Classical singularities and Semi-Poisson statistics in quantum chaos and disordered systems

We investigate a 1D disordered Hamiltonian with a non analytical step-like dispersion relation whose level statistics is exactly described by Semi-Poisson statistics(SP). It is shown that this result is robust, namely, does not depend neither on the microscopic details of the potential nor on a magnetic flux but only on the type of non-analyticity. We also argue that a deterministic kicked rotator with a non-analytical step-like potential has the same spectral properties. Semi-Poisson statistics (SP), typical of pseudo-integrable billiards, has been frequently claimed to describe critical statistics, namely, the level statistics of a disordered system at the Anderson transition (AT). However we provide convincing evidence they are indeed different: each of them has its origin in a different type of classical singularities.Comment: typos corrected, 4 pages, 3 figure

Universality in quantum chaos and the one parameter scaling theory

We adapt the one parameter scaling theory (OPT) to the context of quantum chaos. As a result we propose a more precise characterization of the universality classes associated to Wigner-Dyson and Poisson statistics which takes into account Anderson localization effects. Based also on the OPT we predict a new universality class in quantum chaos related to the metal-insulator transition and provide several examples. In low dimensions it is characterized by classical superdiffusion or a fractal spectrum, in higher dimensions it can also have a purely quantum origin as in the case of disordered systems. Our findings open the possibility of studying the metal insulator transition experimentally in a much broader type of systems.Comment: 4 pages, 2 figures, acknowledgment added, typos correcte

Computability of the causal boundary by using isocausality

Recently, a new viewpoint on the classical c-boundary in Mathematical Relativity has been developed, the relations of this boundary with the conformal one and other classical boundaries have been analyzed, and its computation in some classes of spacetimes, as the standard stationary ones, has been carried out. In the present paper, we consider the notion of isocausality given by Garc\'ia-Parrado and Senovilla, and introduce a framework to carry out isocausal comparisons with standard stationary spacetimes. As a consequence, the qualitative behavior of the c-boundary (at the three levels: point set, chronology and topology) of a wide class of spacetimes, is obtained.Comment: 44 pages, 5 Figures, latex. Version with minor changes and the inclusion of Figure

A semiclassical theory of the Anderson transition

We study analytically the metal-insulator transition in a disordered conductor by combining the self-consistent theory of localization with the one parameter scaling theory. We provide explicit expressions of the critical exponents and the critical disorder as a function of the spatial dimensionality, $d$. The critical exponent $\nu$ controlling the divergence of the localization length at the transition is found to be $\nu = {1 \over 2}+ {1 \over {d-2}}$. This result confirms that the upper critical dimension is infinity. Level statistics are investigated in detail. We show that the two level correlation function decays exponentially and the number variance is linear with a slope which is an increasing function of the spatial dimensionality.Comment: 4 pages, journal versio

Derivation of the physical parameters of the jet in S5 0836+710 from stability analysis

A number of extragalactic jets show periodic structures at different scales that can be associated with growing instabilities. The wavelengths of the developing instability modes and their ratios depend on the flow parameters, so the study of those structures can shed light on jet physics at the scales involved. In this work, we use the fits to the jet ridgeline obtained from different observations of S5 B0836$+$710 and apply stability analysis of relativistic, sheared flows to derive an estimate of the physical parameters of the jet. Based on the assumption that the observed structures are generated by growing Kelvin-Helmholtz (KH) instability modes, we have run numerical calculations of stability of a relativistic, sheared jet over a range of different jet parameters. We have spanned several orders of magnitude in jet-to-ambient medium density ratio, and jet internal energy, and checked different values of the Lorentz factor and shear layer width. This represents an independent method to obtain estimates of the physical parameters of a jet. By comparing the fastest growing wavelengths of each relevant mode given by the calculations with the observed wavelengths reported in the literature, we have derived independent estimates of the jet Lorentz factor, specific internal energy, jet-to-ambient medium density ratio and Mach number. We obtain a jet Lorentz factor $\gamma \simeq 12$, specific internal energy of $\varepsilon \simeq 10^{-2}\,c^2$, jet-to-ambient medium density ratio of $\eta\approx 10^{-3}$, and an internal (classical) jet Mach number of $M_\mathrm{j}\approx 12$. We also find that the wavelength ratios are better recovered by a transversal structure with a width of $\simeq 10\,\%$ of the jet radius. This method represents a powerful tool to derive the jet parameters in all jets showing helical patterns with different wavelengths.Comment: Accepted for publication in A&A, 15 pages, 12 figure

