The topological classification of one-dimensional symmetric quantum walks

We give a topological classification of quantum walks on an infinite 1D lattice, which obey one of the discrete symmetry groups of the tenfold way, have a gap around some eigenvalues at symmetry protected points, and satisfy a mild locality condition. No translation invariance is assumed. The classification is parameterized by three indices, taking values in a group, which is either trivial, the group of integers, or the group of integers modulo 2, depending on the type of symmetry. The classification is complete in the sense that two walks have the same indices if and only if they can be connected by a norm continuous path along which all the mentioned properties remain valid. Of the three indices, two are related to the asymptotic behaviour far to the right and far to the left, respectively. These are also stable under compact perturbations. The third index is sensitive to those compact perturbations which cannot be contracted to a trivial one. The results apply to the Hamiltonian case as well. In this case all compact perturbations can be contracted, so the third index is not defined. Our classification extends the one known in the translation invariant case, where the asymptotic right and left indices add up to zero, and the third one vanishes, leaving effectively only one independent index. When two translationally invariant bulks with distinct indices are joined, the left and right asymptotic indices of the joined walk are thereby fixed, and there must be eigenvalues at $1$ or $-1$ (bulk-boundary correspondence). Their location is governed by the third index. We also discuss how the theory applies to finite lattices, with suitable homogeneity assumptions.Comment: 36 pages, 7 figure

Nonequilibrium dynamical mean-field calculations based on the non-crossing approximation and its generalizations

We solve the impurity problem which arises within nonequilibrium dynamical mean-field theory for the Hubbard model by means of a self-consistent perturbation expansion around the atomic limit. While the lowest order, known as the non-crossing approximation (NCA), is reliable only when the interaction U is much larger than the bandwidth, low-order corrections to the NCA turn out to be sufficient to reproduce numerically exact Monte Carlo results in a wide parameter range that covers the insulating phase and the metal-insulator crossover regime at not too low temperatures. As an application of the perturbative strong-coupling impurity solver we investigate the response of the double occupancy in the Mott insulating phase of the Hubbard model to a dynamical change of the interaction or the hopping, a technique which has been used as a probe of the Mott insulating state in ultracold fermionic gases.Comment: 14 pages, 9 figure

Far-infrared line observations of planetary nebulae. 1: The O 3 spectrum

Observations of the far-infrared fine structure lines of O III have been obtained for six planetary nebulae. The infrared measurements are combined with optical O III line fluxes to probe physical conditions in the gas. From the observed line intensity ratios, a simultaneous solution was obtained for electron temperature and density, as well as means of evaluating the importance of inhomogeneities. Densities determined from the far-infrared O III lines agree well density diagnostics from other ions, indicating a fairly homogeneous density in the emitting gas. Temperatures are determined separately from the O III 4363/5007 A and 5007 A/52 micron intensity ratios and compared. Systematically higher values are derived from the former ratio, which is expected from a nebula which is not isothermal. Allowance for the presence of temperature variations within these nebulae raises their derived oxygen abundances, determinations to be reconciled with the solar value

On the origin of white dwarfs with carbon-dominated atmospheres: the case of H1504+65

We explore different evolutionary scenarios to explain the helium deficiency observed in H1504+65, the most massive known PG1159 star. We concentrate mainly on the possibility that this star could be the result of mass loss shortly after the born-again and during the subsequent evolution through the [WCL] stage. This possibility is sustained by recent observational evidence of extensive mass-loss events in Sakurai's object and is in line with the recent finding that such mass losses give rise to PG1159 models with thin helium-rich envelopes and large rates of period change, as demanded by the pulsating star PG1159-035. We compute the post born again evolution of massive sequences by taking into account different mass-loss rate histories. Our results show that stationary winds during the post-born-again evolution fail to remove completely the helium-rich envelope so as to explain the helium deficiency observed in H1504+65. Stationary winds during the Sakurai and [WCL] stages only remove at most half of the envelope surviving the violent hydrogen burning during the born-again phase. In view of our results, the recently suggested evolutionary connection born-again stars --> H1504+65 --> white dwarfs with carbon-rich atmospheres is difficult to sustain unless the whole helium-rich envelope could be ejected by non-stationary mass-loss episodes during the Sakurai stage.Comment: 5 pages, 2 figures. To be published in Astronomy & Astrophysic

