An extension of Fourier analysis for the n-torus in the magnetic field and its application to spectral analysis of the magnetic Laplacian

We solved the Schr{\"o}dinger equation for a particle in a uniform magnetic field in the n-dimensional torus. We obtained a complete set of solutions for a broad class of problems; the torus T^n = R^n / {\Lambda} is defined as a quotient of the Euclidean space R^n by an arbitrary n-dimensional lattice {\Lambda}. The lattice is not necessary either cubic or rectangular. The magnetic field is also arbitrary. However, we restrict ourselves within potential-free problems; the Schr{\"o}dinger operator is assumed to be the Laplace operator defined with the covariant derivative. We defined an algebra that characterizes the symmetry of the Laplacian and named it the magnetic algebra. We proved that the space of functions on which the Laplacian acts is an irreducible representation space of the magnetic algebra. In this sense the magnetic algebra completely characterizes the quantum mechanics in the magnetic torus. We developed a new method for Fourier analysis for the magnetic torus and used it to solve the eigenvalue problem of the Laplacian. All the eigenfunctions are given in explicit forms.Comment: 32 pages, LaTeX, minor corrections are mad

Rotating Boson Star with Large Self-interaction in (2+1) dimensions

Solutions for rotating boson stars in (2+1) dimensional gravity with a negative cosmological constant are obtained numerically. The mass, particle number, and radius of the (2+1) dimensional rotating boson star are shown. Consequently we find the region where the stable boson star can exist.Comment: 14 pages, 6 figures, RevTe

Magnetic translation groups in an n-dimensional torus

A charged particle in a uniform magnetic field in a two-dimensional torus has a discrete noncommutative translation symmetry instead of a continuous commutative translation symmetry. We study topology and symmetry of a particle in a magnetic field in a torus of arbitrary dimensions. The magnetic translation group (MTG) is defined as a group of translations that leave the gauge field invariant. We show that the MTG on an n-dimensional torus is isomorphic to a central extension of a cyclic group Z_{nu_1} x ... x Z_{nu_{2l}} x T^m by U(1) with 2l+m=n. We construct and classify irreducible unitary representations of the MTG on a three-torus and apply the representation theory to three examples. We shortly describe a representation theory for a general n-torus. The MTG on an n-torus can be regarded as a generalization of the so-called noncommutative torus.Comment: 29 pages, LaTeX2e, title changed, re-organized, to be published in Journal of Mathematical Physic

Short gamma-ray bursts within 200 Mpc

We present a systematic search for short-duration gamma-ray bursts (GRBs) in the local Universe based on 14 yr of observations with the Neil Gehrels Swift Observatory. We cross-correlate the GRB positions with the GLADE catalogue of nearby galaxies, and find no event at a distance ≲100 Mpc and four plausible candidates in the range 100 Mpc ≲ D ≲ 200 Mpc. Although affected by low statistics, this number is higher than the one expected for chance alignments to random galaxies, and possibly suggests a physical association between these bursts and nearby galaxies. By assuming a local origin, we use these events to constrain the range of properties for X-ray counterparts of neutron star mergers. Optical upper limits place tight constraints on the onset of a blue kilonova, and imply either low masses (⁠≲10−3M⊙⁠) of lanthanide-poor ejecta or unfavorable orientations (θ_(obs) ≳ 30 deg). Finally, we derive that the all-sky rate of detectable short GRBs within 200 Mpc is 1.3^(+1.7)_(−0.8) yr⁻¹ (68 per cent confidence interval), and discuss the implications for the GRB outflow structure. If these candidates are instead of cosmological origin, we set a upper limit of ≲2.0 yr⁻¹ (90 per cent confidence interval) to the rate of nearby events detectable with operating gamma-ray observatories, such as Swift and Fermi

Detailed Classification of Swift's Gamma-Ray Bursts

Earlier classification analyses found three types of gamma-ray bursts (short, long and intermediate in duration) in the BATSE sample. Recent works have shown that these three groups are also present in the RHESSI and the BeppoSAX databases. The duration distribution analysis of the bursts observed by the Swift satellite also favors the three-component model. In this paper, we extend the analysis of the Swift data with spectral information. We show, using the spectral hardness and the duration simultaneously, that the maximum likelihood method favors the three-component against the two-component model. The likelihood also shows that a fourth component is not needed.Comment: Accepted for publication in The Astrophysical Journa

