From Floquet to Dicke: quantum spin-Hall insulator interacting with quantum light

Time-periodic perturbations due to classical electromagnetic fields are useful to engineer the topological properties of matter using the Floquet theory. Here we investigate the effect of quantized electromagnetic fields by focusing on the quantized light-matter interaction on the edge state of a quantum spin-Hall insulator. A Dicke-type superradiant phase transition occurs at arbitrary weak coupling, the electronic spectrum acquires a finite gap and the resulting ground state manifold is topological with Chern number $\pm 1$. When the total number of excitations is conserved, a photocurrent is generated along the edge, being pseudo-quantized as $\omega\ln(1/\omega)$ in the low frequency limit, and decaying as $1/\omega$ for high frequencies with $\omega$ the photon frequency. The photon spectral function exhibits a clean Goldstone mode, a Higgs like collective mode at the optical gap and the polariton continuum.Comment: 5 pages, 3 figures, revised versio

Diphoton Background to Higgs Boson Production at the LHC with Soft Gluon Effects

The detection and the measurement of the production cross section of a light Higgs boson at the CERN Large Hadron Collider demand the accurate prediction of the background distributions of photon pairs. To improve this theoretical prediction, we present the soft-gluon resummed calculation of the $p p \to \gamma \gamma X$ cross section, including the exact one loop $g g \to \gamma \gamma g$ contribution. By incorporating the known fixed order results and the leading terms in the higher order corrections, the resummed cross section provides a reliable prediction for the inclusive diphoton invariant mass and transverse momentum distributions. Given our results, we propose the search for the Higgs boson in the inclusive diphoton mode with a cut on the transverse momentum of the photon pair, without the requirement of an additional tagged jet.Comment: 5 pages, 4 figures. A figure with discussion, and a reference added. Minor improvements of wording. Conclusion unchange

Nonrepetitive colorings of lexicographic product of graphs

A coloring $c$ of the vertices of a graph $G$ is nonrepetitive if there exists no path $v_1v_2\ldots v_{2l}$ for which $c(v_i)=c(v_{l+i})$ for all $1\le i\le l$. Given graphs $G$ and $H$ with $|V(H)|=k$, the lexicographic product $G[H]$ is the graph obtained by substituting every vertex of $G$ by a copy of $H$, and every edge of $G$ by a copy of $K_{k,k}$. %Our main results are the following. We prove that for a sufficiently long path $P$, a nonrepetitive coloring of $P[K_k]$ needs at least $3k+\lfloor k/2\rfloor$ colors. If $k>2$ then we need exactly $2k+1$ colors to nonrepetitively color $P[E_k]$, where $E_k$ is the empty graph on $k$ vertices. If we further require that every copy of $E_k$ be rainbow-colored and the path $P$ is sufficiently long, then the smallest number of colors needed for $P[E_k]$ is at least $3k+1$ and at most $3k+\lceil k/2\rceil$. Finally, we define fractional nonrepetitive colorings of graphs and consider the connections between this notion and the above results

Shear failure in rock using different constant normal load

SEILDEL – HABERFIELD’s [1] work was based on the analysis of the regular triangular asperities and assumed that the asperities were rigid. They used normal stiffness shear stress (CNS) to measure the joint dilatation rate and extended the LADANYI – ARCHAMBAULT’s [2] approach. The aim of this research is to investigate the dependence of the constant normal load (CNL) on the rate of the dilatation. Three points were chosen on the bilinear failure envelope: the first in the first linear part, the second in transition stress, and the third in the second part of the bilinear failure envelope. 12 regular triangular cementmortar specimens were used to carry out this research. These cementmortar specimens were investigated by TISA – KOVARI [3] before so all the material and shearing constants were well-known. The other purpose of this research was to observe the influence of the normal stress on the dilatation–displacement curves

Coloring half-planes and bottomless rectangles

We prove lower and upper bounds for the chromatic number of certain hypergraphs defined by geometric regions. This problem has close relations to conflict-free colorings. One of the most interesting type of regions to consider for this problem is that of the axis-parallel rectangles. We completely solve the problem for a special case of them, for bottomless rectangles. We also give an almost complete answer for half-planes and pose several open problems. Moreover we give efficient coloring algorithms