Eight-quark interactions as a chiral thermometer

A NJL Lagrangian extended to six and eight quark interactions is applied to study temperature effects (SU(3) flavor limit, massless case), and (realistic massive case). The transition temperature can be considerably reduced as compared to the standard approach, in accordance with recent lattice calculations. The mesonic spectra built on the spontaneously broken vacuum induced by the 't Hooft interaction strength, as opposed to the commonly considered case driven by the four-quark coupling, undergoes a rapid crossover to the unbroken phase, with a slope and at a temperature which is regulated by the strength of the OZI violating eight-quark interactions. This strength can be adjusted in consonance with the four-quark coupling and leaves the spectra unchanged, except for the sigma meson mass, which decreases. A first order transition behavior is also a possible solution within the present approach.Comment: 4 pages, 4 figures, prepared for the proceedings of Quark Matter 2008 - 20th International Conference on Ultra-Relativistic Nucleus Nucleus Collisions, February 4-10, Jaipur (India

Harmonic analysis and the Riemann-Roch theorem

This paper is a continuation of papers: arXiv:0707.1766 [math.AG] and arXiv:0912.1577 [math.AG]. Using the two-dimensional Poisson formulas from these papers and two-dimensional adelic theory we obtain the Riemann-Roch formula on a projective smooth algebraic surface over a finite field.Comment: 7 pages; to appear in Doklady Mathematic

Optical properties of a disordered metallic film: local vs. collective phenomena

We apply the dual-varibles approach to the problem of the optical response of an disordered film of metal particles with dipole-dipole interaction. Long range dipole-dipole interaction makes the effect of spatial correlations significant, so that dual-variables technique provides a desirable improvement of the coherent-potential results. It is shown that the effect of nonlocality is more pronounced for a medium-range concentration of the particles. The result is compared with the non-local cluster approach. It is shown that short-range correlations accounted in the cluster method reveal themselves in the spectral properties of the response, whereas long-range phenomena kept in the dual technique are more pronounced in the k-dependence of the Green's function.Comment: 8 pages, 3 figure

Role of current quark mass dependent multi-quark interactions in low lying meson mass spectra

We call attention to a class of current-quark mass dependent multi-quark interaction terms which break explicitly the chiral $SU(3)_L\times SU(3)_R$ and $U_A(1)$ symmetries. They complete the set of effective quark interactions that contribute at the same order in $N_c$ as the 't Hooft flavor determinant interaction and the eight quark interactions in the phase of spontaneously broken chiral symmetry. The $N_c$ classification scheme matches the counting rules based on arguments set by the scale of spontaneous chiral symmetry breaking. Together with the leading in $N_c$ four quark Nambu-Jona-Lasinio Lagrangian and current quark mass matrix, the model is apt to account for the correct empirical ordering and magnitude of the splitting of states in the low lying mass spectra of spin zero mesons. The new terms turn out to be essential for the ordering $m_K < m_\eta$ in the pseudoscalar sector and $m_{\kappa_0} < m_{a_0}\sim m_{f0}$ for the scalars.Comment: 6 pages, 1 figure, prepared for the proceedings of the workshop "Excited QCD 2013", 03-09 February 2013 in Bjelasnica Mountain, Sarajevo, Bosni

Unified molecular field theory of nematic, smectic-A, and smectic-C phases

A unified mean-field molecular theory of nematic (NU), smectic A (SmA), and smectic C (SmC) liquid crystal phases, composed of uniaxial nonpolar molecules, is developed taking into account the variation of all orientational and translational order parameters in these phases. Numerical results, obtained by direct global minimization of the free energy, are presented in the form of three typical phase diagrams of different topology. Temperature variation of the relevant order parameters in different sequences of phases is analyzed for various cross sections of the phase diagrams. The present model enables one to reproduce all possible sequences of phase transitions between the given phases including isotropic (Iso)-NU-SmA-SmC, Iso-NU-SmC, Iso-SmA-SmC, and Iso-SmC. The properties of the NAC point, where the NU, SmA, and SmC structures coexist, are considered in detail and the shape of the phase diagram in the vicinity of the NAC point is compared with existing experimental data