Pascal Monceau

Generalized coherent states for arbitrary quantum systems

Recent developments [3] in the construction of coherent states for an arbitrary quantum system with Hamiltonian H are presented here. These CS families {|J,γ〉} are required to solve the unity, to be temporally stable, e -iHt/ħ |J,γ〉 =| J,γ+ ωt〉, and the J functional dependence of the energy mean value 〈J, γ | H |J,γ〉 = E(J) is assigned possibly along lines which are classically meaningful. Further extensions are finally proposed.

Anomalous dimension exponents on fractal structures for the Ising and three-state Potts model

Abstract We provide an overall picture of the magnetic critical behavior of the Ising and three-state Potts models on fractal structures. The results brought out from Monte Carlo simulations for several Hausdorff dimensions betweenxa01 andxa03 show that this behavior can be understood in the framework of weak universality. Moreover, the maxima of the susceptibility follow power laws in a very reliable way, which allows us to calculate the ratio of the exponents γ / ν and the anomalous dimension exponent η in a reliable way. At last, the evolution of these exponents with the Hausdorff dimension is discussed.

Statistics of local environments in fractals

Abstract The study of random configurations of Sierpinski carpets enables us to observe the fluctuations and mean values of local connectedness. The law of variation of these mean values with the order of iteration is deduced numerically in exact agreement with analytical considerations where new “simplex” statistical subdimensions appear.

Scaling law of Wolff cluster surface energy

We study the scaling properties of the clusters grown by the Wolff algorithm on seven different Sierpinski-type fractals of Hausdorff dimension

Screened Coulomb scattering versus Thomson scattering

1l{d}_{f}l~3

Direct evidence for weak universality on fractal structures

in the framework of the Ising model. The mean absolute value of the surface energy of Wolff cluster follows a power law with respect to the lattice size. Moreover, we investigate the probability density distribution of the surface energy of the Wolff cluster and are able to establish a different scaling relation. It enables us to introduce an exponent that is associated to the surface energy of the Wolff cluster. Finally, this exponent is linked to a dynamical exponent via an inequality.

Magnetic critical behavior of fractals in dimensions between 2 and 3

We examine a simplified approach to the classical scattering of a particle by a neutral atom, first for a Thomson-like model and then for different screened Coulomb potentials. As an application we discuss in detail why, in the experiments of Geiger and Marsden on the scattering of α particles by matter, screening effects are negligible. On the way we encounter several unusual phenomena in classical scattering theory.