Critical Points in the Linear Sigma Model with Quarks

We employ a simple effective model to study the chiral dynamics of two flavors of quarks at finite temperature and density. In particular, we determine the phase diagram in the plane of temperature and baryon chemical potential as a function of the pion mass. An interesting phase structure occurs which results in zero, one or two critical points depending on the value of the vacuum pion mass.Comment: 16 pages plus 5 figure

Weak and strong coupling limits of the two-dimensional Fr\"ohlich polaron with spin-orbit Rashba interaction

The continuous progress in fabricating low-dimensional systems with large spin-orbit couplings has reached a point in which nowadays materials may display spin-orbit splitting energies ranging from a few to hundreds of meV. This situation calls for a better understanding of the interplay between the spin-orbit coupling and other interactions ubiquitously present in solids, in particular when the spin-orbit splitting is comparable in magnitude with characteristic energy scales such as the Fermi energy and the phonon frequency. In this article, the two-dimensional Fr\"ohlich electron-phonon problem is reformulated by introducing the coupling to a spin-orbit Rashba potential, allowing for a description of the spin-orbit effects on the electron-phonon interaction. The ground state of the resulting Fr\"ohlich-Rashba polaron is studied in the weak and strong coupling limits of the electron-phonon interaction for arbitrary values of the spin-orbit splitting. The weak coupling case is studied within the Rayleigh-Schr\"odinger perturbation theory, while the strong-coupling electron-phonon regime is investigated by means of variational polaron wave functions in the adiabatic limit. It is found that, for both weak and strong coupling polarons, the ground state energy is systematically lowered by the spin-orbit interaction, indicating that the polaronic character is strengthened by the Rashba coupling. It is also shown that, consistently with the lowering of the ground state, the polaron effective mass is enhanced compared to the zero spin-orbit limit. Finally, it is argued that the crossover between weakly and strongly coupled polarons can be shifted by the spin-orbit interaction.Comment: 11 pages, 5 figure

A Neural Network model with Bidirectional Whitening

We present here a new model and algorithm which performs an efficient Natural gradient descent for Multilayer Perceptrons. Natural gradient descent was originally proposed from a point of view of information geometry, and it performs the steepest descent updates on manifolds in a Riemannian space. In particular, we extend an approach taken by the "Whitened neural networks" model. We make the whitening process not only in feed-forward direction as in the original model, but also in the back-propagation phase. Its efficacy is shown by an application of this "Bidirectional whitened neural networks" model to a handwritten character recognition data (MNIST data).Comment: 16page

Photon emission in a constant magnetic field in 2+1 dimensional space-time

We calculate by the proper-time method the amplitude of the two-photon emission by a charged fermion in a constant magnetic field in (2+1)-dimensional space-time. The relevant dynamics reduces to that of a supesymmetric quantum-mechanical system with one bosonic and one fermionic degrees of freedom.Comment: 18 pages. v2: references added, some significant changes in the introductio

A representative sample of Be Stars I: Sample Selection, Spectral Classification and Rotational Velocities

We present a sample of 58 Be stars containing objects of spectral types O9 to B8.5 and luminosity classes III to V. We have obtained 3670 - 5070 Angstrom spectra of the sample which are used to derive spectral types and rotational velocities. We discuss the distribution of spectral types and rotational velocities obtained and conclude that there are no significant selection effects in our sample.Comment: 10 Pages, 9 Figures, Accepted for publication in A&A

Width and extremal height distributions of fluctuating interfaces with window boundary conditions

We present a detailed study of squared local roughness (SLRDs) and local extremal height distributions (LEHDs), calculated in windows of lateral size $l$, for interfaces in several universality classes, in substrate dimensions $d_s = 1$ and $d_s = 2$. We show that their cumulants follow a Family-Vicsek type scaling, and, at early times, when $\xi \ll l$ ($\xi$ is the correlation length), the rescaled SLRDs are given by log-normal distributions, with their $n$th cumulant scaling as $(\xi/l)^{(n-1)d_s}$. This give rise to an interesting temporal scaling for such cumulants $\left\langle w_n \right\rangle_c \sim t^{\gamma_n}$, with $\gamma_n = 2 n \beta + {(n-1)d_s}/{z} = \left[ 2 n + {(n-1)d_s}/{\alpha} \right] \beta$. This scaling is analytically proved for the Edwards-Wilkinson (EW) and Random Deposition interfaces, and numerically confirmed for other classes. In general, it is featured by small corrections and, thus, it yields exponents $\gamma_n$'s (and, consequently, $\alpha$, $\beta$ and $z$) in nice agreement with their respective universality class. Thus, it is an useful framework for numerical and experimental investigations, where it is, usually, hard to estimate the dynamic $z$ and mainly the (global) roughness $\alpha$ exponents. The stationary (for $\xi \gg l$) SLRDs and LEHDs of Kardar-Parisi-Zhang (KPZ) class are also investigated and, for some models, strong finite-size corrections are found. However, we demonstrate that good evidences of their universality can be obtained through successive extrapolations of their cumulant ratios for long times and large $l$'s. We also show that SLRDs and LEHDs are the same for flat and curved KPZ interfaces.Comment: 11 pages, 10 figures, 4 table

The optical-ultraviolet continuum of Seyfert 2 galaxies

This paper aims to understand the continuum of Seyfert 2 galaxies. By fitting the single galaxies in the sample of Heckman et al. (1995) with composite models (shock+ photoionization from the active center), we show that five main components characterize the SED of the continuum. Shocks play an important role since they produce a high temperature zone where soft X-rays are emitted. We show that in the optical-UV range, the slope of the NLR emission reproduces the observed values, and may be the main component of the featureless continuum. The presence of star forming regions cannot be excluded in the circumnuclear region of various Seyfert galaxies. An attempt is made to find their fingerprints in the observed AGN spectra. Finally, it is demonstrated that multi-cloud models are necessary to interpret the spectra of single objects, even in the global investigation of a sample of galaxies.Comment: 26 pages, LaTeX (including 5 Tables) + 17 PostScript figures. To appear in "The Astrophysical Journal