High temperature color conductivity at next-to-leading log order

The non-Abelian analog of electrical conductivity at high temperature has previously been known only at leading logarithmic order: that is, neglecting effects suppressed only by an inverse logarithm of the gauge coupling. We calculate the first sub-leading correction. This has immediate application to improving, to next-to-leading log order, both effective theories of non-perturbative color dynamics, and calculations of the hot electroweak baryon number violation rate.Comment: 47 pages, 6+2 figure

Uranium(III) coordination chemistry and oxidation in a flexible small-cavity macrocycle

U(III) complexes of the conformationally flexible, small-cavity macrocycle trans-calix[2]benzene[2]pyrrolide (L)2–, [U(L)X] (X = O-2,6-tBu2C6H3, N(SiMe3)2), have been synthesized from [U(L)BH4] and structurally characterized. These complexes show binding of the U(III) center in the bis(arene) pocket of the macrocycle, which flexes to accommodate the increase in the steric bulk of X, resulting in long U–X bonds to the ancillary ligands. Oxidation to the cationic U(IV) complex [U(L)X][B(C6F5)4] (X = BH4) results in ligand rearrangement to bind the smaller, harder cation in the bis(pyrrolide) pocket, in a conformation that has not been previously observed for (L)2–, with X located between the two ligand arene rings

Magnetic permeability of near-critical 3d abelian Higgs model and duality

The three-dimensional abelian Higgs model has been argued to be dual to a scalar field theory with a global U(1) symmetry. We show that this duality, together with the scaling and universality hypotheses, implies a scaling law for the magnetic permeablity chi_m near the line of second order phase transition: chi_m ~ t^nu, where t is the deviation from the critical line and nu ~ 0.67 is a critical exponent of the O(2) universality class. We also show that exactly on the critical lines, the dependence of magnetic induction on external magnetic field is quadratic, with a proportionality coefficient depending only on the gauge coupling. These predictions provide a way for testing the duality conjecture on the lattice in the Coulomb phase and at the phase transion.Comment: 11 pages; updated references and small changes, published versio

Optimization of the magnetic dynamo

In stars and planets, magnetic fields are believed to originate from the motion of electrically conducting fluids in their interior, through a process known as the dynamo mechanism. In this Letter, an optimization procedure is used to simultaneously address two fundamental questions of dynamo theory: "Which velocity field leads to the most magnetic energy growth?" and "How large does the velocity need to be relative to magnetic diffusion?" In general, this requires optimization over the full space of continuous solenoidal velocity fields possible within the geometry. Here the case of a periodic box is considered. Measuring the strength of the flow with the root-mean-square amplitude, an optimal velocity field is shown to exist, but without limitation on the strain rate, optimization is prone to divergence. Measuring the flow in terms of its associated dissipation leads to the identification of a single optimal at the critical magnetic Reynolds number necessary for a dynamo. This magnetic Reynolds number is found to be only 15% higher than that necessary for transient growth of the magnetic field.Comment: Optimal velocity field given approximate analytic form. 4 pages, 4 figure

Can transport peak explain the low-mass enhancement of dileptons at RHIC?

We propose a novel relation between the low-mass enhancement of dielectrons observed at PHENIX and transport coefficients of QGP such as the charge diffusion constant $D$ and the relaxation time $\tau_{\rm J}$. We parameterize the transport peak in the spectral function using the second-order relativistic dissipative hydrodynamics by Israel and Stewart. Combining the spectral function and the full (3+1)-dimensional hydrodynamical evolution with the lattice EoS, theoretical dielectron spectra and the experimental data are compared. Detailed analysis suggests that the low-mass dilepton enhancement originates mainly from the high-temperature QGP phase where there is a large electric charge fluctuation as obtained from lattice QCD simulations.Comment: To appear in the conference proceedings for Quark Matter 2011, May 23 - May 28, Annecy, Franc

Symmetric path integrals for stochastic equations with multiplicative noise

A Langevin equation with multiplicative noise is an equation schematically of the form dq/dt = - F(q) + e(q) xi, where e(q) xi is Gaussian white noise whose amplitude e(q) depends on q itself. I show how to convert such equations into path integrals. The definition of the path integral depends crucially on the convention used for discretizing time, and I specifically derive the correct path integral when the convention used is the natural, time-symmetric one that time derivatives are (q_t - q_{t-\Delta t}) / \Delta t and coordinates are (q_t + q_{t-\Delta t}) / 2. [This is the convention that permits standard manipulations of calculus on the action, like naive integration by parts.] It has sometimes been assumed in the literature that a Stratanovich Langevin equation can be quickly converted to a path integral by treating time as continuous but using the rule \theta(t=0) = 1/2. I show that this prescription fails when the amplitude e(q) is q-dependent.Comment: 8 page

Integrability of one degree of freedom symplectic maps with polar singularities

In this paper, we treat symplectic difference equations with one degree of freedom. For such cases, we resolve the relation between that the dynamics on the two dimensional phase space is reduced to on one dimensional level sets by a conserved quantity and that the dynamics is integrable, under some assumptions. The process which we introduce is related to interval exchange transformations.Comment: 10 pages, 2 figure

Selective decay by Casimir dissipation in fluids

The problem of parameterizing the interactions of larger scales and smaller scales in fluid flows is addressed by considering a property of two-dimensional incompressible turbulence. The property we consider is selective decay, in which a Casimir of the ideal formulation (enstrophy in 2D flows, helicity in 3D flows) decays in time, while the energy stays essentially constant. This paper introduces a mechanism that produces selective decay by enforcing Casimir dissipation in fluid dynamics. This mechanism turns out to be related in certain cases to the numerical method of anticipated vorticity discussed in \cite{SaBa1981,SaBa1985}. Several examples are given and a general theory of selective decay is developed that uses the Lie-Poisson structure of the ideal theory. A scale-selection operator allows the resulting modifications of the fluid motion equations to be interpreted in several examples as parameterizing the nonlinear, dynamical interactions between disparate scales. The type of modified fluid equation systems derived here may be useful in modelling turbulent geophysical flows where it is computationally prohibitive to rely on the slower, indirect effects of a realistic viscosity, such as in large-scale, coherent, oceanic flows interacting with much smaller eddies

Criteria for strong and weak random attractors

The theory of random attractors has different notions of attraction, amongst them pullback attraction and weak attraction. We investigate necessary and sufficient conditions for the existence of pullback attractors as well as of weak attractors