In-medium Properties of Θ+\Theta^{+} as a Kπ\piN structure in Relativistic Mean Field Theory

The properties of nuclear matter are discussed with the relativistic mean-field theory (RMF).Then, we use two models in studying the in-medium properties of $\Theta^+$: one is the point-like $\Theta^*$ in the usual RMF and the other is a K$\pi$N structure for the pentaquark. It is found that the in-medium properties of $\Theta^+$ are dramatically modified by its internal structure. The effective mass of $\Theta^+$ in medium is, at normal nuclear density, about 1030 MeV in the point-like model, while it is about 1120 MeV in the model of K$\pi$N pentaquark. The nuclear potential depth of $\Theta^+$ in the K$\pi$N model is approximately -37.5 MeV, much shallower than -90 MeV in the usual point-like RMF model.Comment: 8 pages, 5 figure

The properties of kaonic nuclei in relativistic mean-field theory

The static properties of some possible light and moderate kaonic nuclei, from C to Ti, are studied in the relativistic mean-field theory. The 1s and 1p state binding energies of $K^-$ are in the range of $73\sim 96$ MeV and $22\sim 63$ MeV, respectively. The binding energies of 1p states increase monotonically with the nucleon number A. The upper limit of the widths are about $42\pm 14$ MeV for the 1s states, and about $71\pm 10$ MeV for the 1p states. The lower limit of the widths are about $12\pm 4$ MeV for the 1s states, and $21\pm 3$ MeV for the 1p states. If $V_{0}\leq 30$ MeV, the discrete $K^-$ bound states should be identified in experiment. The shrinkage effect is found in the possible kaonic nuclei. The interior nuclear density increases obviously, the densest center density is about $2.1\rho_{0}$.Comment: 9 pages, 2 tables and 1 figure, widths are considered, changes a lo

Fine-Scale Variations in Eucritic Pyroxene FeO/MnO: Process vs. Provenance.

Most asteroidal igneous rocks are eucrite-like basalts and gabbros, composed mostly of ferroan low- and high-Ca pyroxenes and calcic plagioclase, plus smaller amounts of silica (most commonly tridymite), ilmenite, chromite, troilite, Ca-phosphate, metal and sometimes ferroan olivine. Eucrite-like mafic rocks are fragments of the crusts of differentiated asteroids, and most are likely from 4 Vesta

Multiple G-It\^{o} integral in the G-expectation space

In this paper, motivated by mathematic finance we introduce the multiple G-It\^{o} integral in the G-expectation space, then investigate how to calculate. We get the the relationship between Hermite polynomials and multiple G-It\^{o} integrals which is a natural extension of the classical result obtained by It\^{o} in 1951.Comment: 9 page

Translation-symmetry protected topological orders on lattice

In this paper we systematically study a simple class of translation-symmetry protected topological orders in quantum spin systems using slave-particle approach. The spin systems on square lattice are translation invariant, but may break any other symmetries. We consider topologically ordered ground states that do not spontaneously break any symmetry. Those states can be described by Z2A or Z2B projective symmetry group. We find that the Z2A translation symmetric topological orders can still be divided into 16 sub-classes corresponding to 16 new translation-symmetry protected topological orders. We introduced four $Z_2$ topological indices $\zeta_{\v{k}}=0,1$ at $\v {k}=(0,0)$, $(0,\pi)$, $(\pi, 0)$, $(\pi ,\pi)$ to characterize those 16 new topological orders. We calculated the topological degeneracies and crystal momenta for those 16 topological phases on even-by-even, even-by-odd, odd-by-even, and odd-by-odd lattices, which allows us to physically measure such topological orders. We predict the appearance of gapless fermionic excitations at the quantum phase transitions between those symmetry protected topological orders. Our result can be generalized to any dimensions. We find 256 translation-symmetry protected Z2A topological orders for a system on 3D lattice