The C-Theorem and Chiral Symmetry Breaking in Asymptotically Free Vectorlike Gauge Theories

We confront Cardy's suggested c-function for four-dimensional field theories with the spontaneous breaking of chiral symmetries in asymptotically free vectorlike gauge theories with fermions transforming according to different representations under the gauge group. Assuming that the infrared limit of the c-function is determined by the dimension of the associated Goldstone manifold, we find that this c-function always decreases between the ultraviolet and infrared fixed points.Comment: 8 pages, no figures, a few references adde

Investigation on the Use of a Multiphase Eulerian CFD solver to simulate breaking waves

The main challenge in CFD multiphase simulations of breaking waves is the wide range of interfacial length scales occurring in the flow: from the free surface measurable in meters down to the entrapped air bubbles with size of a fraction of a millimeter. This paper presents a preliminary investigation on a CFD model capable of handling this problem. The model is based on a solver, available in the open-source CFD toolkit OpenFOAM, which combines the Eulerian multi-fluid approach for dispersed flows with a numerical interface sharpening method. The solver, enhanced with additional formulations for mass and momentum transfer among phases, was satisfactorily tested against an experimental bubble column flow. The model was then used to simulate the propagation of a laboratory solitary breaking wave. The motion of the free surface was successfully reproduced up to the breaking point. Further implementations are needed to simulate the air entrainment phenomeno

QCD3 and the Replica Method

Using the replica method, we analyze the mass dependence of the QCD3 partition function in a parameter range where the leading contribution is from the zero momentum Goldstone fields. Three complementary approaches are considered in this article. First, we derive exact relations between the QCD3 partition function and the QCD4 partition function continued to half-integer topological charge. The replica limit of these formulas results in exact relations between the corresponding microscopic spectral densities of QCD3 and QCD4. Replica calculations, which are exact for QCD4 at half-integer topological charge, thus result in exact expressions for the microscopic spectral density of the QCD3 Dirac operator. Second, we derive Virasoro constraints for the QCD3 partition function. They uniquely determine the small-mass expansion of the partition function and the corresponding sum rules for inverse Dirac eigenvalues. Due to de Wit-'t Hooft poles, the replica limit only reproduces the small mass expansion of the resolvent up to a finite number of terms. Third, the large mass expansion of the resolvent is obtained from the replica limit of a loop expansion of the QCD3 partition function. Because of Duistermaat-Heckman localization exact results are obtained for the microscopic spectral density in this way.Comment: LaTeX, 41 pages. References and some clarifying remarks adde

Random Matrix Theory for the Hermitian Wilson Dirac Operator and the chGUE-GUE Transition

We introduce a random two-matrix model interpolating between a chiral Hermitian (2n+nu)x(2n+nu) matrix and a second Hermitian matrix without symmetries. These are taken from the chiral Gaussian Unitary Ensemble (chGUE) and Gaussian Unitary Ensemble (GUE), respectively. In the microscopic large-n limit in the vicinity of the chGUE (which we denote by weakly non-chiral limit) this theory is in one to one correspondence to the partition function of Wilson chiral perturbation theory in the epsilon regime, such as the related two matrix-model previously introduced in refs. [20,21]. For a generic number of flavours and rectangular block matrices in the chGUE part we derive an eigenvalue representation for the partition function displaying a Pfaffian structure. In the quenched case with nu=0,1 we derive all spectral correlations functions in our model for finite-n, given in terms of skew-orthogonal polynomials. The latter are expressed as Gaussian integrals over standard Laguerre polynomials. In the weakly non-chiral microscopic limit this yields all corresponding quenched eigenvalue correlation functions of the Hermitian Wilson operator.Comment: 27 pages, 4 figures; v2 typos corrected, published versio

Microscopic eigenvalue correlations in QCD with imaginary isospin chemical potential

We consider the chiral limit of QCD subjected to an imaginary isospin chemical potential. In the epsilon-regime of the theory we can perform precise analytical calculations based on the zero-momentum Goldstone modes in the low-energy effective theory. We present results for the spectral correlation functions of the associated Dirac operators.Comment: 13 pages, 2 figures, RevTe

