Convergent sequences of perturbative approximations for the anharmonic oscillator II. Compact time approach

We present an alternative pathway in the application of the variation improvement of ordinary perturbation theory exposed in [1] which can preserve the internal symmetries of a model by means of a time compactification.Comment: 21 pages, 4 Postscript figures available through anonymous ftp at ftp://algol.lpm.univ-montp2.fr ; replaces version which could not be postscripted presumably for lack of figures.uu fil

Convergent sequences of perturbative approximations for the anharmonic oscillator I. Harmonic approach

We present numerical evidence that a simple variational improvement of the ordinary perturbation theory of the quantum anharmonic oscillator can give a convergent sequence of approximations even in the extreme strong coupling limit, the purely anharmonic case. Some of the new techniques of this paper can be extended to renormalizable field theories.Comment: 29 pages, 12 Postscript figures available through anonymous ftp at ftp://algol.lpm.univ-montp2.fr ; replaces earlier version which could not be postscripted presumably due to lack of figures.uu fil

Photonic Hall Effect in ferrofluids: Theory and Experiments

An experimental and theoretical study on the Photonic Hall Effect (PHE) in liquid and gelled samples of ferrofluids is presented. The ferrofluids are aqueous colloidal suspensions of Fe(_{2})CoO(_{4}) particles, which can be considered as anisotropic and absorbing Rayleigh scatterers. The PHE is found to be produced by the orientation of the magnetic moments of the particles, as is also the case for the Faraday effect. The dependence of the PHE with respect to the concentration of the scatterers, the magnetic field and the polarization of the incident light is measured in liquid and in gelled samples and is compared to a simple model based on the use of a scattering matrix and the single scattering approximation.Comment: 20 pages, 11 figures, submitte

On off-shell bosonic string amplitudes

We give a simple prescription for computing, in the framework of the bosonic string theory, off-shell one-loop amplitudes with any number of external massless particles, both for the open and for the closed string. We discuss their properties and, in particular, for the two-string one-loop amplitudes we show their being transverse.Comment: 12 pages, Latex. One reference added. Introduction and conclusions expanded. Some other minor changes in the tex

Almost Sure Convergence of Solutions to Non-Homogeneous Stochastic Difference Equation

We consider a non-homogeneous nonlinear stochastic difference equation X_{n+1} = X_n (1 + f(X_n)\xi_{n+1}) + S_n, and its important special case X_{n+1} = X_n (1 + \xi_{n+1}) + S_n, both with initial value X_0, non-random decaying free coefficient S_n and independent random variables \xi_n. We establish results on \as convergence of solutions X_n to zero. The necessary conditions we find tie together certain moments of the noise \xi_n and the rate of decay of S_n. To ascertain sharpness of our conditions we discuss some situations when X_n diverges. We also establish a result concerning the rate of decay of X_n to zero.Comment: 22 pages; corrected more typos, fixed LaTeX macro