Eg versus x relation from photoluminescence and electron microprobe investigations in p-type Hg1−xCdxTe (0.35 =< x =< 0.7)

Combined photoluminescence (at 10 T 300 K) and electron microprobe investigations have been carried out with HgCdTe samples grown from the melt or from solution. By exciting the samples through metallic masks with 200 μm diameter holes fixed with respect to the sample care was taken to pick-up both characteristic X-ray radiation as well as the photoluminescence from the same sample area. The Eg versus x relation determined in this way at T = 30 K has been compared with data from the interband absorption edge by other authors

A far-infrared study of N/O abundance ratio in galactic H 2 regions

Far-infrared lines of N++ and O++ in several galactic H II regions were measured in an effort to probe the abundance ratio N/O. New measurements are presented for W32 (630.8-0.0), Orion A, and G75.84+0.4. The combination of (N III) 57.3 millimicrons and (O III) 88.4 and 51.8 millimicrons yields measurements of N++/O++ that are largely insensitive to electron temperature, density uncertainties, and to clumping of the ionized gas, due to the similarity of the critical densities for these transitions. In the observed nebulae, N++/O++ should be indicative of N/O, a ratio that is of special importance in nucleosynthesis theory. Measurements are compared with previous measurements of M17 and W51. For nebulae in the solar circle, N++/O++ is greater than the N/O values derived from optical studies of N+/O+ in low ionization zones of the same nebulae. We find that N++/O++ in W43 is significantly higher than for the other H II regions in the sample. Since W43 is located at R = 5 kpc, which is the smallest galactocentric distance in our sample, our data appear consistent with the presence of a negative abundance gradient d(N/O)dR

Depinning exponents of the driven long-range elastic string

We perform a high-precision calculation of the critical exponents for the long-range elastic string driven through quenched disorder at the depinning transition, at zero temperature. Large-scale simulations are used to avoid finite-size effects and to enable high precision. The roughness, growth, and velocity exponents are calculated independently, and the dynamic and correlation length exponents are derived. The critical exponents satisfy known scaling relations and agree well with analytical predictions.Comment: 6 pages, 5 figure

The QSO evolution derived from the HBQS and other complete QSO surveys

An ESO Key programme dedicated to an Homogeneous Bright QSO Survey (HBQS) has been completed. 327 QSOs (Mb<-23, 0.3<z<2.2) have been selected over 555 deg^2 with 15<B<18.75. For B<16.4 the QSO surface density turns out to be a factor 2.2 higher than what measured by the PG survey, corresponding to a surface density of 0.013+/-.006 deg^{-2}. If the Edinburgh QSO Survey is included, an overdensity of a factor 2.5 is observed, corresponding to a density of 0.016+/-0.005 deg^{-2}. In order to derive the QSO optical luminosity function (LF) we used Monte Carlo simulations that take into account of the selection criteria, photometric errors and QSO spectral slope distribution. The LF can be represented with a Pure Luminosity Evolution (L(z)\propto(1+z)^k) of a two power law both for q_0=0.5 and q_0=0.1. For q_0=0.5 k=3.26, slower than the previous Boyle's (1992) estimations of k=3.45. A flatter slope beta=-3.72 of the bright part of the LF is also required. The observed overdensity of bright QSOs is concentrated at z<0.6. It results that in the range 0.3<z<0.6 the luminosity function is flatter than observed at higher redshifts. In this redshift range, for Mb<-25, 32 QSOs are observed instead of 19 expected from our best-fit PLE model. This feature requires a luminosity dependent luminosity evolution in order to satisfactorily represent the data in the whole 0.3<z<2.2 interval.Comment: Invited talk in "Wide Field Spectroscopy" (20-24 May 1996, Athens), eds. M. Kontizas et al. 6 pages and 3 eps figures, LaTex file, uses epfs.sty and crckapb.sty (included