A Class of Exact Solutions For N-Anyons in a N-body Potential

A class of exact solutions are obtained for the problem of N-anyons interacting via the N-body potential $V (\vec x_1,\vec x_2,...,\vec x_N)$ = $-{e^2\over\sqrt{{1\over N}\sum_{i<j} (\vec x_i-\vec x_j)^2}}$ Unlike the oscillator case the resulting spectrum is not linear in the anyon parameter $\alpha (0\leq \alpha\leq 1)$. However, a la oscillator case, cross-over between the ground states is shown to occur for N-anyons $(N\geq 3)$ experiencing the above potential.Comment: 10 pages, no figure, latex fil

Few-anyon systems in a parabolic dot

The energy levels of two and three anyons in a two-dimensional parabolic quantum dot and a perpendicular magnetic field are computed as power series in 1/|J|, where J is the angular momentum. The particles interact repulsively through a coulombic (1/r) potential. In the two-anyon problem, the reached accuracy is better than one part in 10^5. For three anyons, we study the combined effects of anyon statistics and coulomb repulsion in the ``linear'' anyonic states.Comment: LaTeX, 6 pages, 4 postscript figure

Approximate formula for the ground state energy of anyons in 2D parabolic well

We determine approximate formula for the ground state energy of anyons in 2D parabolic well which is valid for the arbitrary anyonic factor \nu and number of particles N in the system. We assume that centre of mass motion energy is not excluded from the energy of the system. Formula for ground state energy calculated by variational principle contains logarithmic divergence at small distances between two anyons which is regularized by cut-off parameter. By equating this variational formula to the analogous formula of Wu near bosonic limit (\nu ~ 0)we determine the value of the cut-off and thus derive the approximate formula for the ground state energy for the any \nu and N. We checked this formula at \nu=1, when anyons become fermions, for the systems containing two to thirty particles. We find that our approximate formula has an accuracy within 6%. It turns out, at the big number N limit the ground state energy has square root dependence on factor \nu.Comment: 7 page

From Gauging Nonrelativistic Translations to N-Body Dynamics

We consider the gauging of space translations with time-dependent gauge functions. Using fixed time gauge of relativistic theory, we consider the gauge-invariant model describing the motion of nonrelativistic particles. When we use gauge-invariant nonrelativistic velocities as independent variables the translation gauge fields enter the equations through a d\times (d+1) matrix of vielbein fields and their Abelian field strengths, which can be identified with the torsion tensors of teleparallel formulation of relativity theory. We consider the planar case (d=2) in some detail, with the assumption that the action for the dreibein fields is given by the translational Chern-Simons term. We fix the asymptotic transformations in such a way that the space part of the metric becomes asymptotically Euclidean. The residual symmetries are (local in time) translations and rigid rotations. We describe the effective interaction of the d=2 N-particle problem and discuss its classical solution for N=2. The phase space Hamiltonian H describing two-body interactions satisfies a nonlinear equation H={\cal H}(\vec x,\vec p;H) which implies, after quantization, a nonstandard form of the Schr\"odinger equation with energy dependent fractional angular momentum eigenvalues. Quantum solutions of the two-body problem are discussed. The bound states with discrete energy levels correspond to a confined classical motion (for the planar distance between two particles r\le r_0) and the scattering states with continuum energy correspond to the classical motion for r>r_0. We extend our considerations by introducing an external constant magnetic field and, for N=2, provide the classical and quantum solutions in the confined and unconfined regimes.Comment: LaTeX, 38 pages, 1 picture include

Du marketing stratégique au marketing opérationnel : devenir le leader français de la construction à hautes exigences

Avant de se lancer dans quelconque activité, il est vital pour une entreprise d’en avoir analysé l’environnement, d’en déterminer les menaces et opportunités, tout comme ses points forts et ses faiblesses. Cela lui permettra alors d’établir ses facteurs clés de succès, sur lesquels elle s’appuiera pour se différencier des concurrents et élaborer sa stratégie. Dans un milieu ultra-concurrentiel, il faut avoir une stratégie affutée et bien ficelée pour se démarquer, et savoir entre autre s’entourer des bons collaborateurs. Après avoir segmenté le marché, l’entreprise peut alors cibler les segments sur lesquels elle va se focaliser et se développer. C’est à partir de ces éléments que sera élaboré le plan d’action stratégique, regroupant toutes les opérations à mettre en œuvre afin d’atteindre les objectifs fixés par l’entreprise au préalable. De la communication traditionnelle à la communication 2.0, de l’innovation au déploiement des ressources et compétences, les modes de développement sont multiples mais demandent une gestion sans faille, ainsi qu’un budget et un planning précis