Two interacting atoms in a cavity: exact solutions, entanglement and decoherence

We address the problem of two interacting atoms of different species inside a cavity and find the explicit solutions of the corresponding eigenvalues and eigenfunctions using a new invariant. This model encompasses various commonly used models. By way of example we obtain closed expressions for concurrence and purity as a function of time for the case where the cavity is prepared in a number state. We discuss the behaviour of these quantities and and their relative behaviour in the concurrence-purity plane.Comment: 10 pages, 3 figure

Canonically Transformed Detectors Applied to the Classical Inverse Scattering Problem

The concept of measurement in classical scattering is interpreted as an overlap of a particle packet with some area in phase space that describes the detector. Considering that usually we record the passage of particles at some point in space, a common detector is described e.g. for one-dimensional systems as a narrow strip in phase space. We generalize this concept allowing this strip to be transformed by some, possibly non-linear, canonical transformation, introducing thus a canonically transformed detector. We show such detectors to be useful in the context of the inverse scattering problem in situations where recently discovered scattering echoes could not be seen without their help. More relevant applications in quantum systems are suggested.Comment: 8 pages, 15 figures. Better figures can be found in the original article, wich can be found in http://www.sm.luth.se/~norbert/home_journal/electronic/v12s1.html Related movies can be found in www.cicc.unam.mx/~mau

Decoherence at constant excitation

We present a simple exactly solvable extension of of the Jaynes-Cummings model by adding dissipation. This is done such that the total number of excitations is conserved. The Liouville operator in the resulting master equation can be reduced to blocks of $4\times 4$ matrices

Direct detection of exoplanet host star companion γ Cep B and revised masses for both stars and the sub-stellar object

Context. The star γ Cep is known as a single-lined spectroscopic triple system at a distance of 13.8 pc, composed of a K1 III-IV primary star with V = 3.2 mag, a stellar-mass companion in a 66-67 year orbit (Torres 2007, ApJ, 654, 1095), and a substellar companion with M_p sin i = 1.7 M_(Jup) that is most likely a planet (Hatzes et al. 2003, ApJ, 599, 1383). Aims. We aim to obtain a first direct detection of the stellar companion, to determine its current orbital position (for comparison with the spectroscopic and astrometric data), its infrared magnitude and, hence, mass. Methods. We use the Adaptive Optics camera CIAO at the Japanese 8 m telescope Subaru on Mauna Kea, Hawaii, with the semi-transparent coronograph to block most of the light from the bright primary γ Cep A, and to detect at the same time the faint companion B. In addition, we also used the IR camera Ω Cass at the Calar Alto 3.5 m telescope, Spain, to image γ Cep A and B by adding up many very short integrations (without AO). Results. γ Cep B is clearly detected on our CIAO and Ω Cass images. We use a photometric standard star to determine the magnitude of B after PSF subtraction in the Subaru image, and the magnitude difference between A and B in the Calar Alto images, and find an average value of K = 7.3 ± 0.2 mag. The separations and position angles between A and B are measured on 15 July 2006 and 11 and 12 Sept. 2006, B is slightly south of west of A. Conclusions. By combining the radial velocity, astrometric, and imaging data, we have refined the binary orbit and determined the dynamical masses of the two stars in the γ Cep system, namely 1.40 ± 0.12 M_☉ for the primary and 0.409 ± 0.018 M_☉ for the secondary (consistent with being a M4 dwarf). We also determine the minimum mass of the sub-stellar companion to be M_p sin i = 1.60 ± 0.13 M_(Jup)

Optimal control of a dengue epidemic model with vaccination

We present a SIR+ASI epidemic model to describe the interaction between human and dengue fever mosquito populations. A control strategy in the form of vaccination, to decrease the number of infected individuals, is used. An optimal control approach is applied in order to find the best way to fight the disease.Comment: This is a preprint of a paper accepted for presentation at ICNAAM 2011, Halkidiki, Greece, 19-25 September 2011, and to appear in AIP Conference Proceedings, volume 138

Modeling and Optimal Control Applied to a Vector Borne Disease

A model with six mutually-exclusive compartments related to Dengue disease is presented. In this model there are three vector control tools: insecticides (larvicide and adulticide) and mechanical control. The problem is studied using an Optimal Control (OC) approach. The human data for the model is based on the Cape Verde Dengue outbreak. Some control measures are simulated and their consequences analyzed

Insecticide control in a Dengue epidemics model

A model for the transmission of dengue disease is presented. It consists of eight mutually-exclusive compartments representing the human and vector dynamics. It also includes a control parameter (insecticide) in order to fight the mosquitoes. The main goal of this work is to investigate the best way to apply the control in order to effectively reduce the number of infected humans and mosquitoes. A case study, using data of the outbreak that occurred in 2009 in Cape Verde, is presented.Comment: Accepted 28/07/2010 in the special session "Numerical Optimization" of the 8th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2010), Rhodes, Greece, 19-25 September 201