Renormalization group for the probability distribution of magnetic impurities in a random-field ϕ4\phi^4 model

Extending the usual Ginzburg-Landau theory for the random-field Ising model, the possibility of dimensional reduction is reconsidered. A renormalization group for the probability distribution of magnetic impurities is applied. New parameters corresponding to the extra $\phi^4$ coupling constants in the replica Hamiltonian are introduced. Although they do not affect the critical phenomena near the upper critical dimension, they can when dimensions are lowered.Comment: 16 pages, 11 figures, revte

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

Phase Structure of a Four- and Eight-Fermion Interaction Model at Finite Temperature and Chemical Potential in Arbitrary Dimensions

The phase structure of a four- and eight-fermion interaction model is investigated at finite temperature and chemical potential in arbitrary space-time dimensions, $2\leq D<4$. The effective potential and the gap equation are calculated in the leading order of the 1/N expansion. If the first order phase transition takes place, the phase boundary dividing the symmetric and the broken phase is modified by the eight-fermion interaction.Comment: 20 pages, 26 figures; revised argument and added reference for section

The Second Swift BAT Gamma-Ray Burst Catalog

We present the second Swift Burst Alert Telescope (BAT) catalog of gamma-ray bursts (GRBs), which contains 476 bursts detected by the BAT between 2004 December 19 and 2009 December 21. This catalog (hereafter the BAT2 catalog) presents burst trigger time, location, 90% error radius, duration, fluence, peak flux, time-averaged spectral parameters and time-resolved spectral parameters measured by the BAT. In the correlation study of various observed parameters extracted from the BAT prompt emission data, we distinguish among long-duration GRBs (L-GRBs), short-duration GRBs (S-GRBs), and short-duration GRBs with extended emission (S-GRBs with E.E.) to investigate differences in the prompt emission properties. The fraction of L-GRBs, S-GRBs and S-GRBs with E.E. in the catalog are 89%, 8% and 2% respectively. We compare the BAT prompt emission properties with the BATSE, BeppoSAX and HETE-2 GRB samples. We also correlate the observed prompt emission properties with the redshifts for the GRBs with known redshift. The BAT T90 and T50 durations peak at 70 s and 30 s, respectively. We confirm that the spectra of the BAT S-GRBs are generally harder than those of the L-GRBs. The time-averaged spectra of the BAT S-GRBs with E.E. are similar to those of the L-GRBs. Whereas, the spectra of the initial short spikes of the S-GRBs with E.E. are similar to those of the S-GRBs. We show that the BAT GRB samples are significantly softer than the BATSE bright GRBs, and that the time-averaged Epeak of the BAT GRBs peaks at 80 keV which is significantly lower energy than those of the BATSE sample which peak at 320 keV. The time-averaged spectral properties of the BAT GRB sample are similar to those of the HETE-2 GRB samples. By time-resolved spectral analysis, we find that only 10% of the BAT observed photon indices are outside the allowed region of the synchrotron shock model.Comment: 65 pages, 33 figures, 13 tables, Accepted in ApJS, Nine machine-readable tables are available at http://swift.gsfc.nasa.gov/docs/swift/results/bat2_catalog

