Semiclassical Approach to Chaotic Quantum Transport

We describe a semiclassical method to calculate universal transport properties of chaotic cavities. While the energy-averaged conductance turns out governed by pairs of entrance-to-exit trajectories, the conductance variance, shot noise and other related quantities require trajectory quadruplets; simple diagrammatic rules allow to find the contributions of these pairs and quadruplets. Both pure symmetry classes and the crossover due to an external magnetic field are considered.Comment: 33 pages, 11 figures (appendices B-D not included in journal version

Partner orbits and action differences on compact factors of the hyperbolic plane. Part I: Sieber-Richter pairs

Physicists have argued that periodic orbit bunching leads to universal spectral fluctuations for chaotic quantum systems. To establish a more detailed mathematical understanding of this fact, it is first necessary to look more closely at the classical side of the problem and determine orbit pairs consisting of orbits which have similar actions. In this paper we specialize to the geodesic flow on compact factors of the hyperbolic plane as a classical chaotic system. We prove the existence of a periodic partner orbit for a given periodic orbit which has a small-angle self-crossing in configuration space which is a `2-encounter'; such configurations are called `Sieber-Richter pairs' in the physics literature. Furthermore, we derive an estimate for the action difference of the partners. In the second part of this paper [13], an inductive argument is provided to deal with higher-order encounters.Comment: to appear on Nonlinearit

From error bounds to the complexity of first-order descent methods for convex functions

This paper shows that error bounds can be used as effective tools for deriving complexity results for first-order descent methods in convex minimization. In a first stage, this objective led us to revisit the interplay between error bounds and the Kurdyka-\L ojasiewicz (KL) inequality. One can show the equivalence between the two concepts for convex functions having a moderately flat profile near the set of minimizers (as those of functions with H\"olderian growth). A counterexample shows that the equivalence is no longer true for extremely flat functions. This fact reveals the relevance of an approach based on KL inequality. In a second stage, we show how KL inequalities can in turn be employed to compute new complexity bounds for a wealth of descent methods for convex problems. Our approach is completely original and makes use of a one-dimensional worst-case proximal sequence in the spirit of the famous majorant method of Kantorovich. Our result applies to a very simple abstract scheme that covers a wide class of descent methods. As a byproduct of our study, we also provide new results for the globalization of KL inequalities in the convex framework. Our main results inaugurate a simple methodology: derive an error bound, compute the desingularizing function whenever possible, identify essential constants in the descent method and finally compute the complexity using the one-dimensional worst case proximal sequence. Our method is illustrated through projection methods for feasibility problems, and through the famous iterative shrinkage thresholding algorithm (ISTA), for which we show that the complexity bound is of the form $O(q^{k})$ where the constituents of the bound only depend on error bound constants obtained for an arbitrary least squares objective with $\ell^1$ regularization

The Dwarf Galaxy Population of the Dorado group down to Mv=-11

We present V and I CCD photometry of suspected low-surface brightness dwarf galaxies detected in a survey covering ~2.4 deg^2 around the central region of the Dorado group of galaxies. The low-surface brightness galaxies were chosen based on their sizes and magnitudes at the limiting isophote of 26.0V\mu. The selected galaxies have magnitudes brighter than V=20 (Mv=-11 for an assumed distance to the group of 17.2 Mpc), with central surface brightnesses \mu0>22.5 V mag/arcsec^2, scale lengths h>2'', and diameters > 14'' at the limiting isophote. Using these criteria, we identified 69 dwarf galaxy candidates. Four of them are large very low-surface brightness galaxies that were detected on a smoothed image, after masking high surface brightness objects. Monte Carlo simulations performed to estimate completeness, photometric uncertainties and to evaluate our ability to detect extended low-surface brightness galaxies show that the completeness fraction is, on average, > 80% for dwarf galaxies with $-17<M_{V}<-10.5$ and 22.5<\mu0<25.5 V mag/arcsec^2, for the range of sizes considered by us (D>14''). The V-I colors of the dwarf candidates vary from -0.3 to 2.3 with a peak on V-I=0.98, suggesting a range of different stellar populations in these galaxies. The projected surface density of the dwarf galaxies shows a concentration towards the group center similar in extent to that found around five X-ray groups and the elliptical galaxy NGC1132 studied by Mulchaey and Zabludoff (1999), suggesting that the dwarf galaxies in Dorado are probably physically associated with the overall potential well of the group.Comment: 32 pages, 16 postscript figures and 3 figures in GIF format, aastex v5.0. To appear in The Astronomical Journal, January 200

On multiplicities in length spectra of arithmetic hyperbolic three-orbifolds

Asymptotic laws for mean multiplicities of lengths of closed geodesics in arithmetic hyperbolic three-orbifolds are derived. The sharpest results are obtained for non-compact orbifolds associated with the Bianchi groups SL(2,o) and some congruence subgroups. Similar results hold for cocompact arithmetic quaternion groups, if a conjecture on the number of gaps in their length spectra is true. The results related to the groups above give asymptotic lower bounds for the mean multiplicities in length spectra of arbitrary arithmetic hyperbolic three-orbifolds. The investigation of these multiplicities is motivated by their sensitive effect on the eigenvalue spectrum of the Laplace-Beltrami operator on a hyperbolic orbifold, which may be interpreted as the Hamiltonian of a three-dimensional quantum system being strongly chaotic in the classical limit.Comment: 29 pages, uuencoded ps. Revised version, to appear in NONLINEARIT

