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

Maximization of thermal entanglement of arbitrarily interacting two qubits

We investigate the thermal entanglement of interacting two qubits. We maximize it by tuning a local Hamiltonian under a given interaction Hamiltonian. We prove that the optimizing local Hamiltonian takes a simple form which dose not depend on the temperature and that the corresponding optimized thermal entanglement decays as $1/(T log T)$ at high temperatures. We also find that at low temperatures the thermal entanglement is maximum without any local Hamiltonians and that the second derivative of the maximized thermal entanglement changes discontinuously at the boundary between the high- and low-temperature phases.Comment: 23 pages, 4 figure

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

Scaling Theory of Antiferromagnetic Heisenberg Ladder Models

The $S=1/2$ antiferromagnetic Heisenberg model on multi-leg ladders is investigated. Criticality of the ground-state transition is explored by means of finite-size scaling. The ladders with an even number of legs and those with an odd number of legs are distinguished clearly. In the former, the energy gap opens up as $\Delta E\sim{J_\perp}$, where ${J_\perp}$ is the strength of the antiferromagnetic inter-chain coupling. In the latter, the critical phase with the central charge $c=1$ extends over the whole region of ${J_\perp}>0$.Comment: 12 pages with 9 Postscript figures. To appear in J. Phys. A: Math. Ge

Electronic Structure of Multiple Dots

We calculate, via spin density functional theory (SDFT) and exact diagonalization, the eigenstates for electrons in a variety of external potentials, including double and triple dots. The SDFT calculations employ realistic wafer profiles and gate geometries and also serve as the basis for the exact diagonalization calculations. The exchange interaction J between electrons is the difference between singlet and triplet ground state energies and reflects competition between tunneling and the exchange matrix element, both of which result from overlap in the barrier. For double dots, a characteristic transition from singlet ground state to triplet ground state (positive to negative J) is calculated. For the triple dot geometry with 2 electrons we also find the electronic structure with exact diagonalization. For larger electron number (18 and 20) we use only SDFT. In contrast to the double dot case, the triple dot case shows a quasi-periodic fluctuation of J with magnetic field which we attribute to periodic variations of the basis states in response to changing flux quanta threading the triple dot structure.Comment: 3 pages, 4 figure

A Cross-Whiskers Junction as a Novel Fabrication Process for Intrinsic Josephson Junction

A Bi2Sr2CaCu2O8+d cross-whiskers junction has been successfully discovered as a novel intrinsic Josephson junction without using any technique for micro-fabrication. Two Bi2Sr2CaCu2O8+d whisker crystals were placed crosswise on a MgO substrate and heated at 850C for 30 min. They were electrically connected at their c-planes. The measurement terminals were made at the four ends of the whiskers. The I-V characteristics of the cross-whiskers junction at 5K were found to show a clear multiple-branch structure with a spacing of approximately 15 mV that is a feature of the intrinsic Josephson junction. The critical current density Jc was estimated to be 1170 A/cm2. The branch-structure was strongly suppressed by the magnetic field above 1kOe.Comment: 4 pages, PDF fil

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