A renormalized large-n solution of the U(n) x U(n) linear sigma model in the broken symmetry phase

Dyson-Schwinger equations for the U(n) x U(n) symmetric matrix sigma model reformulated with two auxiliary fields in a background breaking the symmetry to U(n) are studied in the so-called bare vertex approximation. A large n solution is constructed under the supplementary assumption so that the scalar components are much heavier than the pseudoscalars. The renormalizability of the solution is investigated by explicit construction of the counterterms.Comment: RevTeX4, 14 pages, 2 figures. Version published in Phys. Rev.

Phase Transitions and Critical Behavior for Charged Black Holes

We investigate the thermodynamics of a four-dimensional charged black hole in a finite cavity in asymptotically flat and asymptotically de Sitter space. In each case, we find a Hawking-Page-like phase transition between a black hole and a thermal gas very much like the known transition in asymptotically anti-de Sitter space. For a ``supercooled'' black hole--a thermodynamically unstable black hole below the critical temperature for the Hawking-Page phase transition--the phase diagram has a line of first-order phase transitions that terminates in a second order point. For the asymptotically flat case, we calculate the critical exponents at the second order phase transition and find that they exactly match the known results for a charged black hole in anti-de Sitter space. We find strong evidence for similar phase transitions for the de Sitter black hole as well. Thus many of the thermodynamic features of charged anti-de Sitter black holes do not really depend on asymptotically anti-de Sitter boundary conditions; the thermodynamics of charged black holes is surprisingly universal.Comment: LaTeX, 14 pages, 9 eps figures; higher resolution figures available on reques

Functionalization of semiconductor surfaces by organic layers: Concerted cycloaddition versus stepwise free-radical reaction mechanism

In the age when the miniaturization trend that has driven the semiconductor industry is reaching its limits, organic modification of semiconductors is emerging as a field that could give much-needed impetus. We review the current state of understanding of the functionalization of C(100), Si(100), and Ge(100) surfaces through chemisorption of alkenes and alkynes, focussing on adsorbate structural control. While reactions on C(100) show most of the properties expected for concerted cycloaddition reactions such as [2+2] and [4+2] (Diels-Alder) processes, reactions on Si(100) present a wide range of variant behaviour, including in some cases the prominence of non-cycloaddition products. More general stepwise free-radical addition processes are seen to provide a better description of reactions on Si(100), their prominence being attributed to either the non-existence or ineffectiveness of p bonding within surface silicon dimers. The investigations of these systems provide not only insight into driving mechanisms for chemisorption but also motivation for the development of new techniques of organic functionalization on semiconductors

Chaplygin Gas Cosmology - Unification of Dark Matter and Dark Energy

The models that unify dark matter and dark energy based upon the Chaplygin gas fail owing to the suppression of structure formation by the adiabatic speed of sound. Including string theory effects, in particular the Kalb-Ramond field, we show how nonadiabatic perturbations allow a successful structure formation.Comment: 7 pages, presented by N. B. at IRGAC 2006, Barcelona, 11-15 July 2006, typos corrected, concluding paragraph slightly expanded, final version, accepted in J. Phys. A, special issu

Hybrid Chaplygin gas and phantom divide crossing

Hybrid Chaplygin gas model is put forward, in which the gases play the role of dark energy. For this model the coincidence problem is greatly alleviated. The effective equation of state of the dark energy may cross the phantom divide $w=-1$. Furthermore, the crossing behaviour is decoupled from any gravity theories. In the present model, $w<-1$ is only a transient behaviour. There is a de Sitter attractor in the future infinity. Hence, the big rip singularity, which often afflicts the models with matter whose effective equation of state less than -1, is naturally disappear. There exist stable scaling solutions, both at the early universe and the late universe. We discuss the perturbation growth of this model. We find that the index is consistent with observations.Comment: 11 pages, 4 figures, V3: discussions on the perturbation growth added, V4: minor corrections, to match the published versio

Non-Commutativity of the Zero Chemical Potential Limit and the Thermodynamic Limit in Finite Density Systems

Monte Carlo simulations of finite density systems are often plagued by the complex action problem. We point out that there exists certain non-commutativity in the zero chemical potential limit and the thermodynamic limit when one tries to study such systems by reweighting techniques. This is demonstrated by explicit calculations in a Random Matrix Theory, which is thought to be a simple qualitative model for finite density QCD. The factorization method allows us to understand how the non-commutativity, which appears at the intermediate steps, cancels in the end results for physical observables.Comment: 7 pages, 9 figure

The motion of stars near the Galactic center: A comparison of the black hole and fermion ball scenarios

After a discussion of the properties of degenerate fermion balls, we analyze the orbits of the stars S0-1 and S0-2, which have the smallest projected distances to Sgr A*, in the supermassive black hole as well as in the fermion ball scenarios of the Galactic center. It is shown that both scenarios are consistent with the data, as measured during the last six years by Genzel et al. and Ghez et al. The free parameters of the projected orbit of a star are the unknown components of its velocity v_z and distance z to Sgr A* in 1995.4, with the z-axis being in the line of sight. We show, in the case of S0-1 and S0-2, that the z-v_z phase-space which fits the data, is much larger for the fermion ball than for the black hole scenario. Future measurements of the positions or radial velocities of S0-1 and S0-2 could reduce this allowed phase-space and eventually rule out one of the currently acceptable scenarios. This may shed some light into the nature of the supermassive compact dark object, or dark matter in general at the center of our Galaxy.Comment: 30 pages, 12 figures, Latex, aasms4 styl

Fermion determinants in matrix models of QCD at nonzero chemical potential

The presence of a chemical potential completely changes the analytical structure of the QCD partition function. In particular, the eigenvalues of the Dirac operator are distributed over a finite area in the complex plane, whereas the zeros of the partition function in the complex mass plane remain on a curve. In this paper we study the effects of the fermion determinant at nonzero chemical potential on the Dirac spectrum by means of the resolvent, G(z), of the QCD Dirac operator. The resolvent is studied both in a one-dimensional U(1) model (Gibbs model) and in a random matrix model with the global symmetries of the QCD partition function. In both cases we find that, if the argument z of the resolvent is not equal to the mass m in the fermion determinant, the resolvent diverges in the thermodynamic limit. However, for z =m the resolvent in both models is well defined. In particular, the nature of the limit $z \rightarrow m$ is illuminated in the Gibbs model. The phase structure of the random matrix model in the complex m and \mu-planes is investigated both by a saddle point approximation and via the distribution of Yang-Lee zeros. Both methods are in complete agreement and lead to a well-defined chiral condensate and quark number density.Comment: 27 pages, 6 figures, Late

Phase transitions in self-gravitating systems. Self-gravitating fermions and hard spheres models

We discuss the nature of phase transitions in self-gravitating systems both in the microcanonical and in the canonical ensemble. We avoid the divergence of the gravitational potential at short distances by considering the case of self-gravitating fermions and hard spheres models. Three kinds of phase transitions (of zeroth, first and second order) are evidenced. They separate a ``gaseous'' phase with a smoothly varying distribution of matter from a ``condensed'' phase with a core-halo structure. We propose a simple analytical model to describe these phase transitions. We determine the value of energy (in the microcanonical ensemble) and temperature (in the canonical ensemble) at the transition point and we study their dependance with the degeneracy parameter (for fermions) or with the size of the particles (for a hard spheres gas). Scaling laws are obtained analytically in the asymptotic limit of a small short distance cut-off. Our analytical model captures the essential physics of the problem and compares remarkably well with the full numerical solutions.Comment: Submitted to Phys. Rev. E. New material adde