Persistent currents in mesoscopic cavities and the effect of level crossings as random variables

In the present article we perform analytical and numerical calculations related to persistent currents in 2D isolated mesoscopic annular cavities threaded by a magnetic flux. The system considered has a high number of open channels and therefore the single particle spectrum exhibits many level crossings as the flux varies. We determine the effect of the distribution of level crossings in the typical persistent current.Comment: 23 pages, including 6 figure

Gromov, Cauchy and causal boundaries for Riemannian, Finslerian and Lorentzian manifolds

Recently, the old notion of causal boundary for a spacetime V has been redefined in a consistent way. The computation of this boundary $\partial V$ for a standard conformally stationary spacetime V = R x M, suggests a natural compactification $M_B$ associated to any Riemannian metric on M or, more generally, to any Finslerian one. The corresponding boundary $\partial_B M$ is constructed in terms of Busemann-type functions. Roughly, $\partial_B M$ represents the set of all the directions in M including both, asymptotic and "finite" (or "incomplete") directions. This Busemann boundary $\partial_B M$ is related to two classical boundaries: the Cauchy boundary and the Gromov boundary. Our aims are: (1) to study the subtleties of both, the Cauchy boundary for any generalized (possibly non-symmetric) distance and the Gromov compactification for any (possibly incomplete) Finsler manifold, (2) to introduce the new Busemann compactification $M_B$, relating it with the previous two completions, and (3) to give a full description of the causal boundary $\partial V$ of any standard conformally stationary spacetime.Comment: Final version with minor modifications, to appear in Memoirs of the American Mathematical Society. 80 pages, 10 figures, late

Drinfel'd Twists and Algebraic Bethe Ansatz

We study representation theory of Drinfel'd twists, in terms of what we call F matrices, associated to finite dimensional irreducible modules of quantum affine algebras, and which factorize the corresponding (unitary) R matrices. We construct explicitly such factorizing F matrices for irreducible tensor products of the fundamental representations of the quantum affine algebra sl2 and its associated Yangian. We then apply these constructions to the XXX and XXZ quantum spins chains of finite length in the framework of the Algebraic Bethe Ansatz.Comment: 45 pages, late

Hausdorff separability of the boundaries for spacetimes and sequential spaces

There are several ideal boundaries and completions in General Relativity sharing the topological property of being sequential, i.e., determined by the convergence of its sequences and, so, by some limit operator $L$. As emphasized in a classical article by Geroch, Liang and Wald, some of them have the property, commonly regarded as a drawback, that there are points of the spacetime $M$ non $T_1$-separated from points of the boundary $\partial M$. Here we show that this problem can be solved from a general topological viewpoint. In particular, there is a canonical minimum refinement of the topology in the completion $\overline{M}$ which $T_2$-separates the spacetime $M$ and its boundary $\partial M$ ---no matter the type of completion one chooses. Moreover, we analyze the case of sequential spaces and show how the refined $T_2$-separating topology can be constructed from a modification $L^*$ of the original limit operator $L$. Finally, we particularize this procedure to the case of the causal boundary and show how the separability of $M$ and $\partial M$ can be introduced as an abstract axiom in its definition.Comment: 29 pages, 8 figures, late

On the final definition of the causal boundary and its relation with the conformal boundary

The notion of causal boundary $\partial M$ for a strongly causal spacetime $M$ has been a controversial topic along last decades: on one hand, some attempted definitions were not fully consistent, on the other, there were simple examples where an open conformal embedding i:M\hookarrow M_{0} could be defined, but the corresponding conformal boundary $\partial_{i}M$ disagreed drastically with the causal one. Nevertheless, the recent progress in this topic suggests a definitive option for $\partial M$, which is developed here in detail. Our study has two parts: (I) To give general arguments on a boundary in order to ensure that it is admissible as a causal boundary at the three natural levels, i.e., as a point set, as a chronological space and as a topological space. Then, the essential uniqueness of our choice is stressed, and the relatively few admissible alternatives are discussed. (II) To analyze the role of the conformal boundary $\partial_{i}M$. We show that, in general, $\partial_{i}M$ may present a very undesirable structure. Nevertheless, it is well-behaved under certain general assumptions, and its accessible part $\partial_{i}^{*}M$ agrees with the causal boundary. This study justifies both boundaries. On one hand, the conformal boundary $\partial_{i}^{*}M$, which cannot be defined for a general spacetime but is easily computed in particular examples, appears now as a special case of the causal boundary. On the other, the new redefinition of the causal boundary not only is free of inconsistencies and applicable to any strongly causal spacetime, but also recovers the expected structure in the cases where a natural conformal boundary is available. The cases of globally hyperbolic spacetimes and asymptotically conformally flat ends are especially studied.Comment: Revisded version, including the correction of Appendix 3.6 (51 pages, 13 figures). To appear in Adv. Th. Math. Phy

