Modular Groups of Quantum Fields in Thermal States

For a quantum field in a thermal equilibrium state we discuss the group generated by time translations and the modular action associated with an algebra invariant under half-sided translations. The modular flows associated with the algebras of the forward light cone and a space-like wedge admit a simple geometric description in two dimensional models that factorize in light-cone coordinates. At large distances from the domain boundary compared to the inverse temperature the flow pattern is essentially the same as time translations, whereas the zero temperature results are approximately reproduced close to the edge of the wedge and the apex of the cone. Associated with each domain there is also a one parameter group with a positive generator, for which the thermal state is a ground state. Formally, this may be regarded as a certain converse of the Unruh-effect.Comment: 28 pages, 4 figure

Asymptotic statistics of the n-sided planar Voronoi cell: II. Heuristics

We develop a set of heuristic arguments to explain several results on planar Poisson-Voronoi tessellations that were derived earlier at the cost of considerable mathematical effort. The results concern Voronoi cells having a large number n of sides. The arguments start from an entropy balance applied to the arrangement of n neighbors around a central cell. It is followed by a simplified evaluation of the phase space integral for the probability p_n that an arbitrary cell be n-sided. The limitations of the arguments are indicated. As a new application we calculate the expected number of Gabriel (or full) neighbors of an n-sided cell in the large-n limit.Comment: 22 pages, 10 figure

The Dependence of Dynamo α\alpha-Effect on Reynolds Numbers, Magnetic Prandtl Number, and the Statistics of MHD Turbulence

We generalize the derivation of dynamo coefficient $\alpha$ of Field et al (1999) to include the following two aspects: first, the de-correlation times of velocity field and magnetic field are different; second, the magnetic Prandtl number can be arbitrary. We find that the contributions of velocity field and magnetic field to the $\alpha$ effect are not equal, but affected by their different statistical properties. In the limit of large kinetic Reynolds number and large magnetic Reynolds number, $\alpha$-coefficient may not be small if the de-correlation times of velocity field and magnetic field are shorter than the eddy turn-over time of the MHD turbulence. We also show that under certain circumstances, for example if the kinetic helicity and current helicity are comparable, $\alpha$ depends insensitively on magnetic Prandtl number, while if either the kinetic helicity or the current helicity is dominated by the other one, a different magnetic Prandtl number will significantly change the dynamo $\alpha$ effect.Comment: 44 pages, 4 figures, to appear in ApJ (vol. 552

Xenon forms stable compound with fluorine

Experiments show that xenon and fluorine combine readily at 400 deg C to form xenon tetrafluoride, which is colorless, crystalline, chemically stable and solid at room temperature. This process can be used for the separation of xenon from mixtures with other noble gases

RG flow of the Polyakov-loop potential: First status report

We study SU(2) Yang-Mills theory at finite temperature in the framework of the functional renormalization group. We concentrate on the effective potential for the Polyakov loop which serves as an order parameter for confinement. In this first status report, we focus on the behaviour of the effective Polyakov-loop potential at high temperatures. In addition to the standard perturbative result, our findings provide information about the ``RG improved'' backreactions of Polyakov-loop fluctuations on the potential. We demonstrate that these fluctuations establish the convexity of the effective potential.Comment: 10 pages, 2 figure

Four Pion Final States with Tagged Photons at Electron Positron Colliders

A Monte Carlo generator has been constructed to simulate the reaction e^+e^- \to \gamma + 4 \pi, where the photon is assumed to be observed in the detector. Only initial state radiation is considered. Additional collinear photon radiation has been incorporated with the technique of structure functions. Predictions are presented for cms energies of 1GeV, 3GeV and 10GeV, corresponding to the energies of DAPHNE, BEBC and of B-meson factories. The event rates are sufficiently high to allow for a precise measurement of R(Q^2) in the region of Q between approximately 1GeV and 2.5GeV. For the construction of the program we employ isospin relations between the amplitudes governing tau decays into four pions and electron positron annihilation into four pions. Estimates of the kinematic breaking of these isospin relations as a consequence of the \pi^- -- \pi^0 mass difference are given.Comment: LATEX, 27 pages, 9 figures, discussion of the kinematic breaking of isospin relations extended, typos corrected, some formulations change