The Auxiliary Field Method in Quantum Mechanical Four-Fermi Models -- A Study Toward Chiral Condensation in QED

A study for checking validity of the auxiliary field method (AFM) is made in quantum mechanical four-fermi models which act as a prototype of models for chiral symmetry breaking in Quantum Electrodynamics. It has been shown that AFM, defined by an insertion of Gaussian identity to path integral formulas and by the loop expansion, becomes more accurate when taking higher order terms into account under the bosonic model with a quartic coupling in 0- and 1-dimensions as well as the model with a four-fermi interaction in 0-dimension. The case is also confirmed in terms of two models with the four-fermi interaction among $N$ species in 1-dimension (the quantum mechanical four-fermi models): higher order corrections lead us toward the exact energy of the ground state. It is found that the second model belongs to a WKB-exact class that has no higher order corrections other than the lowest correction. Discussions are also made for unreliability on the continuous time representation of path integration and for a new model of QED as a suitable probe for chiral symmetry breaking.Comment: 30 pages, 12 figure

A New Symmetric Expression of Weyl Ordering

For the creation operator \adag and the annihilation operator $a$ of a harmonic oscillator, we consider Weyl ordering expression of (\adag a)^n and obtain a new symmetric expression of Weyl ordering w.r.t. \adag a \equiv N and a\adag =N+1 where $N$ is the number operator. Moreover, we interpret intertwining formulas of various orderings in view of the difference theory. Then we find that the noncommutative parameter corresponds to the increment of the difference operator w.r.t. variable $N$. Therefore, quantum (noncommutative) calculations of harmonic oscillators are done by classical (commutative) ones of the number operator by using the difference theory. As a by-product, nontrivial relations including the Stirling number of the first kind are also obtained.Comment: 15 pages, Latex2e, the title before replacement is "Orderings of Operators in Quantum Physics", new proofs by using a difference operator added, some references added, to appear in Modern Physics Letters

Time boundary terms and Dirac constraints

Time boundary terms usually added to action principles are systematically handled in the framework of Dirac's canonical analysis. The procedure begins with the introduction of the boundary term into the integral Hamiltonian action and then the resulting action is interpreted as a Lagrangian one to which Dirac's method is applied. Once the general theory is developed, the current procedure is implemented and illustrated in various examples which are originally endowed with different types of constraints.Comment: 12 page

Strategy for understanding gas-solid riser hydrodynamics and other LANL status items

The talk presents the status of work in progress in the area of momentum transport theory in turbulent gas-solid multiphase flow. Previous installments have reported details of the theory, and validation results. This talk provides a grand overview of how the details of dynamic simulations in 3D, 2D, 1D and 0D, all fit together to form a consistent strategy for understanding gas-solid riser hydrodynamics. The circulating fluidized bed is the canonical example for showing how the strategy works. Performance of the procedure is shown by comparison to data recently obtained by Sandia National Laboratory. Status of other LANL efforts is also mentioned

Accurate Modelling of Left-Handed Metamaterials Using Finite-Difference Time-Domain Method with Spatial Averaging at the Boundaries

The accuracy of finite-difference time-domain (FDTD) modelling of left-handed metamaterials (LHMs) is dramatically improved by using an averaging technique along the boundaries of LHM slabs. The material frequency dispersion of LHMs is taken into account using auxiliary differential equation (ADE) based dispersive FDTD methods. The dispersive FDTD method with averaged permittivity along the material boundaries is implemented for a two-dimensional (2-D) transverse electric (TE) case. A mismatch between analytical and numerical material parameters (e.g. permittivity and permeability) introduced by the time discretisation in FDTD is demonstrated. The expression of numerical permittivity is formulated and it is suggested to use corrected permittivity in FDTD simulations in order to model LHM slabs with their desired parameters. The influence of switching time of source on the oscillation of field intensity is analysed. It is shown that there exists an optimum value which leads to fast convergence in simulations.Comment: 17 pages, 7 figures, submitted to Journal of Optics A Nanometa special issu

Toward a General Theory for Multiphase Turbulence Part I: Development and Gauging of the Model Equations

A formalism for developing multiphase turbulence models is introduced by analogy to the phenomenological method used for single-phase turbulence. A sample model developed using the formalism is given in detail. The procedure begins with ensemble averaging of the exact conservation equations, with closure accomplished by using a combination of analytical and experimental results from the literature. The resulting model is applicable to a wide range of common multiphase flows including gas-solid, liquid-solid and gas-liquid (bubbly) flows. The model is positioned for ready extension to three-phase turbulence, or for use in two-phase turbulence in which one phase is accounted for in multiple size classes, representing polydispersivity. The formalism is expected to suggest directions toward a more fundamentally based theory, similar to the way that early work in single-phase turbulence has led to the spectral theory. The approach is unique in that a portion of the total energy decay rate is ascribed to each phase, as is dictated by the exact averaged equations, and results in a transport equation for energy decay rate associated with each phase. What follows is a straightforward definition of a turbulent viscosity for each phase, and accounts for the effect of exchange of fluctuational energy among phases on the turbulent shear viscosity. The model also accounts for the effect of slip momentum transfer among the phases on the production of turbulence kinetic energy and on the tensor character of the Reynolds stress. Collisional effects, when appropriate, are included by superposition. The model reduces to a standard form in limit of a single, pure material, and is expected to do a credible job of describing multiphase turbulent flows in a wide variety of regimes using a single set of coefficients

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

Numerical simulation of two-dimensional single- and multiple-material flow fields

Over the last several years, Sandia National Laboratories has had an interest in developing capabilities to predict the flow fields around vehicles entering or exiting the water at a wide range of speeds. Such prediction schemes have numerous engineering applications in the design of weapon systems. For example, such a scheme could be used to predict the forces and moments experienced by an air-launched anti-submarine weapon on water-entry. Furthermore, a water-exit prediction capability could be used to model the complicated surface closure jet resulting from a missile being shot out of the water. The CCICE (Cell-Centered Implicit Continuous-fluid Eulerian) code developed at Los Alamos National Laboratory (LANL) was chosen to provide the fluid dynamics solver for high speed water-entry and water-exit problems. This implicit time-marching, two-dimensional, conservative, finite-volume code solves the multi-material, compressible, inviscid fluid dynamics equations. The incompressible version of the CCICE code, CCMAC (cell-Centered Marker and Cell), was chosen for low speed water- entry and water-exit problems in order to reduce the computational expense. These codes were chosen to take advantage of certain advances in numerical methods for computational fluid dynamics (CFD) that have taken place at LANL. Notable among these advances is the ability to perform implicit, multi-material, compressible flow simulations, with a fully cell-centered data structure. This means that a single set of control volumes are used, on which a discrete form of the conservation laws is satisfied. This is in control to the more classical staggered mesh methods, in which separate control volumes are defined for mass and momentum. 12 refs

Meson mass at real and imaginary chemical potentials

The chemical-potential dependence of pi and sigma meson masses is analyzed at both real and imaginary chemical potentials, $\mu_\mathrm{R}$ and $\mu_\mathrm{I}$, by using the Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model that possesses both the extended ${\mathbb Z}_3$ symmetry and the chiral symmetry. In the $\mu_\mathrm{I}$ region, the meson masses have the Roberge-Weiss periodicity. Assuming that the meson masses will be measured at finite $\mu_\mathrm{I}$ by lattice QCD in future, we simulate how meson masses at finite $\mu_\mathrm{R}$ are extracted from those at finite $\mu_\mathrm{I}$, and propose a reliable extraction method.Comment: 8 pages, 6 figures, typo corrected, some discussions clarified, version accepted for publication in Phys. Rev.