The Magnetic Fields of the Quiet Sun

This work reviews our understanding of the magnetic fields observed in the quiet Sun. The subject has undergone a major change during the last decade (quiet revolution), and it will remain changing since the techniques of diagnostic employed so far are known to be severely biased. Keeping these caveats in mind, our work covers the main observational properties of the quiet Sun magnetic fields: magnetic field strengths, unsigned magnetic flux densities, magnetic field inclinations, as well as the temporal evolution on short time-scales (loop emergence), and long time-scales (solar cycle). We also summarize the main theoretical ideas put forward to explain the origin of the quiet Sun magnetism. A final prospective section points out various areas of solar physics where the quiet Sun magnetism may have an important physical role to play (chromospheric and coronal structure, solar wind acceleration, and solar elemental abundances).Comment: Review talk presented to the 6th Solar Polarization Workshop held in Maui HI, USA, May-June 201

Brain Damage and Motor Cortex Impairment in Chronic Obstructive Pulmonary Disease: Implication of Nonrapid Eye Movement Sleep Desaturation

Nonrapid eye movement (NREM) sleep desaturation may cause neuronal damage due to the withdrawal of cerebrovascular reactivity. The current study (1) assessed the prevalence of NREM sleep desaturation in nonhypoxemic patients with chronic obstructive pulmonary disease (COPD) and (2) compared a biological marker of cerebral lesion and neuromuscular function in patients with and without NREM sleep desaturation

Quantitative Stellar Spectral Classification. II. Early Type Stars

The method developed by Stock and Stock (1999) for stars of spectral types A to K to derive absolute magnitudes and intrinsic colors from the equivalent widths of absorption lines in stellar spectra is extended to B-type stars. Spectra of this type of stars for which the Hipparcos Catalogue gives parallaxes with an error of less than 20% were observed with the CIDA 1-meter reflector equipped with a Richardson spectrograph with a Thompson 576x384 CCD detector. The dispersion is 1.753 A/pixel using a 600 lines/mm grating in the first order. In order to cover the spectral range 3850 A to 5750 A the grating had to be used in two different positions, with an overlap in the region from 4800 A to 4900 A. A total of 116 stars was oberved, but not all with both grating positions. A total of 12 measureable absorption lines was identified in the spectra and their equivalent widths were measured. These were related to the absolute magnitudes derived from the Hipparcos Catalogue and to the intrinsic colors (deduced from the MK spectral types) using linear and second order polynomials and two or three lines as independent variables. The best solutions were obtained with polynomials of three lines, reproducing the absolute magnitudes with an average residual of about 0.40 magnitudes and the intrinsic colors with an average residual of 0.016 magnitudes.Comment: 17 pages including 4 figures, accepted by Rev.Mex.A.

Quantitative Stellar Spectral Classification. III. Spectral Resolution

The method developed by Stock and Stock (1999) to derive absolute magnitudes and intrinsic colors is applied to simulated low-resolution spectra. The simulation is made by convolving real spectra with a Gaussian function, $\sigma$ (the full width at half maximum) related to the final spectral resolution. The accuracy with which the stellar parameters are determined indicates that the method may be applied to typical objective-prism spectra. We show that changes in the spectral resolution do not significantly affect the stellar parameters obtained with this method for early-type stars, whereas for later-type stars an improved approach is necessary.Comment: 12 pages, 7 figures embedded, Accepted by RevMexA

Algorithmic Complexity in Noise Induced Transport Systems

Time correlated fluctuations interacting with a spatial asymmetry potential are sufficient conditions to give rise to transport of Brownian particles. The transfer of information coming from the nonequilibrium bath, viewed as a source of negentropy, give rise to the correlated noise. The algorithmic complexity of an object provides a means of quantitating its information contents. The Kolmogorov information entropy or algorithmic complexity is investigated in order to quantitate the transfer of information that occurs in computational models showing noise induced transport. The complexity is measured in terms of the average number of bits per time unit necessary to specify the sequence generated by the system.Comment: 7 pages, 2 figure