A Non-Hermitean Particle in a Disordered World

There has been much recent work on the spectrum of the random non-hermitean Hamiltonian which models the physics of vortex line pinning in superconductors. This note is loosely based on the talk I gave at the conference "New Directions in Statistical Physics" held in Taipei, August 1997. We describe here new results in spatial dimensions higher than one. We also give an expression for the spectrum within the WKB approximation.Comment: latex file, 23 pages, 7 .ps figure

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

Walk entropies on graphs

Entropies based on walks on graphs and on their line-graphs are defined. They are based on the summation over diagonal and off-diagonal elements of the thermal Green’s function of a graph also known as the communicability. The walk entropies are strongly related to the walk regularity of graphs and line-graphs. They are not biased by the graph size and have significantly better correlation with the inverse participation ratio of the eigenmodes of the adjacency matrix than other graph entropies. The temperature dependence of the walk entropies is also discussed. In particular, the walk entropy of graphs is shown to be non-monotonic for regular but non-walk-regular graphs in contrast to non-regular graphs

Fundamental relation between longitudinal and transverse conductivities in the quantum Hall system

We investigate the relation between the diagonal ($\sigma_{xx}$) and off-diagonal ($\sigma_{xy}$) components of the conductivity tensor in the quantum Hall system. We calculate the conductivity components for a short-range impurity potential using the linear response theory, employing an approximation that simply replaces the self-energy by a constant value $-i \hbar /(2 \tau)$ with $\tau$ the scattering time. The approximation is equivalent to assuming that the broadening of a Landau level due to disorder is represented by a Lorentzian with the width $\Gamma = \hbar /(2 \tau)$. Analytic formulas are obtained for both $\sigma_{xx}$ and $\sigma_{xy}$ within the framework of this simple approximation at low temperatures. By examining the leading terms in $\sigma_{xx}$ and $\sigma_{xy}$, we find a proportional relation between $\mathrm{d}\sigma_{xy}/\mathrm{d}B$ and $B \sigma_{xx}^2$. The relation, after slight modification to account for the long-range nature of the impurity potential, is shown to be in quantitative agreement with experimental results obtained in the GaAs/AlGaAs two-dimensional electron system at the low magnetic-field regime where spin splitting is negligibly small.Comment: 21 pages, 8 figures, accepted for publication in J. Phys.: Condens. Matte

Measuring Nonequilibrium Temperature of Forced Oscillators

The meaning of temperature in nonequilibrium thermodynamics is considered by using a forced harmonic oscillator in a heat bath, where we have two effective temperatures for the position and the momentum, respectively. We invent a concrete model of a thermometer to testify the validity of these different temperatures from the operational point of view. It is found that the measured temperature depends on a specific form of interaction between the system and a thermometer, which means the zeroth law of thermodynamics cannot be immediately extended to nonequilibrium cases.Comment: 8 page