The Excitation Spectrum of Two-Dimensional Bose Gases in the Gross–Pitaevskii Regime

We consider a system of N bosons, in the two-dimensional unit torus. We assume particles to interact through a repulsive two-body potential, with a scattering length that is exponentially small in N (Gross–Pitaevskii regime). In this setting, we establish the validity of the predictions of Bogoliubov theory, determining the ground state energy of the Hamilton operator and its low-energy excitation spectrum, up to errors that vanish in the limit N→ ∞

Migraine: An Overview

The pathophysiology of migraine is not completely understood and continues to be investigated. The complexity of interactions taking place in the sensory neuronal network with the mediation of all different neurotransmitters involved gives the measure of the extreme difficulty connected with the knowledge of migraine pathogenesis and in particular of its cardinal sign. Neuronal components are relevant in migraine pathophysiology: there could be a generalized interictal abnormal excitability of the cerebral cortex in migraine, possibly favoring the occurrence of spreading depression with consequent activation of the trigeminal system. Many theories have been formulated in these last sixty years about the pathogenesis of migraine and other forms of primary headache, but the problem is still far to be fully clarified. The present review is focused on the description of different theories on the migraine pathogenesis

Bose-Einstein condensation for two dimensional bosons in the Gross-Pitaevskii regime

We consider systems of N bosons trapped on the two-dimensional unit torus, in the Gross-Pitaevskii regime, where the scattering length of the repulsive interaction is exponentially small in the number of particles. We show that low-energy states exhibit complete Bose-Einstein condensation, with almost optimal bounds on the number of orthogonal excitations.Comment: 72 pages, improved rate of condensatio

Amerigo Vepucci e um moderno crítico argentino

(Primeiro Parágrafo do Artigo)Entre os resultados francamente positivos que podem ser creditados à obra realizado pelo saudoso Magnaghi, que no campos dos estudos vespuccianos, dois pelo menos, podem agora ser considerados aquisições definitivas: a inversão da tradicional relação entre os dois grupos diferentes de fontes: - o das velhas impressões, e os dos esquecidos manuscritos que, por via de regra, eram considerados apócrifos: - e o respeito com que é preciso considerar a figura do nosso grande navegador