Real-time thermal Schwinger-Dyson equation for quark self-energy in Landau gauge

By means of a formal expression of the Cornwall-Jackiw-Tomboulis effective potential for quark propagator at finite temperature and finite quark chemical potential, we derive the real-time thermal Schwinger-Dyson equation for quark propagator in Landau gauge. Denote the inverse quark propagator by $A(p^2)\not{p}-B(p^2)$, we argue that, when temperature $T$ is less than the given infrared momentum cutoff $p_c$, $A(p^2)=1$ is a feasible approximation and can be assumed in discussions of chiral symmetry phase transition problem in QCD.Comment: 8 pages, Latex, no figur

Electrochemical growth of three-dimensionally ordered macroporous metals as photonic crystals

Over the last two decades three dimensionally ordered macroporous (3-DOM) materials have turned out to be very promising in many applications ranging from optics, plasmonics, to catalyst scaffolds. The thesis presents a systematic study on formation and characterisation of 3-DOM metals as photonic crystals. Metals are nearly perfect reflectors with low adsorption at microwave or millimetre wavelengths. Meanwhile they generally absorb visible light because of their negative imaginary part of the dielectric constant that could destroy the band gap in the visible though they. Howevers, for noble metals such as gold, silver and copper, considering the Drude-like behaviour, the adsorption will be small enough to achieve a complete photonic band gap for optical or even shorter wavelengths, with silver performing the best. In order to fabricate the 3-DOM metallic nanostructures, template-directed electrochemical deposition has been employed in which, initially a highly ordered film of submircon sized colloidal spheres is deposited on to electronically conducting substrates, for instance, indium-tin oxide (ITO) coated glass substrate, through evaporation-induced self-assembly; and subsequently it is infiltrated with metallic elements electrochemically reduced from corresponding electrolytes; fiannly removal of the colloidal templating film reveals a metallic film comprised of periodically arranged spherical voids. Field Emission Gun Scanning Electron Microscopy (FEGSEM) was used to examine the surface morphology and periodicity of the 3-DOM metallic films. It revealed that highly ordered structures are homogenous and uniform over a large scale for both the original colloidal templates and metallic inverse structures. However for silver electroplated from either silver thiosulfate or silver chlorate bath, voids in the template are fully infiltrated, including both the interstitial spaces between the colloidal spheres and any cracks between film domains, forming a complete solid network over large length scales; for copper the filling factors are strongly dependent on the bath chemistry and in copper sulfate bath isolated macroporous domains can be formed due to those in the cracks will be dissolved back to the solution while those reduced from copper glycerol bath resulted in fully infiltrated structures. Moreover, angle-resolved reflectance spectroscopy has further confirmed the three-dimensional periodicity and indicated the inverse structures have stop band properties in the visible wavelength region, consistent with variation in the effective refractive index of the films. In addition, surface enhanced Raman scattering (SERS) spectroscopy has been used to evaluate applications of the inverse metals as SERS-active substrates. SERS has nearly exclusively been associated with three noble metals copper, silver (by far the most important) and gold. The 3-DOM metallic thin films possess excellent features for SERS detection arising from their long range periodical void geometry, which gives significant enhancement to Raman intensity. Preliminary measurements have demonstrated the 3-DOM metallic structures are well suited for SERS enhancement. Series spectra from different points of each specimen have given reproducible intensities. Variables associated with Raman intensity such as pore size, dye concentration, and film thickness, have been tuned to achieve maximal enhancement for visible and near-IR wavelengths

Quark-Antiquark and Diquark Condensates in Vacuum in a 3D Two-Flavor Gross-Neveu Model

The effective potential analysis indicates that, in a 3D two-flavor Gross-Neveu model in vacuum, depending on less or bigger than the critical value 2/3 of $G_S/H_P$, where $G_S$ and $H_P$ are respectively the coupling constants of scalar quark-antiquark channel and pseudoscalar diquark channel, the system will have the ground state with pure diquark condensates or with pure quark-antiquark condensates, but no the one with coexistence of the two forms of condensates. The similarities and differences in the interplay between the quark-antiquark and the diquark condensates in vacuum in the 2D, 3D and 4D two-flavor four-fermion interaction models are summarized.Comment: 5 pages, revtex4, no figure, minor typos correcte

Effective potential for composite operators and for an auxiliary scalar field in a Nambu-Jona-Lasinio model

We derive the effective potentials for composite operators in a Nambu-Jona-Lasinio (NJL) model at zero and finite temperature and show that in each case they are equivalent to the corresponding effective potentials based on an auxiliary scalar field. The both effective potentials could lead to the same possible spontaneous breaking and restoration of symmetries including chiral symmetry if the momentum cutoff in the loop integrals is large enough, and can be transformed to each other when the Schwinger-Dyson (SD) equation of the dynamical fermion mass from the fermion-antifermion vacuum (or thermal) condensates is used. The results also generally indicate that two effective potentials with the same single order parameter but rather different mathematical expressions can still be considered physically equivalent if the SD equation corresponding to the extreme value conditions of the two potentials have the same form.Comment: 7 pages, no figur