The Vacuum Structure of Light-Front ϕ1+14\phi^4_{1+1}-Theory

We discuss the vacuum structure of $\phi^4$-theory in 1+1 dimensions quantised on the light-front $x^+ =0$. To this end, one has to solve a non-linear, operator-valued constraint equation. It expresses that mode of the field operator having longitudinal light-front momentum equal to zero, as a function of all the other modes in the theory. We analyse whether this zero mode can lead to a non-vanishing vacuum expectation value of the field $\phi$ and thus to spontaneous symmetry breaking. In perturbation theory, we get no symmetry breaking. If we solve the constraint, however, non-perturbatively, within a mean-field type Fock ansatz, the situation changes: while the vacuum state itself remains trivial, we find a non-vanishing vacuum expectation value above a critical coupling. Exactly the same result is obtained within a light-front Tamm-Dancoff approximation, if the renormalisation is done in the correct way.Comment: 28 pages LaTeX, 1 Postscript figur

Hadron-Hadron Interactions from Nf=2+1+1N_f=2+1+1 Lattice QCD: isospin-1 KKKK scattering length

We present results for the interaction of two kaons at maximal isospin. The calculation is based on $N_f=2+1+1$ flavour gauge configurations generated by the European Twisted Mass Collaboration with pion masses ranging from about $230$ to $450\,\textrm{MeV}$ at three values of the lattice spacing. The elastic scattering length $a_0^{I=1}$ is calculated at several values of the bare strange and light quark masses. We find $M_K a_0 = -0.385(16)_{\textrm{stat}} (^{+0}_{-12})_{m_s}(^{+0}_{-5})_{Z_P}(4)_{r_f}$ as the result of a combined extrapolation to the continuum and to the physical point, where the first error is statistical, and the three following are systematical. This translates to $a_0 = -0.154(6)_{\textrm{stat}}(^{+0}_{-5})_{m_s} (^{+0}_{-2})_{Z_P}(2)_{r_f}\,\textrm{fm}$.Comment: 28 pages, 18 tables, 14 figure

The solubility and oxidation state of nickel in silicate melt at low oxygen fugacities: Results using a mechanically assisted equilibration technique

The solubility of Ni in a silicate melt has been measured using a new, mechanically assisted equilibration technique over a wide range of controlled ƒO2 values. The melt composition corresponds to the 1 atm eutectic in the system CaAl2Si2O8-CaMgSi2O6 + 10 wt% CaO. The experiments were performed at 1300°C and over an ƒO2 range of 10−8.5 to 10−13.75, and over a temperature range of 1270 to 1390°C at a constant gas mixing ratio ( ). The experiment consists of a sample of melt contained within a crucible of Ni metal and held in a 1 atm gas mixing furnace. A Ni spindle is entered into the sample from above and continuously rotated at a constant angular velocity using a viscometer head. The stirring of the sample serves to accelerate the approach to equilibrium between the liquid sample and the metal crucible (and spindle). This arrangement allows relatively rapid equilibration of Ni content following changes to higher or lower ƒO2 values. Samples of the melt may be taken at any time for analysis and thus the equilibrium solubility of Ni in the silicate melt may be determined from unambiguous experimental reversals. The Ni contents of samples, analysed both by INAA and by ICP-AES, range from 25 to 5300 ppm. The data presented in this paper indicate that the oxidation state of Ni in the investigated melt is Ni2+ over the entire range of ƒO2 investigated. This conclusion contrasts with recent reports in the literature of an inflection in the ƒO2 dependence of Ni solubility, which has been interpreted as solution of neutral Ni at low ƒO2 (Morse et al., 1991; Colson, 1992; Ehlers et al., 1992). We also present data for the temperature dependence of Ni solubility in the investigated melt. The solubility decreases with increasing temperature at constant ƒO2. The present results are in good agreement with the metal-loop-equilibration experiments reported by Holzheid et al. (1994)

