Temperature dependence in random matrix models with pairing condensates

We address a number of issues raised by a manuscript of Klein, Toublan, and Verbaarschot (hep-ph/0405180) in which the authors introduce a random matrix model for QCD with two colors, two flavors, and fermions in the fundamental representation. Their inclusion of temperature terms differs from the approach adopted in previous work on this problem (Phys. Rev. D 64, 074016 (2001).) We demonstrate that the two approaches are related by a transformation that leaves the thermodynamic potential invariant and which therefore has no effect on physical observables.Comment: 8 pages, revtex4. v2: typos corrected in reference

Diquark and Pion Condensation in Random Matrix Models for two-color QCD

We introduce a random matrix model with the symmetries of QCD with two colors at nonzero isospin and baryon chemical potentials and temperature. We analyze its phase diagram and find phases with condensation of pion and diquark states in addition to the phases with spontaneously broken chiral symmetries. In the limit of small chemical potentials and quark masses, we reproduce the mean field results obtained from chiral Lagrangians. As in the case of QCD with three colors, the presence of two chemical potentials breaks the flavor symmetry and leads to phases that are characterized by different behaviors of the chiral condensates for each flavor. In particular, the phase diagram we obtain is similar to QCD with three colors and three flavors of quarks of equal masses at zero baryon chemical potential and nonzero isospin and strange chemical potentials. A tricritical point of the superfluid transitions found in lattice calculations and from an analysis in terms of chiral Lagrangians does not appear in the random matrix model. Remarkably, at fixed isospin chemical potential, for the regions outside of the superfluid phases, the phase diagram in the temperature - baryon chemical potential plane for two colors and three colors are qualitatively the same.Comment: 19 pages, 7 figures, RevTeX

The QCD Phase Diagram at Nonzero Temperature, Baryon and Isospin Chemical Potentials in Random Matrix Theory

We introduce a random matrix model with the symmetries of QCD at finite temperature and chemical potentials for baryon number and isospin. We analyze the phase diagram of this model in the chemical potential plane for different temperatures and quark masses. We find a rich phase structure with five different phases separated by both first and second order lines. The phases are characterized by the pion condensate and the chiral condensate for each of the flavors. In agreement with lattice simulations, we find that in the phase with zero pion condensate the critical temperature depends in the same way on the baryon number chemical potential and on the isospin chemical potential. At nonzero quark mass, we remarkably find that the critical end point at nonzero temperature and baryon chemical potential is split in two by an arbitrarily small isospin chemical potential. As a consequence, there are two crossovers that separate the hadronic phase from the quark-gluon plasma phase at high temperature. Detailed analytical results are obtained at zero temperature and in the chiral limit.Comment: 13 pages, 5 figures, REVTeX

Development of predictive simulation capability for reactive multiphase flow

This is the final report of a Laboratory Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). The objective of the project was to develop a self-sustained research program for advanced computer simulation of industrial reactive multiphase flows. The prototype research problem was a three-phase alumina precipitator used in the Bayer process, a key step in aluminum refining. Accomplishments included the development of an improved reaction mechanism of the alumina precipitation growth process, the development of an efficient methods for handling particle size distribution in multiphase flow simulation codes, the incorporation of precipitation growth and agglomeration kinetics in LANL's CFDLIB multiphase flow code library and the evaluation of multiphase turbulence closure models for bubbly flow simulations

Random matrix models for phase diagrams

We describe a random matrix approach that can provide generic and readily soluble mean-field descriptions of the phase diagram for a variety of systems ranging from QCD to high-T_c materials. Instead of working from specific models, phase diagrams are constructed by averaging over the ensemble of theories that possesses the relevant symmetries of the problem. Although approximate in nature, this approach has a number of advantages. First, it can be useful in distinguishing generic features from model-dependent details. Second, it can help in understanding the `minimal' number of symmetry constraints required to reproduce specific phase structures. Third, the robustness of predictions can be checked with respect to variations in the detailed description of the interactions. Finally, near critical points, random matrix models bear strong similarities to Ginsburg-Landau theories with the advantage of additional constraints inherited from the symmetries of the underlying interaction. These constraints can be helpful in ruling out certain topologies in the phase diagram. In this Key Issue, we illustrate the basic structure of random matrix models, discuss their strengths and weaknesses, and consider the kinds of system to which they can be applied.Comment: 29 pages, 2 figures, uses iopart.sty. Author's postprint versio

