Conductance distributions in disordered quantum spin-Hall systems

We study numerically the charge conductance distributions of disordered quantum spin-Hall (QSH) systems using a quantum network model. We have found that the conductance distribution at the metal-QSH insulator transition is clearly different from that at the metal-ordinary insulator transition. Thus the critical conductance distribution is sensitive not only to the boundary condition but also to the presence of edge states in the adjacent insulating phase. We have also calculated the point-contact conductance. Even when the two-terminal conductance is approximately quantized, we find large fluctuations in the point-contact conductance. Furthermore, we have found a semi-circular relation between the average of the point-contact conductance and its fluctuation.Comment: 9 pages, 17 figures, published versio

The gravitational instability of a stream of co-orbital particles

We describe the dynamics of a stream of equally spaced macroscopic particles in orbit around a central body (e.g. a planet or star). A co-orbital configuration of small bodies may be subject to gravitational instability, which takes the system to a spreading, disordered and collisional state. We detail the linear instability's mathematical and physical features using the shearing sheet model and subsequently track its nonlinear evolution with local N-body simulations. This model provides a convenient tool with which to understand the gravitational and collisional dynamics of narrow belts, such as Saturn's F-ring and the streams of material wrenched from tidally disrupted bodies. In particular, we study the tendency of these systems to form long-lived particle aggregates. Finally, we uncover an unexpected connection between the linear dynamics of the gravitational instability and the magnetorotational instability.Comment: 11 pages, 7 figures, 1 table. MNRAS, accepte

Witten's Invariants of Rational Homology Spheres at Prime Values of KK and Trivial Connection Contribution

We establish a relation between the coefficients of asymptotic expansion of trivial connection contribution to Witten's invariant of rational homology spheres and the invariants that T.~Ohtsuki extracted from Witten's invariant at prime values of $K$. We also rederive the properties of prime $K$ invariants discovered by H.~Murakami and T.~Ohtsuki. We do this by using the bounds on Taylor series expansion of the Jones polynomial of algebraically split links, studied in our previous paper. These bounds are enough to prove that Ohtsuki's invariants are of finite type. The relation between Ohtsuki's invariants and trivial connection contribution is verified explicitly for lens spaces and Seifert manifolds.Comment: 32 pages, no figures, LaTe

Multifractal properties of critical eigenstates in two-dimensional systems with symplectic symmetry

The multifractal properties of electronic eigenstates at the metal-insulator transition of a two-dimensional disordered tight-binding model with spin-orbit interaction are investigated numerically. The correlation dimensions of the spectral measure $\widetilde{D}_{2}$ and of the fractal eigenstate $D_{2}$ are calculated and shown to be related by $D_{2}=2\widetilde{D}_{2}$. The exponent $\eta=0.35\pm 0.05$ describing the energy correlations of the critical eigenstates is found to satisfy the relation $\eta=2-D_{2}$.Comment: 6 pages RevTeX; 3 uuencoded, gzipped ps-figures to appear in J. Phys. Condensed Matte

Kasagi et al. Reply:

Bremsstrahlung in α Decay of 210Po: Do α Particles Emit Photons in Tunneling?(http://hdl.handle.net/10097/35812)(Comment

Anderson transition in three-dimensional disordered systems with symplectic symmetry

The Anderson transition in a 3D system with symplectic symmetry is investigated numerically. From a one-parameter scaling analysis the critical exponent $\nu$ of the localization length is extracted and estimated to be $\nu = 1.3 \pm 0.2$. The level statistics at the critical point are also analyzed and shown to be scale independent. The form of the energy level spacing distribution $P(s)$ at the critical point is found to be different from that for the orthogonal ensemble suggesting that the breaking of spin rotation symmetry is relevant at the critical point.Comment: 4 pages, revtex, to appear in Physical Review Letters. 3 figures available on request either by fax or normal mail from [email protected] or [email protected]

Mesoscopic Stern-Gerlach spin filter by nonuniform spin-orbit interaction

A novel spin filtering in two-dimensional electron system with nonuniform spin-orbit interactions (SOI) is theoretically studied. The strength of SOI is modulated perpendicular to the charge current. A spatial gradient of effective magnetic field due to the nonuniform SOI causes the Stern-Gerlach type spin separation. The direction of the polarization is perpendicular to the current and parallel to the spatial gradient. Almost 100 % spin polarization can be realized even without applying any external magnetic fields and without attaching ferromagnetic contacts. The spin polarization persists even in the presence of randomness.Comment: 6 pages, 5 figures (2 color figures), to appear in Phys. Rev. B, Rapid Commu

Accretion in the Early Kuiper Belt II. Fragmentation

We describe new planetesimal accretion calculations in the Kuiper Belt that include fragmentation and velocity evolution. All models produce two power law cumulative size distributions, N_C propto r^{-q}, with q = 2.5 for radii less than 0.3-3 km and q = 3 for radii exceeding 1-3 km. The power law indices are nearly independent of the initial mass in the annulus, the initial eccentricity of the planetesimal swarm, and the initial size distribution of the planetesimal swarm. The transition between the two power laws moves to larger radii as the initial eccentricity increases. The maximum size of objects depends on their intrinsic tensile strength; Pluto formation requires a strength exceeding 300 erg per gram. Our models yield formation timescales for Pluto-sized objects of 30-40 Myr for a minimum mass solar nebula. The production of several `Plutos' and more than 10^5 50 km radius Kuiper Belt objects leaves most of the initial mass in 0.1-10 km radius objects that can be collisionally depleted over the age of the solar system. These results resolve the puzzle of large Kuiper Belt objects in a small mass Kuiper Belt.Comment: to appear in the Astronomical Journal (July 1999); 54 pages including 7 tables and 13 figure

A combinatorial approach to knot recognition

This is a report on our ongoing research on a combinatorial approach to knot recognition, using coloring of knots by certain algebraic objects called quandles. The aim of the paper is to summarize the mathematical theory of knot coloring in a compact, accessible manner, and to show how to use it for computational purposes. In particular, we address how to determine colorability of a knot, and propose to use SAT solving to search for colorings. The computational complexity of the problem, both in theory and in our implementation, is discussed. In the last part, we explain how coloring can be utilized in knot recognition