Star-forming Cloud Complexes in the Central Molecular Zone of NGC 253

We report 350 and 230 GHz observations of molecular gas and dust in the starburst nucleus of NGC 253 at 20-40 pc (1"-2") resolution. The data contain CO(3-2), HCN(4-3), CO(2-1), 13CO(2-1), C18O(2-1), and continuum at 0.87 mm and 1.3 mm toward the central kiloparsec. The CO(2-1) size of the galaxy's central molecular zone (CMZ) is measured to be about 300 pc x 100 pc at the half maximum of intensity. Five clumps of dense and warm gas stand out in the CMZ at arcsecond resolution, and they are associated with compact radio sources due to recent massive star formation. They contribute one third of the CO emission in the central 300 pc and have 12CO peak brightness temperatures around 50 K, molecular gas column densities on the order of 10^{4} Msun pc^{-2}, gas masses on the order of 10^{7} Msun in the size scale of 20 pc, volume-averaged gas densities of n(H2) ~ 4000 cm^{-3}, and high HCN-to-CO ratios suggestive of higher fractions of dense gas than in the surrounding environment. It is suggested that these are natal molecular cloud complexes of massive star formation. The CMZ of NGC 253 is also compared with that of our Galaxy in CO(2-1) at the same 20 pc resolution. Their overall gas distributions are strikingly similar. The five molecular cloud complexes appear to be akin to such molecular complexes as Sgr A, Sgr B2, Sgr C, and the l=1.3deg cloud in the Galactic center. On the other hand, the starburst CMZ in NGC 253 has higher temperatures and higher surface (and presumably volume) densities than its non-starburst cousin.Comment: ApJ in press, 18 page

SMA CO(J=6-5) and 435 micron interferometric imaging of the nuclear region of Arp 220

We have used the Submillimeter Array (SMA) to make the first interferometric observations (beam size ~1") of the 12CO J=6-5 line and 435 micron (690 GHz) continuum emission toward the central region of the nearby ULIRG Arp 220. These observations resolve the eastern and western nuclei from each other, in both the molecular line and dust continuum emission. At 435 micron, the peak intensity of the western nucleus is stronger than the eastern nucleus, and the difference in peak intensities is less than at longer wavelengths. Fitting a simple model to the dust emission observed between 1.3 mm and 435 micron suggests that dust emissivity power law index in the western nucleus is near unity and steeper in the eastern nucleus, about 2, and that the dust emission is optically thick at the shorter wavelength. Comparison with single dish measurements indicate that the interferometer observations are missing ~60% of the dust emission, most likely from a spatially extended component to which these observations are not sensitive. The 12CO J=6-5 line observations clearly resolve kinematically the two nuclei. The distribution and kinematics of the 12CO J=6-5 line appear to be very similar to lower J CO lies observed at similar resolution. Analysis of multiple 12CO line intensities indicates that the molecular gas in both nuclei have similar excitation conditions, although the western nucleus is warmer and denser. The excitation conditions are similar to those found in other extreme environments, including M82, Mrk 231, and BR 1202-0725. Simultaneous lower resolution observations of the 12CO, 13CO, and C18O J=2-1 lines show that the 13CO and C18O lines have similar intensities, which suggests that both of these lines are optically thick, or possibly that extreme high mass star formation has produced in an overabundance of C18O.Comment: 13 pages (emulateapj), 10 figures, Accepted for publication in Ap

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

Development of Protacs to Target Cancer-promoting Proteins for Ubiquitination and Degradation

The proteome contains hundreds of proteins that in theory could be excellent therapeutic targets for the treatment of human diseases. However, many of these proteins are from functional classes that have never been validated as viable candidates for the development of small molecule inhibitors. Thus, to exploit fully the potential of the Human Genome Project to advance human medicine, there is a need to develop generic methods of inhibiting protein activity that do not rely on the target protein’s function. We previously demonstrated that a normally stable protein, methionine aminopeptidase-2 or MetAP-2, could be artificially targeted to an Skp1-Cullin-F-box (SCF) ubiquitin ligase complex for ubiquitination and degradation through a chimeric bridging molecule or Protac (proteolysis targeting chimeric molecule). This Protac consisted of an SCFß-TRCP-binding phosphopeptide derived from I{kappa}B{alpha} linked to ovalicin, which covalently binds MetAP-2. In this study, we employed this approach to target two different proteins, the estrogen (ER) and androgen (AR) receptors, which have been implicated in the progression of breast and prostate cancer, respectively. We show here that an estradiol-based Protac can enforce the ubiquitination and degradation of the {alpha} isoform of ER in vitro, and a dihydroxytestosterone-based Protac introduced into cells promotes the rapid disappearance of AR in a proteasome-dependent manner. Future improvements to this technology may yield a general approach to treat a number of human diseases, including cancer