[en] The interaction of a Gaussian mode with a homogeneous and an inhomogeneous laser transition is described. The interaction of the beam with the medium in a laser is treated by taking into account the spatial distribution of both radiation and gain. The intensity characteristics are very different from those obtained for a one-dimensional interaction of a plane wave with a saturating medium. In the presence of a small-signal gain profile the threshold condition requires much higher inversion densities along the optic axis than by ignoring this profile. For gas lasers, for instance, having a small-signal gain profile that is approximately described by a zero-order Bessel function, the threshold inversion density can be about 50 percent higher. For high-power systems the saturation of the medium by the Gaussian intensity distribution results in a considerable amount of radial radiation transport. For homogeneous transitions this amount is about equal to the stimulated emission and for inhomogeneous transitions it is about half of it, independent of the beamwidth. Further, it is found that if one slowly passes the threshold condition for laser action, the intensity jumps from zero to a certain value and vice versa. This effect has also been verified experimentally. (auth)

[en] We introduce a group of virtual sources for generating Lommel–Gauss beams based on beam superposition to analyze nonparaxial propagation. We typically derive the paraxial approximation and integral representations of the nth-order Lommel–Gauss beams. The first three orders of the nonparaxial corrections for the on-axis field of the Lommel–Gauss beams are analytically obtained. The on-axis intensity distribution of the corresponding nonparaxial corrections is also provided. (paper)

[en] Published in summary form only

[en] The distribution of masses for neutron stars is analyzed using the Bayesian statistical inference, evaluating the likelihood of two a priori gaussian peaks distribution by using fifty-five measured points obtained in a variety of systems. The results strongly suggest the existence of a bimodal distribution of the masses, with the first peak around 1.35M_⊙ ± 0.06M_⊙ and a much wider second peak at 1.73M_⊙ ± 0.36M_⊙. We compared the two gaussian's model centered at 1.35M_⊙ and 1.55M_⊙ against a "single gaussian" model with 1.50M_⊙ ± 0.11M_⊙ using 3σ that provided a wide peak covering objects the full range of observed of masses. In order to compare models, BIC (Baysesian Information Criterion) can be used and a strong evidence for two distributions model against one peak model was found. The results support earlier views related to the different evolutionary histories of the members for the first two peaks, which produces a natural separation (in spite that no attempt to "label" the systems has been made). However, the recently claimed low-mass group, possibly related to O - Mg - Ne core collapse events, has a monotonically decreasing likelihood and has not been identified within this sample. (author)

[en] The set of quantum Gaussian channels acting on one bosonic mode can be classified according to the action of the group of Gaussian unitaries. We look for bounds on the classical capacity for channels belonging to such a classification. Lower bounds can be efficiently calculated by restricting the study to Gaussian encodings, for which we provide analytical expressions.

[en] In the theory of extreme values of Gaussian processes, many results are expressed in terms of the Pickands constant ${\mathcal{H}}_{\mathrm{\alpha <!--\; ??\; -->}}$. This constant depends on the local self-similarity exponent α of the process, i.e. locally it is a fractional Brownian motion (fBm) of Hurst index $H=\mathrm{\alpha <!--\; ??\; -->}/2$. Despite its importance, only two values of the Pickands constant are known: ${\mathcal{H}}_1=1$ and ${\mathcal{H}}_2=1/\sqrt{\mathrm{\pi <!--\; ??\; -->}}$. Here, we extend the recent perturbative approach to fBm to include drift terms. This allows us to investigate the Pickands constant ${\mathcal{H}}_{\mathrm{\alpha <!--\; ??\; -->}}$ around standard Brownian motion ($\mathrm{\alpha <!--\; ??\; -->}=1$) and to derive the new exact result ${\mathcal{H}}_{\mathrm{\alpha <!--\; ??\; -->}}=1-<!--\; ???\; -->(\mathrm{\alpha <!--\; ??\; -->}-<!--\; ???\; -->1){\mathrm{\gamma <!--\; ??\; -->}}_{\text{E}}+\mathcal{O}{(\mathrm{\alpha <!--\; ??\; -->}-<!--\; ???\; -->1)}^2$. (letter)

[en] Published in summary form only

No abstract available

[en] Full text: We present first-principles theoretical calculations of the structural, electronic and magnetic properties of small metallic gold clusters whose size covers 9 to 16 atoms. The studies make use of a linear combination of atomic Gaussian-type orbitals within the context of Kohn-Sham density functional theory. Appealing to an empirical many-body potential in which the electronic degree of freedom is treated in some average sense, the lowest energy structures of these clusters are first determined using the parallel tempering multi canonical basin hopping plus genetic algorithm [P. J. Hsu and S. K. Lai, J. Chem. Phys. 124, 044711 (2006)]. These structures are then employed as initial atomic configurations in the density functional theory. A comparison of the structures obtained from these two methods permit an understanding on the role played by electrons in their distribution on atoms in clusters, and hence unraveling the unanticipated magnetic property. The relevant issue of the stability of a cluster and the factors that give rise to the amazing magnetic properties will be reported. (author)

No abstract available