On the Spectrum and Nature of the Peculiar Type Ia Supernova 1991T

A parameterized supernova synthetic-spectrum code is used to study line identifications in the photospheric-phase spectra of the peculiar Type Ia SN 1991T, and to extract some constraints on the composition structure of the ejected matter. The inferred composition structure is not like that of any hydrodynamical model for Type Ia supernovae. Evidence that SN 1991T was overluminous for an SN Ia is presented, and it is suggested that this peculiar event probably was a substantially super-Chandrasekhar explosion that resulted from the merger of two white dwarfs.Comment: 1 text, 7 figures, submitted to MNRA

Resonant-state expansion of the Green's function of open quantum systems

Our series of recent work on the transmission coefficient of open quantum systems in one dimension will be reviewed. The transmission coefficient is equivalent to the conductance of a quantum dot connected to leads of quantum wires. We will show that the transmission coefficient is given by a sum over all discrete eigenstates without a background integral. An apparent "background" is in fact not a background but generated by tails of various resonance peaks. By using the expression, we will show that the Fano asymmetry of a resonance peak is caused by the interference between various discrete eigenstates. In particular, an unstable resonance can strongly skew the peak of a nearby resonance.Comment: 7 pages, 7 figures. Submitted to International Journal of Theoretical Physics as an article in the Proceedings for PHHQP 2010 (http://www.math.zju.edu.cn/wjd/

Supernova Resonance-Scattering Profiles in the Presence of External Illumination

We discuss a simple model for the formation of a supernova spectral line by resonance scattering in the presence of external illumination of the line-forming region by light from circumstellar interaction (toplighting). The simple model provides a clear understanding of the most conspicuous toplighting effect: a rescaling or, as we prefer, a ``muting'' of the line profile relative to the continuum. This effect would be present in more realistic models, but would be harder to isolate. An analytic expression for a muting factor for a P-Cygni line is derived that depends on the ratio E of the toplighting specific intensity to the specific intensity from the supernova photosphere. If E<1, the line profile is reduced in scale or ``muted''. If E=1, the line profile vanishes altogether. If E>1, the line profile flips vertically: then having an absorption component near the observer-frame line center wavelength and a blueshifted emission component.Comment: accepted for publication in PAS

Some properties of the resonant state in quantum mechanics and its computation

The resonant state of the open quantum system is studied from the viewpoint of the outgoing momentum flux. We show that the number of particles is conserved for a resonant state, if we use an expanding volume of integration in order to take account of the outgoing momentum flux; the number of particles would decay exponentially in a fixed volume of integration. Moreover, we introduce new numerical methods of treating the resonant state with the use of the effective potential. We first give a numerical method of finding a resonance pole in the complex energy plane. The method seeks an energy eigenvalue iteratively. We found that our method leads to a super-convergence, the convergence exponential with respect to the iteration step. The present method is completely independent of commonly used complex scaling. We also give a numerical trick for computing the time evolution of the resonant state in a limited spatial area. Since the wave function of the resonant state is diverging away from the scattering potential, it has been previously difficult to follow its time evolution numerically in a finite area.Comment: 20 pages, 12 figures embedde

Correct extrapolation of overlap distribution in spin glasses

We study in d=3 dimensions the short range Ising spin glass with Jij=+/-1 couplings at T=0. We show that the overlap distribution is non-trivial in the limit of large system size.Comment: 6 pages, 3 figure

Extinction and the Radial Distribution of Supernova Properties in Their Parent Galaxies

We use a Monte Carlo technique and assumed spatial distributions of dust and supernova (SN) progenitors in a simple model of a characteristic SN--producing disk galaxy to explore the effects of extinction on the radial distributions of SN properties in their parent galaxies. The model extinction distributions and projected radial number distributions are presented for various SN types. Even though the model has no core-collapse SNe within three kpc of the center, a considerable fraction of the core-collapse SNe are projected into the inner regions of inclined parent galaxies owing to their small vertical scale height. The model predicts that because of extinction, SNe projected into the central regions should on average appear dimmer and have a much larger magnitude scatter than those in the outer regions. In particular, the model predicts a strong deficit of bright core-collapse events inside a projected radius of a few kpc. Such a deficit is found to be present in the observations. It is a natural consequence of the characteristic spatial distributions of dust and core-collapse SNe in galaxies, and it leads us to offer an alternative to the conventional interpretation of the Shaw effect.Comment: 14 pages, 4 figure