Exact Solutions for Boson-Fermion Stars in (2+1) dimensions

We solve Einstein equations coupled to a complex scalar field with infinitely large self-interaction, degenerate fermions, and a negative cosmological constant in $(2+1)$ dimensions. Exact solutions for static boson-fermion stars are found when circular symmetry is assumed. We find that the minimum binding energy of boson-fermion star takes a negative value if the value of the cosmological constant is sufficiently small.Comment: 19 pages, 5 figures, RevTeX 3.0, second revised versio

GRB 081029: Understanding Multiple Afterglow Components

We present an analysis of the unusual optical light curve of the gamma-ray burst GRB~081029, which occurred at a redshift of z = 3.8479$. We combine X-ray and optical observations from the Swift X-Ray Telescope and the Swift UltraViolet/Optical Telescope with optical and infrared data obtained using the REM and ROTSE telescopes to construct a detailed data set extending from 86 s to approximately 100,000 s after the BAT trigger. Our data also cover a wide energy range, from 10 keV to 0.77 eV (1.24 Angstrom to 16,000 Angstrom). The X-ray afterglow shows a shallow initial decay followed by a rapid decay starting at about 18,000s. The optical and infrared afterglow, however, shows an uncharacteristic rise at about 5000 s that does not correspond to any feature in the X-ray light curve. Our data are not consistent with synchrotron radiation from a single-component jet interacting with an external medium. We do, however, find that the observed light curve can be explained using multi-component model for the jet.Comment: 4 pages, 3 figures, to appear in the AIP Conference Proceedings for the Gamma-Ray Burst 2010 Conference, Annapolis, MD, USA, November 201

Behavior of bulk high-temperature superconductors of finite thickness subjected to crossed magnetic fields

Crossed magnetic field effects on bulk high-temperature superconductors have been studied both experimentally and numerically. The sample geometry investigated involves finite-size effects along both (crossed) magnetic field directions. The experiments were carried out on bulk melt-processed Y-Ba-Cu-O (YBCO) single domains that had been pre-magnetized with the applied field parallel to their shortest direction (i.e. the c-axis) and then subjected to several cycles of the application of a transverse magnetic field parallel to the sample ab plane. The magnetic properties were measured using orthogonal pick-up coils, a Hall probe placed against the sample surface and Magneto-Optical Imaging (MOI). We show that all principal features of the experimental data can be reproduced qualitatively using a two-dimensional finite-element numerical model based on an E-J power law and in which the current density flows perpendicularly to the plane within which the two components of magnetic field are varied. The results of this study suggest that the suppression of the magnetic moment under the action of a transverse field can be predicted successfully by ignoring the existence of flux-free configurations or flux-cutting effects. These investigations show that the observed decay in magnetization results from the intricate modification of current distribution within the sample cross-section. It is also shown that the model does not predict any saturation of the magnetic induction, even after a large number (~ 100) of transverse field cycles. These features are shown to be consistent with the experimental data.Comment: 41 pages, 9 figures, accepted in Phys. Rev. B Changes : 8 references added, a few precisions added, some typos correcte

A distinct peak-flux distribution of the third class of gamma-ray bursts: A possible signature of X-ray flashes?

Gamma-ray bursts are the most luminous events in the Universe. Going beyond the short-long classification scheme we work in the context of three burst populations with the third group of intermediate duration and softest spectrum. We are looking for physical properties which discriminate the intermediate duration bursts from the other two classes. We use maximum likelihood fits to establish group memberships in the duration-hardness plane. To confirm these results we also use k-means and hierarchical clustering. We use Monte-Carlo simulations to test the significance of the existence of the intermediate group and we find it with 99.8% probability. The intermediate duration population has a significantly lower peak-flux (with 99.94% significance). Also, long bursts with measured redshift have higher peak-fluxes (with 98.6% significance) than long bursts without measured redshifts. As the third group is the softest, we argue that we have {related} them with X-ray flashes among the gamma-ray bursts. We give a new, probabilistic definition for this class of events.Comment: accepted for publication in Ap