Preequilibrium particle emissions and in-medium effects on the pion production in heavy-ion collisions

Within the framework of the Lanzhou quantum molecular dynamics (LQMD) transport model, pion dynamics in heavy-ion collisions near threshold energies and the emission of preequilibrium particles (nucleons and light complex fragments) have been investigated. A density, momentum and isospin dependent pion-nucleon potential based on the $\Delta$-hole model is implemented in the transport approach, which slightly leads to the increase of the $\pi^{-}/\pi^{+}$ ratio, but reduces the total pion yields. It is found that a bump structure of the $\pi^{-}/\pi^{+}$ ratio in the kinetic energy spectra appears at the pion energy close to the $\Delta$(1232) resonance region. The yield ratios of neutrons to protons from the squeeze-out particles perpendicular to the reaction plane are sensitive to the stiffness of nuclear symmetry energy, in particular at the high-momentum (kinetic energy) tails.Comment: 8 pages, 9 figures, submitted EPJA. arXiv admin note: text overlap with arXiv:1509.0479

Momentum dependence of the symmetry potential and its influence on nuclear reactions

A Skyrme-type momentum-dependent nucleon-nucleon force distinguishing isospin effect is parameterized and further implemented in the Lanzhou Quantum Molecular Dynamics (LQMD) model for the first time, which leads to a splitting of nucleon effective mass in nuclear matter. Based on the isospin- and momentum-dependent transport model, we investigate the influence of momentum-dependent symmetry potential on several isospin-sensitive observables in heavy-ion collisions. It is found that symmetry potentials with and without the momentum dependence but corresponding to the same density dependence of the symmetry energy result in different distributions of the observables. The mid-rapidity neutron/proton ratios at high transverse momenta and the excitation functions of the total $\pi^{-}/\pi^{+}$ and $K^{0}/K^{+}$ yields are particularly sensitive to the momentum dependence of the symmetry potential.Comment: 12 pages, 5 figure

Cyclotomic Constructions of Skew Hadamard Difference Sets

We revisit the old idea of constructing difference sets from cyclotomic classes. Two constructions of skew Hadamard difference sets are given in the additive groups of finite fields using unions of cyclotomic classes of order $N=2p_1^m$, where $p_1$ is a prime and $m$ a positive integer. Our main tools are index 2 Gauss sums, instead of cyclotomic numbers.Comment: 15 pages; corrected a few typos; to appear in J. Combin. Theory (A

Strongly Regular Graphs From Unions of Cyclotomic Classes

We give two constructions of strongly regular Cayley graphs on finite fields \F_q by using union of cyclotomic classes and index 2 Gauss sums. In particular, we obtain twelve infinite families of strongly regular graphs with new parameters.Comment: 17 pages; to appear in J. Combin. Theory (B

Semi-regular Relative Difference Sets with Large Forbidden Subgroups

Motivated by a connection between semi-regular relative difference sets and mutually unbiased bases, we study relative difference sets with parameters $(m,n,m,m/n)$ in groups of non-prime-power orders. Let $p$ be an odd prime. We prove that there does not exist a $(2p,p,2p,2)$ relative difference set in any group of order $2p^2$, and an abelian $(4p,p,4p,4)$ relative difference set can only exist in the group $\Bbb{Z}_2^2\times \Bbb{Z}_3^2$. On the other hand, we construct a family of non-abelian relative difference sets with parameters $(4q,q,4q,4)$, where $q$ is an odd prime power greater than 9 and $q\equiv 1$ (mod 4). When $q=p$ is a prime, $p>9$, and $p\equiv$ 1 (mod 4), the $(4p,p,4p,4)$ non-abelian relative difference sets constructed here are genuinely non-abelian in the sense that there does not exist an abelian relative difference set with the same parameters

Josephson junction on one edge of a two dimensional topological insulator affected by magnetic impurity

Current-phase relation in a Josephson junction formed by putting two s-wave superconductors on the same edge of a two dimensional topological insulator is investigated. We consider the case that the junction length is finite and magnetic impurity exists. The similarity and difference with conventional Josephson junction is discussed. The current is calculated in the semiconductor picture. Both the $2\pi$- and $4\pi$-period current-phase relations ($I_{2\pi}(\phi), I_{4\pi}(\phi)$) are studied. There is a sharp jump at $\phi=\pi$ and $\phi=2\pi$ for $I_{2\pi}$ and $I_{4\pi}$ respectively in the clean junction. For $I_{2\pi}$, the sharp jump is robust against impurity strength and distribution. However for $I_{4\pi}$, the impurity makes the jump at $\phi=2\pi$ smooth. The critical (maximum) current of $I_{2\pi}$ is given and we find it will be increased by asymmetrical distribution of impurity.Comment: 7 pages, 5 figure