Analysis of unidirectional non-paraxial invisibility of purely reflective PT-symmetric volume gratings

We study the diffraction produced by a slab of purely reflective PT-symmetric volume Bragg grating that combines modulations of refractive index and gain/loss of the same periodicity with a quarter-period shift between them. Such a complex grating has a directional coupling between the different diffraction orders, which allows us to find an analytic solution for the first three orders of the full Maxwell equations without resorting to the paraxial approximation. This is important, because only with the full equations can the boundary conditions, allowing for the reflections, be properly implemented. Using our solution we analyze unidirectional invisibility of such a grating in a wide variety of configurations.Comment: 17 pages, 11 figures. arXiv admin note: text overlap with arXiv:1412.050

Unified treatment and classification of superintegrable systems with integrals quadratic in momenta on a two dimensional manifold

In this paper we prove that the two dimensional superintegrable systems with quadratic integrals of motion on a manifold can be classified by using the Poisson algebra of the integrals of motion. There are six general fundamental classes of superintegrable systems. Analytic formulas for the involved integrals are calculated in all the cases. All the known superintegrable systems are classified as special cases of these six general classes.Comment: LaTeX, 72 pages. Extended version of the published version in JM

Superintegrability of the Tremblay-Turbiner-Winternitz quantum Hamiltonians on a plane for odd kk

In a recent FTC by Tremblay {\sl et al} (2009 {\sl J. Phys. A: Math. Theor.} {\bf 42} 205206), it has been conjectured that for any integer value of $k$, some novel exactly solvable and integrable quantum Hamiltonian $H_k$ on a plane is superintegrable and that the additional integral of motion is a $2k$th-order differential operator $Y_{2k}$. Here we demonstrate the conjecture for the infinite family of Hamiltonians $H_k$ with odd $k \ge 3$, whose first member corresponds to the three-body Calogero-Marchioro-Wolfes model after elimination of the centre-of-mass motion. Our approach is based on the construction of some $D_{2k}$-extended and invariant Hamiltonian \chh_k, which can be interpreted as a modified boson oscillator Hamiltonian. The latter is then shown to possess a $D_{2k}$-invariant integral of motion \cyy_{2k}, from which $Y_{2k}$ can be obtained by projection in the $D_{2k}$ identity representation space.Comment: 14 pages, no figure; change of title + important addition to sect. 4 + 2 more references + minor modifications; accepted by JPA as an FT

Frequency Shifts and Linewidth Changes of Infrared-Active Phonons in Double-Layered High-Temperature Superconductors

We calculate frequency shifts and changes in linewidths of infrared-active phonons within a shell model for the bare phononic system coupled to an electronic double-layer structure with inter-layer charge transfer. The theoretical concept is applied to YBaCuO yielding a good description of experimental results in the normal state as well as at the transition to the superconducting state.Comment: 8 pages, LaTex, SISSA-CM-93-00

Direct Observation of Controlled Coupling in an Individual Quantum Dot Molecule

We report the direct observation of quantum coupling in individual quantum dot molecules and its manipulation using static electric fields. A pronounced anti-crossing of different excitonic transitions is observed as the electric field is tuned. Comparison of our experimental results with theory shows that the observed anti-crossing occurs between excitons with predominant spatially \emph{direct} and \emph{indirect} character. The electron component of the exciton wavefunction is shown to have molecular character at the anti-crossing and the quantum coupling strength is deduced optically. In addition, we determine the dependence of the coupling strength on the inter-dot separation and identify a field driven transition of the nature of the molecular ground state.Comment: 11 pages, 4 figures submitted to Physical Review Letter

Phylogenetic Analysis of the Zingiberales Based on \u3cem\u3erbc\u3c/em\u3eL Sequences

Morphological data have been used previously to construct phylogenies of the eight families of the Zingiberales one of the most widely accepted monophyletic groups of flowering plants. To provide additional support for phylogenetic relationships within the order, and placement of the order among monocots, we present a parsimony analysis of DNA sequences from the chloroplast-encoded gene, rbcL, for 21 species of Zingiberales and proposed relatives. Five analyses with equal, and differential weights were performed. All analyses resulted in the same most parsimonious tree for taxa within the Zingiberales and the immediate outgroup. The closest sister group to the Zingiberales based on these data is a clade containing Commelinaceae/Haemodoraceae/Pontederiacea. The tree topology within the order based on rbcL sequence data is different from previous morphological analyses. The order can be divided into two sister groups, one containing the Costaceae and Marantaceae, and the other, the remaining six families. All recognized families are monophyletic with the exception of the Musaceae, which is paraphyletic with the Cannaceae. Wtih trees one and two steps longer tha the most parsimonious trees, phylogenetic resolution is rapidly lost, suggesting that the phylogenetic utility of rbcL sequence date for the Zingiberales is limited to interordinal and intrafamilial relationships

Importance of Tests for the Complete Lorentz Structure of the t --> W+ b vertex at Hadron Colliders

The most general Lorentz-invariant decay-density-matrix for $t\to W^{+}b\to (l^{+}\nu)b$, or for $t\to W^{+}b\to (j_{\bar d}j_u)b$, is expressed in terms of eight helicity parameters. The parameters are physically defined in terms of partial-width-intensities for polarized-final-states in $t\to W^{+}b$ decay. The parameters are the partial width, the $b$ quark's chirality parameter $\xi$, the $W^+$ polarimetry parameter $\sigma$, a "pre-SSB" test parameter $\zeta$, and four $W_{L}$-$W_{T}$ interference parameters $\eta$, $\eta^{'}$, $\omega$, $\omega^{'}$ which test for $\tilde T_{FS}$ violation. They can be used to test for non-CKM-type CP violation, anomalous $\Gamma_{L,T}$'s, top weak magnetism, weak electricity, and second-class currents. By stage-two spin-correlation techniques, percent level statistical uncertainites are typical for measurements at the Tevatron, and several mill level uncertainites are typical at the LHC.Comment: Minor clarifications. Expression for r_{+-} corrected. 19 pages LaTex + Tables + 1 Figur