Systematic NLTE study of the -2.6 < [Fe/H] < 0.2 F and G dwarfs in the solar neighbourhood. I. Stellar atmosphere parameters

We present atmospheric parameters for 51 nearby FG dwarfs uniformly distributed over the -2.60 < [Fe/H] < +0.20 metallicity range that is suitable for the Galactic chemical evolution research. Lines of iron, Fe I and Fe II, were used to derive a homogeneous set of effective temperatures, surface gravities, iron abundances, and microturbulence velocities. We used high-resolution (R>60000) Shane/Hamilton and CFHT/ESPaDOnS observed spectra and non-local thermodynamic equilibrium (NLTE) line formation for Fe I and Fe II in the classical 1D model atmospheres. The spectroscopic method was tested with the 20 benchmark stars, for which there are multiple measurements of the infrared flux method (IRFM) Teff and their Hipparcos parallax error is < 10%. We found NLTE abundances from lines of Fe I and Fe II to be consistent within 0.06 dex for every benchmark star, when applying a scaling factor of S_H = 0.5 to the Drawinian rates of inelastic Fe+H collisions. The obtained atmospheric parameters were checked for each program star by comparing its position in the log g-Teff plane with the theoretical evolutionary track in the Yi et al. (2004) grid. Our final effective temperatures lie in between the T_IRFM scales of Alonso et al. (1996) and Casagrande et al. (2011), with a mean difference of +46 K and -51 K, respectively. NLTE leads to higher surface gravity compared with that for LTE. The shift in log g is smaller than 0.1 dex for stars with either [Fe/H] > -0.75, or Teff 4.20. NLTE analysis is crucial for the VMP turn-off and subgiant stars, for which the shift in log g between NLTE and LTE can be up to 0.5 dex. The obtained atmospheric parameters will be used in the forthcoming papers to determine NLTE abundances of important astrophysical elements from lithium to europium and to improve observational constraints on the chemo-dynamical models of the Galaxy evolution.Comment: 18 pages, 14 figures, accepted for publication in Ap

Coupling Biophysical Processes and Water Rights To Simulate Spatially Distributed Water Use in an Intensively Managed Hydrologic System

Humans have significantly altered the redistribution of water in intensively managed hydrologic systems, shifting the spatiotemporal patterns of surface water. Evaluating water availability requires integration of hydrologic processes and associated human influences. In this study, we summarize the development and evaluation of an extensible hydrologic model that explicitly integrates water rights to spatially distribute irrigation waters in a semi-arid agricultural region in the western US, using the Envision integrated modeling platform. The model captures both human and biophysical systems, particularly the diversion of water from the Boise River, which is the main water source that supports irrigated agriculture in this region. In agricultural areas, water demand is estimated as a function of crop type and local environmental conditions. Surface water to meet crop demand is diverted from the stream reaches, constrained by the amount of water available in the stream, the waterrights- appropriated amount, and the priority dates associated with particular places of use. Results, measured by flow rates at gaged stream and canal locations within the study area, suggest that the impacts of irrigation activities on the magnitude and timing of flows through this intensively managed system are well captured. The multi-year averaged diverted water from the Boise River matches observations well, reflecting the appropriation of water according to the water rights database. Because of the spatially explicit implementation of surface water diversion, the model can help diagnose places and times where water resources are likely insufficient to meet agricultural water demands, and inform future water management decisions

Hubble Space Telescope Observations of the Oldest Star Clusters in the LMC

We present V, V-I color-magnitude diagrams (CMDs) for three old star clusters in the Large Magellanic Cloud (LMC): NGC 1466, NGC 2257 and Hodge 11. Our data extend about 3 magnitudes below the main-sequence turnoff, allowing us to determine accurate relative ages and the blue straggler frequencies. Based on a differential comparison of the CMDs, any age difference between the three LMC clusters is less than 1.5 Gyr. Comparing their CMDs to those of M 92 and M 3, the LMC clusters, unless their published metallicities are significantly in error, are the same age as the old Galactic globulars. The similar ages to Galactic globulars are shown to be consistent with hierarchial clustering models of galaxy formation. The blue straggler frequencies are also similar to those of Galactic globular clusters. We derive a true distance modulus to the LMC of (m-M)=18.46 +/- 0.09 (assuming (m-M)=14.61 for M 92) using these three LMC clusters.Comment: 22 pages; to be published in Ap

Spin dynamics with non-abelian Berry gauge fields as a semiclassical constrained hamiltonian system

The dynamics of observables which are matrices depending on \hbar and taking values in classical phase space is defined retaining the terms up to the first order in \hbar of the Moyal bracket. Within this semiclassical approach a first order lagrangian involving gauge fields is studied as a constrained hamiltonian system. This provides a systematic study of spin dynamics in the presence of non-abelian Berry gauge fields. We applied the method to various types of dynamical spin systems and clarified some persisting discussions. In particular employing the Berry gauge field which generates the Thomas precession, we calculated the force exerted on an electron in the external electric and magnetic fields. Moreover, a simple semiclassical formulation of the spin Hall effect is accomplished.Comment: References and some clarification added. Published versio