KIC 9821622: An interesting lithium-rich giant in the Kepler field

We report the discovery of a new exceptional young lithium-rich giant, KIC 9821622, in the \textit{Kepler} field that exhibits an unusually large enhancement of $\alpha$, Fe-peak, and \textit{r}-process elements. From high-resolution spectra obtained with GRACES at Gemini North, we derived fundamental parameters and detailed chemical abundances of 23 elements from equivalent widths and synthesis analysis. By combining atmospheric stellar parameters with available asteroseismic data, we obtained the stellar mass, radius, and age. The data analysis reveals that KIC 9821622 is a Li-rich (A(Li)$_{NLTE}$ = 1.80 $\pm$ 0.2) intermediate-mass giant star ($M$ = 1.64 $M_{\odot}$) located at the red giant branch near the luminosity bump. We find unexpectedly elevated abundances of Fe-peak and \textit{r}-process elements. In addition, as previously reported, we find that this is a young star (2.37 Gyr) with unusually high abundances of $\alpha$-elements ([$\alpha$/Fe] = 0.31). The evolutionary status of KIC 9821622 suggests that its Li-rich nature is the result of internal fresh Li that is synthesized through the Cameron-Fowler mechanism near the luminosity bump. However, its peculiar enhancement of $\alpha$, Fe-peak, and \textit{r}-process elements opens the possibility of external contamination by material enriched by a supernova explosion. Although it is less likely, planet accretion cannot be ruled out.Comment: Letter, 6 pages, 3 figures, Accepted for publication in A&A. - Some language editing include

A model for conservative chaos constructed from multi-component Bose-Einstein condensates with a trap in 2 dimensions

To show a mechanism leading to the breakdown of a particle picture for the multi-component Bose-Einstein condensates(BECs) with a harmonic trap in high dimensions, we investigate the corresponding 2-$d$ nonlinear Schr{\"o}dinger equation (Gross-Pitaevskii equation) with use of a modified variational principle. A molecule of two identical Gaussian wavepackets has two degrees of freedom(DFs), the separation of center-of-masses and the wavepacket width. Without the inter-component interaction(ICI) these DFs show independent regular oscillations with the degenerate eigen-frequencies. The inclusion of ICI strongly mixes these DFs, generating a fat mode that breaks a particle picture, which however can be recovered by introducing a time-periodic ICI with zero average. In case of the molecule of three wavepackets for a three-component BEC, the increase of amplitude of ICI yields a transition from regular to chaotic oscillations in the wavepacket breathing.Comment: 5 pages, 4 figure

A biogeochemical model for North and Northwest Iberia: some applications

The Coastal and Ocean modeling group at the Spanish Institute of Oceanography (IEO) has a broad experience in hydrodynamic modeling with ROMS in the area of West and North Iberia. Our main task consists of providing insight on the coastal and ocean dynamics in support to the intense IEO ecosystem and fisheries research in the area. The NW coast of Iberia is characterized by high levels of primary production that result from relatively frequent and intense inputs of nutrients caused by upwelling, especially in spring and summer. Primary production sustains wealthy fisheries and aquaculture industries, which constitute a prime economic activity in the region. As a first approach to understand the ecosystem variability in the area we focused on the spring bloom. A high resolution (~3 km) configuration of the ROMS physical model with atmospheric forcing coming from the regional agency Meteogalicia (http://www.meteogalicia.es), which has shown to represent the main features of the shelf and slope circulation in the area, was run coupled to the Fasham-type Fennel biogeochemical model (N2PZD2). Any biogeochemical model aimed at providing a reliable representation of the dynamics of a certain area should be tuned according to its characteristics. In an upwelling system, the composition of phytoplankton varies from the beginning to the end of the bloom. When nutrients and irradiance are high, diatoms are the dominant group, whereas flagellates become more important when upwelling relaxes and, consequently, nutrients and light intensity decrease. In the NW Iberian coast, it has been found that Chaetoceros socialis is the dominant diatom species during the spring bloom (Bode et al, 1996, 1998). For this reason, we have decided to use parameters that are characteristic of plankton at the spring bloom. In particular, the parameters of Chaetoceros socialis have been considered for the unique phytoplankton class of the model. We will show comparisons of the model results for 2006 and 2007 with observations at weekly and daily time scales (MODIS chlorophyll-a images, in situ observations from the “Instituto Español de Oceanografía” Pelacus cruises). The spring bloom is reasonably reproduced in the NW and N coasts in time, space and intensity. The variability between the primary production in 2006 and 2007 can be related to the oceanographic conditions thanks to the use of a numerical model. The results are promising and encourage us to move forward to increase the complexity of our models and broaden their range of application. We will show some examples of the use of the IEO models to get some insight on sardine recruitment variability and harmful algal bloom prediction