The Hubbard model on a complete graph: Exact Analytical results

We derive the analytical expression of the ground state of the Hubbard model with unconstrained hopping at half filling and for arbitrary lattice sites.Comment: Email:[email protected]

Extraction of ∣Vcd∣|V_{cd}| and ∣Vcs∣|V_{cs}| from experimental decay rates using lattice QCD D→π(K)ℓνD \to \pi(K) \ell \nu form factors

We present a determination of the Cabibbo-Kobayashi-Maskawa matrix elements $|V_{cd}|$ and $|V_{cs}|$ obtained by combining the momentum dependence of the semileptonic vector form factors $f_+^{D \to \pi}(q^2)$ and $f_+^{D \to K}(q^2)$, recently determined from lattice QCD simulations, with the differential rates measured for the semileptonic $D \to \pi \ell \nu$ and $D \to K \ell \nu$ decays. Our analysis is based on the results for the semileptonic form factors produced by the European Twisted Mass Collaboration with $N_f = 2 + 1 + 1$ flavors of dynamical quarks in the whole range of values of the squared 4-momentum transfer accessible in the experiments. The statistical and systematic correlations between the lattice data as well as those present in the experimental data are properly taken into account. With respect to the standard procedure based on the use of only the vector form factor at zero 4-momentum transfer, we obtain more precise and consistent results: $|V_{cd} |= 0.2341 ~ (74)$ and $|V_{cs} |= 0.970 ~ (33)$. The second-row CKM unitarity is fulfilled within the current uncertainties: $|V_{cd}|^2 + |V_{cs}|^2 + |V_{cb}|^2 = 0.996 ~ (64)$. Moreover, using for the first time hadronic inputs determined from first principles, we have calculated the ratio of the semileptonic $D \to \pi(K)$ decay rates into muons and electrons, which represent a test of lepton universality within the SM, obtaining in the isospin-symmetric limit of QCD: ${\cal{R}}_{LU}^{D\pi} = 0.985~(2)$ and ${\cal{R}}_{LU}^{DK} = 0.975~(1)$.Comment: 8 pages, 2 figures, 8 tables. Version to appear in EPJ

Il dovere di fedelt\ue0 tra simbolismo costituzionale e patriottismo repubblicano

Nel saggio si analizza il dovere di fedelt\ue0 alla Repubblica, sia dal punto di vista dell'aspetto simbolico che tale dovere riveste nell'ambito dell'ordinamento costituzionale, sia dal punto di vista della categoria dei doveri costituzionali. Dopo una disamina delle principali opinioni dottrinali sulle predette questioni, si prospetta una configurazione volta a rafforzare ed estendere il valore deontologico di tale dovere

Domain walls and bubble-droplets in immiscible binary Bose gases

The existence and stability of domain walls (DWs) and bubble-droplet (BD) states in binary mixtures of quasi-one-dimensional ultracold Bose gases with inter- and intra-species repulsive interactions is considered. Previously, DWs were studied by means of coupled systems of Gross-Pitaevskii equations (GPEs) with cubic terms, which model immiscible binary Bose-Einstein condensates (BECs). We address immiscible BECs with two- and three-body repulsive interactions, as well as binary Tonks--Girardeau (TG) gases, using systems of GPEs with cubic and quintic nonlinearities for the binary BEC, and coupled nonlinear Schr\"{o}dinger equations with quintic terms for the TG gases. Exact DW\ solutions are found for the symmetric BEC mixture, with equal intra-species scattering lengths. Stable asymmetric DWs in the BEC mixtures with dissimilar interactions in the two components, as well as of symmetric and asymmetric DWs in the binary TG gas, are found by means of numerical and approximate analytical methods. In the BEC system, DWs can be easily put in motion by phase imprinting. Combining a DW and anti-DW on a ring, we construct BD states for both the BEC and TG models. These consist of a dark soliton in one component (the "bubble"), and a bright soliton (the "droplet") in the other. In the BEC system, these composite states are mobile too.Comment: Phys. Rev. A, in pres

Quantum-tunneling dynamics of a spin-polarized Fermi gas in a double-well potential

We study the exact dynamics of a one-dimensional spin-polarized gas of fermions in a double-well potential at zero and finite temperature. Despite the system is made of non-interacting fermions, its dynamics can be quite complex, showing strongly aperiodic spatio-temporal patterns during the tunneling. The extension of these results to the case of mixtures of spin-polarized fermions in interaction with self-trapped Bose-Einstein condensates (BECs) at zero temperature is considered as well. In this case we show that the fermionic dynamics remains qualitatively similar to the one observed in absence of BEC but with the Rabi frequencies of fermionic excited states explicitly depending on the number of bosons and on the boson-fermion interaction strength. From this, the possibility to control quantum fermionic dynamics by means of Feshbach resonances is suggested.Comment: Accepted for publication in Phys. Rev.

Hypercubic effects in semileptonic decays of heavy mesons, toward B→πℓνB \to \pi \ell \nu, with Nf=2+1+1N_f=2+1+1 Twisted fermions

We present a preliminary study toward a lattice determination of the vector and scalar form factors of the $B \to \pi \ell \nu$ semileptonic decays. We compute the form factors relative to the transition between heavy-light pseudoscalar mesons, with masses above the physical D-mass, and the pion. We simulate heavy-quark masses in the range $m_c^{phys} < m_h < 2m_c^{phys}$. Lorentz symmetry breaking due to hypercubic effects is clearly observed in the data, and included in the decomposition of the current matrix elements in terms of additional form factors. We discuss the size of this breaking as the parent-meson mass increases. Our analysis is based on the gauge configurations produced by the European Twisted Mass Collaboration with $N_f = 2 + 1 + 1$ flavors of dynamical quarks at three different values of the lattice spacing and with pion masses as small as $210$ MeV.Comment: 7 pages, 5 figures; contribution to the XXXVI International Symposium on Lattice Field Theory (LATTICE2018), East Lansing (Michigan State University, USA), July 22-28, 201

Landau-Zener Tunneling of Bose-Einstein Condensates in an Optical Lattice

A theory of the non-symmetric Landau-Zener tunneling of Bose-Einstein condensates in deep optical lattices is presented. It is shown that periodic exchange of matter between the bands is described by a set of linearly coupled nonlinear Schr\"{o}dinger equations. The key role of the modulational instability in rendering the inter-band transitions irreversible is highlighted.Comment: 4 pages, 3 figure

Rigorismo y pluralidad de principios en ética

The problem of the applicability of moral principles is one of the most significant issues of practical reflection. With Kant's practical philosophy, the ethical demands of universality and individuality came to seem incompatible. After reviewing the outlooks of Apel and Simmel, who both offer paradigmatic answers to the “rigorism” of the categorical imperative, this article presents the issue from the perspective of Maliandi's “Convergent Ethics”. It suggests that Maliandi's recognition of an “a priori of conflictivity” and of the bi-dimensional character of reason surmounts the shortages of both Apel's and Simmel's philosophies