Thermodynamic Geometry of Nambu -- Jona Lasinio model

The formalism of Riemannian geometry is applied to study the phase transitions in Nambu -Jona Lasinio (NJL) model. Thermodynamic geometry reliably describes the phase diagram, both in the chiral limit and for finite quark masses. The comparison between the geometrical study of NJL model and of (2+1) Quantum Chromodynamics at high temperature and small baryon density shows a clear connection between chiral symmetry restoration/breaking and deconfinement/confinement regimes

Inflectional loci of scrolls

Let $X\subset \mathbb P^N$ be a scroll over a smooth curve $C$ and let \L=\mathcal O_{\mathbb P^N}(1)|_X denote the hyperplane bundle. The special geometry of $X$ implies that some sheaves related to the principal part bundles of \L are locally free. The inflectional loci of $X$ can be expressed in terms of these sheaves, leading to explicit formulas for the cohomology classes of the loci. The formulas imply that the only uninflected scrolls are the balanced rational normal scrolls.Comment: 9 pages, improved version. Accepted in Mathematische Zeitschrif

Deconfinement transition effects on cosmological parameters and primordial gravitational waves spectrum

The cosmological evolution can be described in terms of directly measurable cosmological scalar parameters (deceleration q, jerk j, snap s, etc⋯) constructed out of high order derivatives of the scale factor. Their behavior at the critical temperature of the quantum chromodynamics (QCD) phase transition in early universe could be a specific tool to study the transition, analogously to the fluctuations of conserved charges in QCD. We analyze the effect of the crossover transition from quarks and gluons to hadrons in early universe on the cosmological scalars and on the gravitational wave spectrum, by using the recent lattice QCD equation of state and including the electroweak degrees of freedom. Near the transition the cosmological parameters follow the behavior of QCD trace anomaly and of the speed of sound of the entire system. The effects of deconfinement turn out to be more relevant for the modification of the primordial spectrum of gravitational waves rather than for the evolution of the cosmological parameters. Our complete analysis, based on lattice QCD simulations and on the hadron resonance gas below the critical temperature, refines previous results

Transport Models for Backscattering and Transmission of Low Energy ( \u3c 3 Kilovolts) Electrons from Solids

This paper deals with the backscattering and the transmission of electrons with energy \u3c 3 keV through thin self supporting films, or on bulk metals. We present the main theoretical models used in such problems, and we analyse mainly the models based on the Boltzmann transport equation, similar to those developed in our laboratory. For any model shown here, we try to give the precise domain in which they give reliable results as well as the limitations connected to the simplifying assumptions. In the case of the most sophisticated model, we give original results for copper. The models are presented in a comparative form, and when it is possible we compare our results with the experimental ones. The theoretical models were applied to Al and Cu. We give, for bulk metals, the values of the backscattering yield, and the energy distributions of backscattered electrons. In the case of thin self supporting films, we studied mainly the backscattering and transmission coefficients, as well as the energy distributions of transmitted and backscattered electrons

Secondary Electron Emission Induced by Electron Bombardment of Polycrystalline Metallic Targets

The aim of the present paper is the analysis of the backward secondary electron emission phenomenon, under electron bombardment, on the basis of experimental and theoretical results. Among the theoretical models, we will mention the phenomenological models, those which use a Monte-Carlo type simulation method, and those based on the numerically solved Boltzmann transport equation. To correlate experimental and theoretical results on all the data characterizing this phenomenon, it is necessary to use an appropriate description for the excitation process of the internal secondary electrons; it also needs a complete description of the transport process for the excited electrons, which incorporates the elastic and inelastic interactions, as well as the energy and angular distribution of the incident primary beam. From this, it follows that it will be necessary, either to use a direct Monte-Carlo simulation method, or, in the case of the transport model, to carry out a preliminary treatment of the primary electron dispersion; this treatment is also based upon a Boltzmann equation resolution. The results of such an analysis will be useful in electron microscopy and in quantitative Auger spectroscopy