Optimization of air-sparged plutonium oxalate/hydroxide precipitators

The high cost of waste management and experimental work makes numerical modeling an inexpensive and attractive tool for optimizing and understanding complex chemical processes. Multiphase {open_quotes}bubble{close_quotes} columns are used extensively at the Los Alamos Plutonium Facility for a variety of different applications. No moving parts and efficient mixing characteristics allow them to be used in glovebox operations. Initially, a bubble column for oxalate precipitations is being modeled to identify the effect of various design parameters such as, draft tube location, air sparge rate and vessel geometry. Two-dimensional planar and axisymmetric models have been completed and successfully compared to literature data. Also, a preliminary three-dimensional model has been completed. These results are discussed in this report along with future work

Bulk high-Tc superconductors with drilled holes: how to arrange the holes to maximize the trapped magnetic flux ?

Drilling holes in a bulk high-Tc superconductor enhances the oxygen annealing and the heat exchange with the cooling liquid. However, drilling holes also reduces the amount of magnetic flux that can be trapped in the sample. In this paper, we use the Bean model to study the magnetization and the current line distribution in drilled samples, as a function of the hole positions. A single hole perturbs the critical current flow over an extended region that is bounded by a discontinuity line, where the direction of the current density changes abruptly. We demonstrate that the trapped magnetic flux is maximized if the center of each hole is positioned on one of the discontinuity lines produced by the neighbouring holes. For a cylindrical sample, we construct a polar triangular hole pattern that exploits this principle; in such a lattice, the trapped field is ~20% higher than in a squared lattice, for which the holes do not lie on discontinuity lines. This result indicates that one can simultaneously enhance the oxygen annealing, the heat transfer, and maximize the trapped field

The pseudo-Goldstone spectrum of 2-colour QCD at finite density

We examine the spectrum of 2-colour lattice QCD with 4 continuum flavours at a finite chemical potential ($\mu$) for quark-number, on a $12^3 \times 24$ lattice. First we present evidence that the system undergoes a transition to a state with a diquark condensate, which spontaneously breaks quark number at $\mu=m_\pi/2$, and that this transition is mean field in nature. We then examine the 3 states that would be Goldstone bosons at $\mu=0$ for zero Dirac and Majorana quark masses. The predictions of chiral effective Lagrangians give a good description of the behaviour of these masses for $\mu < m_\pi/2$. Except for the heaviest of these states, these predictions diverge from our measurements, once $\mu$ is significantly greater than $m_\pi/2$. However, the qualitative behaviour of these masses, indicates that the physics is very similar to that predicted by these effective Lagrangians, and there is some indication that at least part of these discrepancies is due to saturation, a lattice artifact.Comment: 32 pages LaTeX/Revtex, 8 Postscript figure

The entropy of the QCD plasma

Self-consistent approximations in terms of fully dressed propagators provide a simple expression for the entropy of an ultrarelativistic plasma, which isolates the contribution of the elementary excitations as a leading contribution. Further approximations, whose validity is checked on a soluble model involving a scalar field, allow us to calculate the entropy of the QCD plasma. We obtain an accurate description of lattice data for purely gluonic QCD, down to temperatures of about twice the transition temperature.Comment: 12 pages, 3 figures, REVTEX (minor modifications

Lifetime Effects in Color Superconductivity at Weak Coupling

Present computations of the gap of color superconductivity in weak coupling assume that the quarks which participate in the condensation process are infinitely long-lived. However, the quasiparticles in a plasma are characterized by having a finite lifetime. In this article we take into account this fact to evaluate its effect in the computation of the color gap. By first considering the Schwinger-Dyson equations in weak coupling, when one-loop self-energy corrections are included, a general gap equation is written in terms of the spectral densities of the quasiparticles. To evaluate lifetime effects, we then model the spectral density by a Lorentzian function. We argue that the decay of the quasiparticles limits their efficiency to condense. The value of the gap at the Fermi surface is then reduced. To leading order, these lifetime effects can be taken into account by replacing the coupling constant of the gap equation by a reduced effective one.Comment: 16 pages, 2 figures; explanations on the role of the Meissner effect added; 2 references added; accepted for publication in PR