Stationary States in Bistable System Driven by L\'evy Noise

We study the properties of the probability density function (PDF) of a bistable system driven by heavy tailed white symmetric L\'evy noise. The shape of the stationary PDF is found analytically for the particular case of the L\'evy index \alpha = 1 (Cauchy noise). For an arbitrary L\'evy index we employ numerical methods based on the solution of the stochastic Langevin equation and space fractional kinetic equation. In contrast with the bistable system driven by Gaussian noise, in the L\'evy case the positions of maxima of the stationary PDF do not coincide with the positions of minima of the bistable potential. We provide a detailed study of the distance between the maxima and the minima as a function of the potential's depth and L\'evy noise parameters.Comment: Accepted to EPJS

Bhabha scattering at LEP1. Calorimeter event selection

Analitical calculations have been used to describe the calorimeter event selection in small-angle electron-positron scattering at LEP1. The first-order QED correction to the Born cross-section has been derived with leading log and the next-to-leading log approximations. The second- and the third-order corrections were computed with leading accuracy. The present analytical results are illustated by Tabeles and compared with the corresponding results obtained with the Monte Carlo generator BHLUMI.Comment: 26p., submitted to Journ. of Physics