Theoretical investigation of parity violation in p→α scattering

Calculations are presented of the parity-non-conserving (PNC) analyzing power A_z for longitudinally polarized incoming protons in elastic $\overrightarrow{p}\alpha$ scattering below ～50 MeV. The results are given in terms of the PNC as well as the regular, parity-conserving (PC) meson-nucleon coupling constants for single π-, ρ- and ω-exchange. The reliability and parameter dependence of the calculations are discussed in detail. The PC on-shell scattering parameters play an important role in particular for the angular dependence of A_z, which must be known for the actual analysis of measurements and are taken from experiments directly (phase analysis) rather than model calculations. The PNC scattering amplitudes are calculated in DWBA with optical-model wave functions properly antisymmetrized.Short-range correlations between nucleon pairs are taken into account by a Jastrow factor whose appropriate choice is discussed in detail. While absorption from the elastic channel is taken into account by the optical-model wave function, intermediate breakup channels are not included explicitly in the matrix elements.     

Large-Nf chiral transition in the Yukawa model

We investigate the finite-temperature behavior of the Yukawa model in which $N_f$ fermions are coupled with a scalar field ϕ in the limit $N_f\to \infty$. Close to the chiral transition the model shows a crossover between mean-field behavior (observed for $N_f=\infty$) and Ising behavior (observed for any finite $N_f$). We show that this crossover is universal and related to that observed in the weakly-coupled ${\varphi }^4$ theory. It corresponds to the renormalization-group flow from the unstable Gaussian fixed point to the stable Ising fixed point. This equivalence allows us to use results obtained in field theory and in medium-range spin models to compute Yukawa correlation functions in the crossover regime.     

Surface plasmons in a semi-bounded massless Dirac plasma

The collective excitation of surface plasmons in a massless Dirac plasma (e.g., graphene) half-space (bounded by air) is investigated using a relativistic quantum fluid model. The unique features of such surface waves are discussed and compared with those in a Fermi plasma. It is found that in contrast to Fermi plasmas, the long-wavelength surface plasmon frequency (ω) in massless Dirac plasmas is explicitly nonclassical, i.e., $\omega \propto 1/\sqrt{?}$, where $h=2\pi ?$ is the Planck's constant. Besides some apparent similarities between the surface plasmon frequencies in massless Dirac plasmas and Fermi plasmas, several notable differences are also found and discussed. Our findings elucidate the properties of surface plasmons that may propagate in degenerate plasmas where the relativistic and quantum effects play a vital role.     

Regularities of many-body systems interacting by a two-body random ensemble

The ground states of all even–even nuclei have angular momentum, I, equal to zero, $I=0$, and positive parity, $\pi =+$. This feature was believed to be a consequence of the attractive short-range interaction between nucleons. However, in the presence of two-body random interactions, the predominance of $I^{\pi }=0^{+}$ ground states (0 g.s.) was found to be robust both for bosons and for an even number of fermions. For simple systems, such as d bosons, sp bosons, sd bosons, and a few fermions in single-$j$ shells for small $j$, there are a few approaches to predict and/or explain spin I ground state (I g.s.) probabilities. An empirical approach to predict I g.s. probabilities is available for general cases, such as fermions in a single-$j$ ($j>\frac{7}{2}$) or many-$j$ shells and various boson systems, but a more fundamental understanding of the robustness of 0 g.s. dominance is still out of reach. Further interesting results are also reviewed concerning other robust phenomena of many-body systems in the presence of random two-body interactions, such as the odd–even staggering of binding energies, generic collectivity, the behavior of average energies, correlations, and regularities of many-body systems interacting by a displaced two-body random ensemble.     

On the spinorial representation of spacelike surfaces into 4-dimensional Minkowski space

We prove that an isometric immersion of a simply connected Riemannian surface $M$ in four-dimensional Minkowski space, with given normal bundle $E$ and given mean curvature vector $\overrightarrow{H}\in \Gamma \left(E\right)$, is equivalent to a normalized spinor field $\phi \in \Gamma (\Sigma E\otimes \Sigma M)$ solution of a Dirac equation $D\phi =\overrightarrow{H}\cdot \phi$ on the surface. Using the immersion of the Minkowski space into the complex quaternions, we also obtain a representation of the immersion in terms of the spinor field. We then use these results to describe the flat spacelike surfaces with flat normal bundle and regular Gauss map in four-dimensional Minkowski space, and also the flat surfaces in three-dimensional hyperbolic space, giving spinorial proofs of results by J.A. Gálvez, A. Martínez and F. Milán.