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

Highly polarized injection luminescence in forward-biased ferromagnetic-semiconductor junctions at low spin polarization of current

We consider electron tunneling from a nonmagnetic $n$-type semiconductor ($n$-S) into a ferromagnet (FM) through a very thin forward-biased Schottky barrier resulting in efficient extraction of electron spin from a thin $n$-S layer near FM-S interface at low spin polarization of the current. We show that this effect can be used for an efficient polarization radiation source in a heterostructure where the accumulated spin polarized electrons are injected from $n$-S and recombine with holes in a quantum well. The radiation polarization depends on a bias voltage applied to the FM-S junction.Comment: 4 pages, 2 figure

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