The chiral condensate and dressed Polyakov loop at finite temperature and density have been investigated in the framework of N f = 2 + 1 Nambu-Jona-Lasinio (NJL) model with two degenerate u, d quarks and one strange quark. In the case of explicit chiral symmetry breaking with physical quark masses, it is found that the phase transitions for light u, d quarks and s quark are sequentially happened, and the separation between the transition lines for different flavors becomes wider and wider with the increase of baryon density. For each flavor, the pseudo-critical temperatures for chiral condensate and dressed Polyakov loop differ in a narrow transition range in the lower baryon density region, and the two transitions coincide in the higher baryon density region.

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We present an analysis of the starspot evolution, the surface differential rotation (SDR), the correlation between chromospheric activity indicators and the spatial connection between chromospheric and photospheric activities on the active star Kepler-411, using time-series photometry over four years from Kepler, and spectroscopic data from Keck I 10-m and Lijiang 2.4-m telescopes. We constructed the light curve (LC) by re-performing photometry and reduction from the Target Pixel Files and Cotrending Basis Vectors with a manually redefined aperture using the software pyke3. An efficient program, gemc_lcm, was developed to apply a two-spots model to chosen LC segments with three spot groups at fixed latitudes (30○, 45○), (30○, 60○) and (45○, 60○). We found a periodic variation of the starspots at the period of about 660 d which independs on spot latitudes, and estimated the lower limit of SDR rate α = 0.1016(0.0023) and equatoral rotation period Peq = 9.7810(0.0169) d. Simultaneously, the relative variations of chromospheric activity indicators were derived by subtracting the overall mean spectrum from individual spectrum. It is found that Ca ii H and K emissions are strongly correlated with each other, and there also exists a correlation between Hα and Ca ii H & K emissions, with large dispersion, in accordance with previous results. Furthermore, we find the correlation between Ca ii H and K emissions is different in 2011 and 2012. The chromospheric emission variation shows a highly spatial anticorrelation with the LC, suggesting a spatial connection between the chromospheric active region and spot region.

Electric and magnetic screenings of the thermal gluons are studied by using the background expansion method in a gluodynamic model with dimension-2 gluon condensate. At low temperature, the electric and magnetic gluons are degenerate. With the increasing of temperature, it is found that the electric and magnetic gluons start to split at certain temperature T 0 . The electric screening mass changes rapidly with temperature when T > T 0 , and the Polyakov loop expectation value rises sharply around T 0 from zero in the vacuum to a value around 0.8 at high temperature. This suggests that the color electric deconfinement phase transition is driven by electric gluons. It is also observed that the magnetic screening mass keeps almost the same as its vacuum value, which manifests that the magnetic gluons remains confined. Both the screening masses and the Polyakov loop results are qualitatively in agreement with the Lattice calculations.