Browsing by Author "Kheir-Eddine Boudjemaa"

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    COMPARISON OF VARIOUS LOWER BOUNDS FOR THE GROUND STATE ENERGY OF AN N-BODY SYSTEM
    (Kheir-Eddine Boudjemaa, 2010-09-20) Kheir-Eddine Boudjemaa
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    Optimized Lower Bounds for Five-Body Hamiltonians
    (Kheir-Eddine Boudjemaa, 2009-08-01) Kheir-Eddine Boudjemaa
    A methodology recently proposed for deriving optimized lower bounds for the energies of the ground states of N-body systems is applied to the five-body case. Such lower bounds result from an optimization process over a certain number of parameters. The so-called universal dynamical constraints, i.e., relations between the values of the parameters corresponding to the optimized lower bound and which have the properties to be of dynamical nature and to be independent of the particular form of the potential, are computed in their totality and great calculational details are given. The optimized lower bound obtained in this way proves to be saturated, i.e., identical to the exact result, in the harmonic oscillator case. Particular mass configurations are considered with the corresponding simplifications in the universal dynamical constraints. In relation to the property of saturability in the case of harmonic interactions, particular attention is devoted to five-body systems with harmonic interactions. Various mass configurations are considered and for each case the corresponding ground state energy is derived
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    Time delay in the Einstein-Straus solution
    (Kheir-Eddine Boudjemaa, 2011-02-08) Kheir-Eddine Boudjemaa
    We compute the time delay of strong lensing in the framework of the Einstein-Straus solution in presence of a cosmological constant and restrict ourselves to the case of a spatially flat universe. The calculations are done to first order in the ratio of Schwarzschild radius to peri-lens. We apply our results to the lensed quasar SDSS J1004+4112. Our predictions for the time delay between the images C and D of the quasar range from 6 to 13 years and are compatible with the experimental lower bound.