The Microscopic Spectral Density of the QCD Dirac Operator

We derive the microscopic spectral density of the Dirac operator in $SU(N_c\geq 3)$ Yang-Mills theory coupled to $N_f$ fermions in the fundamental representation. An essential technical ingredient is an exact rewriting of this density in terms of integrations over the super Riemannian manifold $Gl(N_f+1|1)$. The result agrees exactly with earlier calculations based on Random Matrix Theory.Comment: 26 pages, Late

Fine‐scale measurement of diffusivity in a microbial mat with nuclear magnetic resonance imaging

Noninvasive 1H‐nuclear magnetic resonance (NMR) imaging was used to investigate the diffusive properties of microbial mats in two dimensions. Pulsed field gradient NMR was used to acquire images of the H2O diffusion coefficient, Ds, and multiecho imaging NMR was used to obtain images of the water density in two structurally different microbial mats sampled from Solar Lake (Egypt). We found a pronounced lateral and vertical variability of both water density and water diffusion coefficient, correlated with the laminated and heterogeneous distribution of microbial cells and exopolymers within the mats. The average water density varied from 0.5 to 0.9, whereas the average water diffusion coefficient ranged from 0.4 to 0.9 relative to the values obtained in the stagnant water above the mat samples. The apparent water diffusivities estimated from NMR imaging compared well to apparent O2 diffusivities measured with a diffusivity microsensor. Analysis of measured O2 concentration profiles with a diffusion‐reaction model showed that both the magnitude of calculated rates and the depth distribution of calculated O2 consumption/production zones changed when the observed variations of diffusivity were taken into account. With NMR imaging, diffusivity can be determined at high spatial resolution, which can resolve inherent lateral and vertical heterogeneities found in most natural benthic systems

Analytical relationship for the cranking inertia

The wave function of a spheroidal harmonic oscillator without spin-orbit interaction is expressed in terms of associated Laguerre and Hermite polynomials. The pairing gap and Fermi energy are found by solving the BCS system of two equations. Analytical relationships for the matrix elements of inertia are obtained function of the main quantum numbers and potential derivative. They may be used to test complex computer codes one should develop in a realistic approach of the fission dynamics. The results given for the $^{240}$Pu nucleus are compared with a hydrodynamical model. The importance of taking into account the correction term due to the variation of the occupation number is stressed.Comment: 12 pages, 4 figure

Diquark Condensate in QCD with Two Colors at Next-to-Leading Order

We study QCD with two colors and quarks in the fundamental representation at finite baryon density in the limit of light quark masses. In this limit the free energy of this theory reduces to the free energy of a chiral Lagrangian which is based on the symmetries of the microscopic theory. In earlier work this Lagrangian was analyzed at the mean field level and a phase transition to a phase of condensed diquarks was found at a chemical potential of half the diquark mass (which is equal to the pion mass). In this article we analyze this theory at next-to-leading order in chiral perturbation theory. We show that the theory is renormalizable and calculate the next-to-leading order free energy in both phases of the theory. By deriving a Landau-Ginzburg theory for the order parameter we show that the finite one-loop contribution and the next-to-leading order terms in the chiral Lagrangian do not qualitatively change the phase transition. In particular, the critical chemical potential is equal to half the next-to-leading order pion mass, and the phase transition is second order.Comment: 29 pages, 2 figure

The Spectral Density of the QCD Dirac Operator and Patterns of Chiral Symmetry Breaking

We study the spectrum of the QCD Dirac operator for two colors with fermions in the fundamental representation and for two or more colors with adjoint fermions. For $N_f$ flavors, the chiral flavor symmetry of these theories is spontaneously broken according to $SU(2N_f)\to Sp(2N_f)$ and $SU(N_f)\to O(N_f)$, respectively, rather than the symmetry breaking pattern $SU(N_f) \times SU(N_f) \to SU(N_f)$ for QCD with three or more colors and fundamental fermions. In this paper we study the Dirac spectrum for the first two symmetry breaking patterns. Following previous work for the third case we find the Dirac spectrum in the domain $\lambda \ll \Lambda_{\rm QCD}$ by means of partially quenched chiral perturbation theory. In particular, this result allows us to calculate the slope of the Dirac spectrum at $\lambda = 0$. We also show that for $\lambda \ll 1/L^2 \Lambda_{QCD}$ (with $L$ the linear size of the system) the Dirac spectrum is given by a chiral Random Matrix Theory with the symmetries of the Dirac operator.Comment: 27 pages Latex, corrected typo