Bose-Einstein condensation in linear sigma model at Hartree and large N approximation

The BEC of charged pions is investigated in the framework of O(4) linear sigma model. By using Cornwall-Jackiw-Tomboulis formalism, we have derived the gap equations for the effective masses of the mesons at finite temperature and finite isospin density. The BEC is discussed in chiral limit and non-chiral limit at Hartree approximation and also at large N approximation.Comment: 11 pages, 9 figure

The Lyman Break Galaxies: their Progenitors and Descendants

We study the evolution of Lyman Break Galaxies (LBGs) from z=5 to z=0 by tracing the merger trees of galaxies in a large-scale hydrodynamic simulation based on a Lambda cold dark matter model. In particular, we emphasize on the range of properties of the sample selected by the rest-frame V band luminosity, in accordance with recent near-IR observations. The predicted rest-frame V band luminosity function agrees well with the observed one when dust extinction is taken into account. The stellar content and the star formation histories of LBGs are also studied. We find that the LBGs intrinsically brighter than Mv=-21.0 at z=3 have stellar masses of at least 10^9\Msun, with a median of 10^{10}h^{-1}\Msun. The brightest LBGs (Mv<-23) at z=3 merge into clusters/groups of galaxies at z=0, as suggested from clustering studies of LBGs. Roughly one half of the galaxies with -23<Mv<-22 at z=3 fall into groups/clusters, and the other half become typical L* galaxies at z=0 with stellar mass of ~10^{11}\Msun. Descendants of LBGs at the present epoch have formed roughly 30% of their stellar mass by z=3, and the half of their current stellar population is 10 Gyr old, favoring the scenario that LBGs are the precursors of the present day spheroids. We find that the most luminous LBGs have experienced a starburst within 500 Myr prior to z=3, but also have formed stars continuously over a period of 1 Gyr prior to z=3 when all the star formation in progenitors is coadded. We also study the evolution of the mean stellar metallicity distribution of galaxies, and find that the entire distribution shifts to lower metallicity at higher redshift. The observed sub-solar metallicity of LBGs at z=3 is naturally predicted in our simulation.Comment: 29 pages, including 11 figures, ApJ in press. One reference adde

Cube sums of form 3p3p and 3p23p^2 II

Let $p\equiv 2,5\mod 9$ be a prime. We prove that both $3p$ and $3p^2$ are cube sums. We also establish some explicit Gross-Zagier formulae and investigate the 3 part full BSD conjecture of the related elliptic curves

Expanding the thermodynamical potential and the analysis of the possible phase diagram of deconfinement in FL model

The deconfinement phase transition is studied in the FL model at finite temperature and chemical potential. At MFT approximation, the phase transition can only be the first order in the whole $\mu-T$ phase plane. By a Landau expansion we further study the phase transition order and the possible phase diagram of deconfinement. We discuss the possibilities of second order phase transitions in FL model. By our analysis the cubic term in the Landau expansion could be cancelled by the high order fluctuations. By an ansatz of the Landau parameters, we obtain the possible phase diagram with both first and second order phase transition including the tricritical point which is similar to that of the chiral phase transition.Comment: 7 pages, 8 figures, submitted to Chinese Physics