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

Microwave radiometric studies and ground truth measurements of the NASA/USGS Southern California test site

The field measurement program conducted at the NASA/USGS Southern California Test Site is discussed. Ground truth data and multifrequency microwave brightness data were acquired by a mobile field laboratory operating in conjunction with airborne instruments. The ground based investigations were performed at a number of locales representing a variety of terrains including open desert, cultivated fields, barren fields, portions of the San Andreas Fault Zone, and the Salton Sea. The measurements acquired ground truth data and microwave brightness data at wavelengths of 0.8 cm, 2.2 cm, and 21 cm

Supersymmetry in gauge theories with extra dimensions

We show that a quantum-mechanical N=2 supersymmetry is hidden in 4d mass spectrum of any gauge invariant theories with extra dimensions. The N=2 supercharges are explicitly constructed in terms of differential forms. The analysis can be extended to extra dimensions with boundaries, and for a single extra dimension we clarify a possible set of boundary conditions consistent with 5d gauge invariance, although some of the boundary conditions break 4d gauge symmetries.Comment: 18 page

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

The Arp 220 merger on kpc scales

For the first time we study the Eastern nucleus in greater detail and search for the more extended emission in the molecular gas in different CO line transitions of the famous ULIRG Arp 220. Furthermore we present a model of the merger in Arp 220 on large scales with the help of the CO data and an optical and near-infrared composite HST image of the prototypical ULIRG. Using the Plateau de Bure Interferometer (PdBI) we obtained CO(2-1) and (1-0) data at wavelengths of 1 and 3 mm in 1994, 1996, 1997 and 2006 at different beam sizes and spatial resolutions. The simulations of the merger in Arp 220 were performed with the Identikit modeling tool. The model parameters that describe the galaxy merger best give a mass ratio of 1:2 and result in a merger of ~6x10^8 yrs. The low resolution CO(1-0) PdBI observations suggest that there are indications for emission ~10" towards the south, as well as to the north and to the west of the two nuclei.Comment: accepted for publication in ApJ, 14 pages 10 figure

Self-Consistent Velocity Dependent Effective Interactions

The theory of self-consistent effective interactions in nuclei is extended for a system with a velocity dependent mean potential. By means of the field coupling method, we present a general prescription to derive effective interactions which are consistent with the mean potential. For a deformed system with the conventional pairing field, the velocity dependent effective interactions are derived as the multipole pairing interactions in doubly-stretched coordinates. They are applied to the microscopic analysis of the giant dipole resonances (GDR's) of ${}^{148,154}Sm$, the first excited $2^+$ states of Sn isotopes and the first excited $3^-$ states of Mo isotopes. It is clarified that the interactions play crucial roles in describing the splitting and structure of GDR peaks, in restoring the energy weighted sum rule, and in reducing the values of $B(E\lambda)$.Comment: 35 pages, RevTeX, 7 figures (available upon request), to appear in Phys.Rev.

Evidence of Exponential Decay Emission in the Swift Gamma-ray Bursts

We present a systematic study of the steep decay emission from gamma-ray bursts (GRBs) observed by the Swift X-Ray Telescope (XRT). In contrast to the analysis described in recent literature, we produce composite Burst Alert Telescope (BAT) and XRT light curves by extrapolating the XRT data (2-10 keV) into the BAT energy range (15-25 keV) rather than extrapolating the BAT data into the XRT energy band (0.3-10 keV). Based on the fits to the composite light curves, we have confirmed the existence of an exponential decay component which smoothly connects the BAT prompt data to the XRT steep decay for several GRBs. We also find that the XRT steep decay for some of the bursts can be well fit by a combination of a power-law with an exponential decay model. We discuss this exponential component within the frame work of both the internal and the external shock model.Comment: 33 pages, 34 figures; accepted for publication in Ap

A precessing molecular jet signaling an obscured, growing supermassive black hole in NGC1377?

With high resolution (0."25 x 0."18) ALMA CO 3-2 observations of the nearby (D=21 Mpc, 1"=102 pc), extremely radio-quiet galaxy NGC1377, we have discovered a high-velocity, very collimated nuclear outflow which we interpret as a molecular jet with a projected length of +-150 pc. Along the jet axis we find strong velocity reversals where the projected velocity swings from -150 km/s to +150 km/s. A simple model of a molecular jet precessing around an axis close to the plane of the sky can reproduce the observations. The velocity of the outflowing gas is difficult to constrain due to the velocity reversals but we estimate it to be between 240 and 850 km/s and the jet to precess with a period P=0.3-1.1 Myr. The CO emission is clumpy along the jet and the total molecular mass in the high-velocity (+-(60 to 150 km/s)) gas lies between 2e6 Msun (light jet) and 2e7 Msun (massive jet). There is also CO emission extending along the minor axis of NGC1377. It holds >40% of the flux in NGC1377 and may be a slower, wide-angle molecular outflow which is partially entrained by the molecular jet. We discuss the driving mechanism of the molecular jet and suggest that it is either powered by a very faint radio jet or by an accretion disk-wind similar to those found towards protostars. The nucleus of NGC1377 harbours intense embedded activity and we detect emission from vibrationally excited HCN J=4-3 v_2=1f which is consistent with hot gas and dust. We find large columns of H2 in the centre of NGC1377 which may be a sign of a high rate of recent gas infall. The dynamical age of the molecular jet is short (<1 Myr), which could imply that it is young and consistent with the notion that NGC1377 is caught in a transient phase of its evolution. However, further studies are required to determine the age of the molecular jet, its mass and the role it is playing in the growth of the nucleus of NGC1377.Comment: This is a revised and expanded version of a previous submission which now has 13 pages, 6 figures (+ 4 in the Appendix) and is accepted for publication in Astronomy & Astrophysic

Replica Method for Wide Correlators in Gaussian Orthogonal, Unitary And Symplectic Random Matrix Ensembles

We calculate connected correlators in Gaussian orthogonal, unitary and symplectic random matrix ensembles by the replica method in the 1/N-expansion. We obtain averaged one-point Green's functions up to the next-to-leading order O(1/N) and wide two-level correlators up to the first nontrivial order O(1/N^2) and wide three-level correlators up to the first nontrivial order $O(1/N^4)$ by carefully treating fluctuations in saddle-point evaluation.Comment: LaTeX 21 pages, a new result on wide three-level correlators adde