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

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

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

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

Bar-driven Transport of Molecular Gas to Galactic Centers and Its Consequences

We study the characteristics of molecular gas in the central regions of spiral galaxies on the basis of our CO(J=1-0) imaging survey of 20 nearby spiral galaxies using the NRO and OVRO millimeter arrays. Condensations of molecular gas at galactic centers with sizescales < 1 kpc and CO-derived masses M_gas(R<500pc) = 10^8 - 10^9 M_sun are found to be prevalent in the gas-rich L^* galaxies. Moreover, the degree of gas concentration to the central kpc is found to be higher in barred systems than in unbarred galaxies. This is the first statistical evidence for the higher central concentration of molecular gas in barred galaxies, and it strongly supports the theory of bar-driven gas transport. It is most likely that more than half of molecular gas within the central kpc of a barred galaxy was transported there from outside by the bar. The supply of gas has exceeded the consumption of gas by star formation in the central kpc, resulting in the excess gas in the centers of barred systems. The mean rate of gas inflow is statistically estimated to be larger than 0.1 - 1 M_sun/yr. The correlation between gas properties in the central kpc and the type of nuclear spectrum (HII, LINER, or Seyfert) is investigated. A correlation is found in which galaxies with larger gas-to-dynamical mass ratios tend to have HII nuclear spectra, while galaxies with smaller ratios show spectra indicating AGN. Also, the theoretical prediction of bar-dissolution by condensation of gas to galactic centers is observationally tested. It is suggested that the timescale for bar dissolution is larger than 10^8 - 10^10 yr, or a bar in a L^* galaxy is not destroyed by a condensation of 10^8 - 10^9 M_sun gas in the central kpc.Comment: AASTeX, 20 pages, 8 eps figs, ApJ in press (10 Nov. 1999 issue

A year in the life of GW170817: the rise and fall of a structured jet from a binary neutron star merger

We present the results of our year-long afterglow monitoring of GW170817, the first binary neutron star (NS) merger detected by advanced LIGO and advanced Virgo. New observations with the Australian Telescope Compact Array (ATCA) and the Chandra X-ray Telescope were used to constrain its late-time behavior. The broadband emission, from radio to X-rays, is well-described by a simple power-law spectrum with index ~0.585 at all epochs. After an initial shallow rise ~t^0.9, the afterglow displayed a smooth turn-over, reaching a peak X-ray luminosity of ~5e39 erg/s at 160 d, and has now entered a phase of rapid decline ~t^(-2). The latest temporal trend challenges most models of choked jet/cocoon systems, and is instead consistent with the emergence of a relativistic structured jet seen at an angle of ~22 deg from its axis. Within such model, the properties of the explosion (such as its blastwave energy E_K~2E50 erg, jet width theta_c~4 deg, and ambient density n~3E-3 cm^(-3)) fit well within the range of properties of cosmological short GRBs.Comment: 11 pages, 8 figures, 2 tables, MNRAS, in press. Final version, minor changes only relative to original submission dated 21 August 201