that we call MIQCR (Mixed Integer Quadratic Convex Reformulation), is the best one within a convex reformulation scheme, from the continuous relaxation point of view. It is based on the solution of an SDP relaxation of (QP). Computational experiences were carried out with instances of (QP) with one equality constraint. The results show that most of the considered instances, with up to 60 variables, can be solved within 1 hour of CPU time by a standard solver

Designing Protected Area Networks

There is a broad consensus in considering that the loss of biodiversity is accelerating which is due, for example, to the destruction of habitats, overexploitation of wild species and climate change. Many countries have pledged at various international conferences to take swift measures to halt this loss of biodiversity. Among these measures, the creation of protected areas – which also contribute to food and water security, the fight against climate change and people’ health and well-being – plays a decisive role, although it is not sufficient on its own. In this book, we review classic and original problems associated with the optimal design of a network of protected areas, focusing on the modelling and practical solution of these problems. We show how to approach these optimisation problems within a unified framework, that of mathematical programming, a branch of mathematics that focuses on finding good solutions to a problem from a huge number of possible solutions. We describe efficient and often innovative modellings of these problems. Several strategies are also proposed to take into account the inevitable uncertainty concerning the ecological benefits that can be expected from protected areas. These strategies are based on the classical notions of probability and robustness. This book aims to help all those, from students to decision-makers, who are confronted with the establishment of a network of protected areas to identify the most effective solutions, taking into account ecological objectives, various constraints and limited resources. In order to facilitate the reading of this book, most of the problems addressed and the approaches proposed to solve them are illustrated by fully processed examples, and an appendix presents in some detail the basic mathematical concepts related to its content