Finite density QCD with chiral invariant four-fermion interactions

A mean field analysis of finite density QCD is presented including the effects of additional chiral invariant four-fermion interactions. A lattice regularization is used with N_f=4 flavors of staggered fermions. The use of the four-fermion coupling as an improved extrapolation parameter over the bare quark mass in Monte Carlo simulations is discussed. Particular attention is given to the structure of the phase diagram and the order of the chiral phase transition. At zero gauge coupling, the model reduces to a Nambu-Jona-Lasinio model. In this limit the chiral phase transition is found to be second-order near the zero-density critical point and otherwise first-order. In the strong gauge coupling limit a first-order chiral phase transition is found. In this limit the additional four-fermion interactions do not qualitatively change the physics. The results agree with previous studies of QCD as the four-fermion coupling vanishes.Comment: 18 pages, RevTeX, 12 figures using epsf.st

Prophetic Imagination in the Light of Narratology and Disability Studies in Isaiah 40–48

Analyzes Isaiah 40–48 as a single literary work through levels of speakers (frame and subordinate) with implications for its construction of divine potency and communication

A Kingdom of Priests and Its Earthen Altars in Exodus 19–24

Argues that, reversing the trope of subjects visiting the magnificent, the Elohistic history has Yahweh interested in the simplest, flimsiest altars only, which he will visit when and where he is invited to do so. The implication rules out temple-altars and temples for their royal sponsorship

The Face of God and the Etiquette of Eye-Contact: Visitation, Pilgrimage, and Prophetic Vision in Ancient Israelite and Early Jewish Imagination

Uses social poetics to analyze talk in the Bible of looking at Yahweh's fac

Nodal inequalities on surfaces

Given a Laplace eigenfunction on a surface, we study the distribution of its extrema on the nodal domains. It is classically known that the absolute value of the eigenfunction is asymptotically bounded by the 4-th root of the eigenvalue. It turns out that the number of nodal domains where the eigenfunction has an extremum of such order, remains bounded as the eigenvalue tends to infinity. We also observe that certain restrictions on the distribution of nodal extrema and a version of the Courant nodal domain theorem are valid for a rather wide class of functions on surfaces. These restrictions follow from a bound in the spirit of Kronrod and Yomdin on the average number of connected components of level sets.Comment: 14 pages, added a discussion of a connection with the Alexandrov-Backelman-Pucci inequalit

On the divine clockwork: the spectral gap for the correspondence limit of the Nelson diffusion generator for the atomic elliptic state

The correspondence limit of the atomic elliptic state in three dimensions is discussed in terms of Nelson's stochastic mechanics. In previous work we have shown that this approach leads to a limiting Nelson diffusion and here we discuss in detail the invariant measure for this process and show that it is concentrated on the Kepler ellipse in the plane z=0. We then show that the limiting Nelson diffusion generator has a spectral gap; thereby proving that in the infinite time limit the density for the limiting Nelson diffusion will converge to its invariant measure. We also include a summary of the Cheeger and Poincare inequalities both of which are used in our proof of the existence of the spectral gap.Comment: 30 pages, 5 figures, submitted to J. Math. Phy

On Ptolemaic metric simplicial complexes

We show that under certain mild conditions, a metric simplicial complex which satisfies the Ptolemy inequality is a CAT(0) space. Ptolemy's inequality is closely related to inversions of metric spaces. For a large class of metric simplicial complexes, we characterize those which are isometric to Euclidean space in terms of metric inversions.Comment: 13 page

Implementation of arbitrary real-valued correlation filters for the shadow-casting incoherent correlator

International audienceWe describe an incoherent correlator, based on the shadow-casting principle, that is able to implement any real-valued linear correlation filter. The correlation filter and the input image are displayed on commercial liquid-crystal television ~LCTV! panels. Although it cannot handle high-resolution images, the incoherent correlator is lensless, compact, low cost, and uses a white-light source. A bipolar technique is devised to represent any linear filter, computed from a single reference image or composite, in the correlator. We demonstrate experimentally the efficiency of the design in the case of optimal trade-off ~OT! filters and optimal trade-off synthetic discriminant function ~OT-SDF! filter

Spectral Evolution of the Universe

We derive the evolution equations for the spectra of the Universe. Here "spectra" means the eigenvalues of the Laplacian defined on a space, which contain the geometrical information on the space. These equations are expected to be useful to analyze the evolution of the geometrical structures of the Universe. As an application, we investigate the time evolution of the spectral distance between two Universes that are very close to each other; it is the first necessary step for the detailed analysis of the model-fitting problem in cosmology with the spectral scheme. We find out a universal formula for the spectral distance between two very close Universes, which turns out to be independent of the detailed form of the distance nor the gravity theory. Then we investigate its time evolution with the help of the evolution equations we derive. We also formulate the criteria for a good cosmological model in terms of the spectral distance.Comment: To appear in Phys. Rev.

Strings and Aharonov-Bohm Effect in Abelian Higgs Model

We investigate numerically the properties of the Abrikosov-Nielsen-Olesen strings in 4D abelian Higgs model. The fractal dimension D_f of the vortex strings was found to be large in the Coulomb phase and it is close to 2 in the Higgs phase. We also show that the Wilson loop for non-integer charges is correlated with the linking number of the vortex string world sheets and the test particle world trajectory. We find that this topological (Aharonov-Bohm) interaction gives the main contribution to the Wilson loop quantum average for non-integer test charges in the vicinity of the Coulomb-Higgs phase transition.Comment: 8 pages, LaTeX, 5 EPS-figures, uses epsf.st