Extrasolar planetary dynamics with a generalized planar Laplace-Lagrange secular theory

The dynamical evolution of nearly half of the known extrasolar planets in multiple-planet systems may be dominated by secular perturbations. The commonly high eccentricities of the planetary orbits calls into question the utility of the traditional Laplace-Lagrange (LL) secular theory in analyses of the motion. We analytically generalize this theory to fourth-order in the eccentricities, compare the result with the second-order theory and octupole-level theory, and apply these theories to the likely secularly-dominated HD 12661, HD 168443, HD 38529 and Ups And multi-planet systems. The fourth-order scheme yields a multiply-branched criterion for maintaining apsidal libration, and implies that the apsidal rate of a small body is a function of its initial eccentricity, dependencies which are absent from the traditional theory. Numerical results indicate that the primary difference the second and fourth-order theories reveal is an alteration in secular periodicities, and to a smaller extent amplitudes of the planetary eccentricity variation. Comparison with numerical integrations indicates that the improvement afforded by the fourth-order theory over the second-order theory sometimes dwarfs the improvement needed to reproduce the actual dynamical evolution. We conclude that LL secular theory, to any order, generally represents a poor barometer for predicting secular dynamics in extrasolar planetary systems, but does embody a useful tool for extracting an accurate long-term dynamical description of systems with small bodies and/or near-circular orbits.Comment: 14 pages, 12 figures, 1 table, accepted for publication in Ap

Effects of localization and amplification on distribution of intensity transmitted through random media

We numerically study the statistical distribution of intensity transmitted through quasi-one dimensional random media by varying the dimensionless conductance $g$ and the amount of absorption or gain. Markedly non-Rayleigh distribution is found to be well fitted by the analytical formula of Nieuwenhuizen {\it et al}, Phys. Rev. Lett. {\bf 74}, 2674 (1995) with a single parameter $g^\prime$. We show that in the passive random system $g^\prime$ is uniquely related to $g$, while in amplifying/absorbing random media $g^\prime$ also depends on gain/absorption coefficient.Comment: 4 pages, 4 figures, 1 tabl

Endstates in multichannel spinless p-wave superconducting wires

Multimode spinless p-wave superconducting wires with a width W much smaller than the superconducting coherence length \xi are known to have multiple low-energy subgap states localized near the wire's ends. Here we compare the typical energies of such endstates for various terminations of the wire: A superconducting wire coupled to a normal-metal stub, a weakly disordered superconductor wire and a wire with smooth confinement. Depending on the termination, we find that the energies of the subgap states can be higher or lower than for the case of a rectangular wire with hard-wall boundaries.Comment: 10 pages, 7 figure

On hyperovals of polar spaces

We derive lower and upper bounds for the size of a hyperoval of a finite polar space of rank 3. We give a computer-free proof for the uniqueness, up to isomorphism, of the hyperoval of size 126 of H(5, 4) and prove that the near hexagon E-3 has up to isomorphism a unique full embedding into the dual polar space DH(5, 4)

Delocalization and conductance quantization in one-dimensional systems

We investigate the delocalization and conductance quantization in finite one-dimensional chains with only off-diagonal disorder coupled to leads. It is shown that the appearence of delocalized states at the middle of the band under correlated disorder is strongly dependent upon the even-odd parity of the number of sites in the system. In samples with inversion symmetry the conductance equals $2e^{2}/h$ for odd samples, and is smaller for even parity. This result suggests that this even-odd behaviour found previously in the presence of electron correlations may be unrelated to charging effects in the sample.Comment: submitted to PR

Spin and Charge Structure of the Surface States in Topological Insulators

We investigate the spin and charge densities of surface states of the three-dimensional topological insulator $Bi_2Se_3$, starting from the continuum description of the material [Zhang {\em et al.}, Nat. Phys. 5, 438 (2009)]. The spin structure on surfaces other than the 111 surface has additional complexity because of a misalignment of the contributions coming from the two sublattices of the crystal. For these surfaces we expect new features to be seen in the spin-resolved ARPES experiments, caused by a non-helical spin-polarization of electrons at the individual sublattices as well as by the interference of the electron waves emitted coherently from two sublattices. We also show that the position of the Dirac crossing in spectrum of surface states depends on the orientation of the interface. This leads to contact potentials and surface charge redistribution at edges between different facets of the crystal.Comment: Use the correct spin operator. Changes affect the surface states spin structure, but not the spectru

Classical limit of transport in quantum kicked maps

We investigate the behavior of weak localization, conductance fluctuations, and shot noise of a chaotic scatterer in the semiclassical limit. Time resolved numerical results, obtained by truncating the time-evolution of a kicked quantum map after a certain number of iterations, are compared to semiclassical theory. Considering how the appearance of quantum effects is delayed as a function of the Ehrenfest time gives a new method to compare theory and numerical simulations. We find that both weak localization and shot noise agree with semiclassical theory, which predicts exponential suppression with increasing Ehrenfest time. However, conductance fluctuations exhibit different behavior, with only a slight dependence on the Ehrenfest time.Comment: 17 pages, 13 figures. Final versio

Portraits of Complex Networks

We propose a method for characterizing large complex networks by introducing a new matrix structure, unique for a given network, which encodes structural information; provides useful visualization, even for very large networks; and allows for rigorous statistical comparison between networks. Dynamic processes such as percolation can be visualized using animations. Applications to graph theory are discussed, as are generalizations to weighted networks, real-world network similarity testing, and applicability to the graph isomorphism problem.Comment: 6 pages, 9 figure

Should cost effectiveness analyses for NICE always consider future unrelated medical costs?

When developing guidance on the use of new technologies within the NHS, NICE recommends the use of cost effectiveness. Specifically, an intervention is deemed cost effective by NICE if ‘its health benefits are greater than the opportunity costs of programmes displaced to fund the new technology, in the context of a fixed NHS budget. In other words, the general consequences for the wider group of patients in the NHS are considered alongside the effects for those patients who may directly benefit from the technology.’ We argue that the technical guidelines for health technology assessment used by NICE should change given this definition of cost effectiveness. The point at issue is the handling of “unrelated future medical costs”