Distribution of label spacings for genome mapping in nanochannels

In genome mapping experiments, long DNA molecules are stretched by confining them to very narrow channels, so that the locations of sequence-specific fluorescent labels along the channel axis provide large-scale genomic information. It is difficult, however, to make the channels narrow enough so that the DNA molecule is fully stretched. In practice its conformations may form hairpins that change the spacings between internal segments of the DNA molecule, and thus the label locations along the channel axis. Here we describe a theory for the distribution of label spacings that explains the heavy tails observed in distributions of label spacings in genome mapping experiments.Comment: 18 pages, 4 figures, 1 tabl

Hadron-Hadron Interactions from Nf=2+1+1N_f=2+1+1 Lattice QCD: isospin-2 ππ\pi\pi scattering length

We present results for the $I=2$ $\pi\pi$ scattering length using $N_f=2+1+1$ twisted mass lattice QCD for three values of the lattice spacing and a range of pion mass values. Due to the use of Laplacian Heaviside smearing our statistical errors are reduced compared to previous lattice studies. A detailed investigation of systematic effects such as discretisation effects, volume effects, and pollution of excited and thermal states is performed. After extrapolation to the physical point using chiral perturbation theory at NLO we obtain $M_\pi a_0=-0.0442(2)_\mathrm{stat}(^{+4}_{-0})_\mathrm{sys}$.Comment: Edited for typos, overhauled figures, more detailed comparison to existing lattice result

Estimating entanglement measures in experiments

We present a method to estimate entanglement measures in experiments. We show how a lower bound on a generic entanglement measure can be derived from the measured expectation values of any finite collection of entanglement witnesses. Hence witness measurements are given a quantitative meaning without the need of further experimental data. We apply our results to a recent multi-photon experiment [M. Bourennane et al., Phys. Rev. Lett. 92, 087902 (2004)], giving bounds on the entanglement of formation and the geometric measure of entanglement in this experiment.Comment: 4 pages, 1 figure, v2: final versio

Magnification relations for Kerr lensing and testing Cosmic Censorship

A Kerr black hole with mass parameter m and angular momentum parameter a acting as a gravitational lens gives rise to two images in the weak field limit. We study the corresponding magnification relations, namely the signed and absolute magnification sums and the centroid up to post-Newtonian order. We show that there are post-Newtonian corrections to the total absolute magnification and centroid proportional to a/m, which is in contrast to the spherically symmetric case where such corrections vanish. Hence we also propose a new set of lensing observables for the two images involving these corrections, which should allow measuring a/m with gravitational lensing. In fact, the resolution capabilities needed to observe this for the Galactic black hole should in principle be accessible to current and near-future instrumentation. Since a/m >1 indicates a naked singularity, a most interesting application would be a test of the Cosmic Censorship conjecture. The technique used to derive the image properties is based on the degeneracy of the Kerr lens and a suitably displaced Schwarzschild lens at post-Newtonian order. A simple physical explanation for this degeneracy is also given.Comment: 13 pages, version 2: references added, minor changes. To appear in Phys. Rev.

Isospin-0 ππ\pi\pi s-wave scattering length from twisted mass lattice QCD

We present results for the isospin-0 $\pi\pi$ s-wave scattering length calculated with Osterwalder-Seiler valence quarks on Wilson twisted mass gauge configurations. We use three $N_f = 2$ ensembles with unitary (valence) pion mass at its physical value (250$\sim$MeV), at 240$\sim$MeV (320$\sim$MeV) and at 330$\sim$MeV (400$\sim$MeV), respectively. By using the stochastic Laplacian Heaviside quark smearing method, all quark propagation diagrams contributing to the isospin-0 $\pi\pi$ correlation function are computed with sufficient precision. The chiral extrapolation is performed to obtain the scattering length at the physical pion mass. Our result $M_\pi a^\mathrm{I=0}_0 = 0.198(9)(6)$ agrees reasonably well with various experimental measurements and theoretical predictions. Since we only use one lattice spacing, certain systematics uncertainties, especially those arising from unitary breaking, are not controlled in our result.Comment: 21 pages, 5 figures, 6 table