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

Charge Conjugation from Space-Time Inversion

We show that the CPT group of the Dirac field emerges naturally from the PT and P (or T) subgroups of the Lorentz group.Comment: 4 pages, no figure

Surface charging of thick porous water ice layers relevant for ion sputtering experiments

We use a laboratory facility to study the sputtering properties of centimeter-thick porous water ice subjected to the bombardment of ions and electrons to better understand the formation of exospheres of the icy moons of Jupiter. Our ice samples are as similar as possible to the expected moon surfaces but surface charging of the samples during ion irradiation may distort the experimental results. We therefore monitor the time scales for charging and dis- charging of the samples when subjected to a beam of ions. These experiments allow us to derive an electric conductivity of deep porous ice layers. The results imply that electron irradiation and sputtering play a non-negligible role for certain plasma conditions at the icy moons of Jupiter. The observed ion sputtering yields from our ice samples are similar to previous experiments where compact ice films were sputtered off a micro-balance.Comment: arXiv admin note: text overlap with arXiv:1509.0400

Spectral plots and the representation and interpretation of biological data

It is basic question in biology and other fields to identify the char- acteristic properties that on one hand are shared by structures from a particular realm, like gene regulation, protein-protein interaction or neu- ral networks or foodwebs, and that on the other hand distinguish them from other structures. We introduce and apply a general method, based on the spectrum of the normalized graph Laplacian, that yields repre- sentations, the spectral plots, that allow us to find and visualize such properties systematically. We present such visualizations for a wide range of biological networks and compare them with those for networks derived from theoretical schemes. The differences that we find are quite striking and suggest that the search for universal properties of biological networks should be complemented by an understanding of more specific features of biological organization principles at different scales.Comment: 15 pages, 7 figure

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

Representation Class and Geometrical Invariants of Quantum States under Local Unitary Transformations

We investigate the equivalence of bipartite quantum mixed states under local unitary transformations by introducing representation classes from a geometrical approach. It is shown that two bipartite mixed states are equivalent under local unitary transformations if and only if they have the same representation class. Detailed examples are given on calculating representation classes.Comment: 11 page