Narrow Results

In the mean field approximation of (2 + 1)-flavor Nambu–Jona-Lasinio model, we strictly derive several sets of coupled equations for the chiral susceptibility, the quark number susceptibility, etc. at finite temperature and quark chemical potential. The critical exponents of these susceptibilities in the vicinity of the QCD critical end point (CEP) are presented in SU(2) and SU(3) cases, respectively. It is found that these various susceptibilities share almost the same critical behavior near the CEP. The comparisons between the critical exponents for the order parameters and the theoretical predictions are also included.

This paper aims to review the advances achieved in the field of nonlinear optics in relation to phthalocyanines and other related compounds. The main focus is on electronic nonlinear processes, such as second- and third-harmonic generation, and mostly on the work performed by Portuguese and Spanish research groups. Several aspects in which these teams were pioneers are described in more detail. In particular, they performed numerous experiments in solution, thanks to their synthetic efforts in preparing soluble compounds, thus enabling the determination of the nonlinear parameters at a molecular level. They also measured for the first time the real and imaginary components (i.e. the magnitude and the phase) of the nonlinear parameters of phthalocyanines and, in some cases, their frequency dispersion behavior. Such detailed studies allow for the elaboration of microscopic models to identify the electronic levels involved in nonlinear processes. Some Spanish groups were also pioneers in the characterization of the nonlinear optical properties of unsymmetrically substituted phthalocyanines and other related compounds, such as triazolehemiporphyrazines and subphthalocyanines.