RESUMO
We consider a class of single-particle one-dimensional stochastic equations which include external field, additive, and multiplicative noises. We use a parameter θ ∊ [0,1] which enables the unification of the traditional Itô and Stratonovich approaches, now recovered, respectively, as the θ=0 and θ=1/2 particular cases to derive the associated Fokker-Planck equation (FPE). These FPE is a linear one, and its stationary state is given by a q-Gaussian distribution with q=(τ+2M(2-θ))/(τ+2M(1-θ)<3), where τ ≥ 0 characterizes the strength of the confining external field and M ≥ 0 is the (normalized) amplitude of the multiplicative noise. We also calculate the standard kurtosis κ(1) and the q-generalized kurtosis κ(q) (i.e., the standard kurtosis but using the escort distribution instead of the direct one). Through these two quantities we numerically follow the time evolution of the distributions. Finally, we exhibit how these quantities can be used as convenient calibrations for determining the index q from numerical data obtained through experiments, observations, or numerical computations.
RESUMO
We investigate the transfer of orbital angular momentum (OAM) in a type-II optical parametric oscillator (OPO). We produce different kinds of transverse modes on the downconverted beams by pumping the OPO with a first-order Laguerre-Gaussian beam well above threshold. Different operation regimes are attained showing a rich variety of transverse modes bearing OAM.
