A general approximation of quantum graph vertex couplings by scaled Schroedinger operators on thin branched manifolds

We demonstrate that any self-adjoint coupling in a quantum graph vertex can be approximated by a family of magnetic Schroedinger operators on a tubular network built over the graph. If such a manifold has a boundary, Neumann conditions are imposed at it. The procedure involves a local change of graph topology in the vicinity of the vertex; the approximation scheme constructed on the graph is subsequently `lifted' to the manifold. For the corresponding operator a norm-resolvent convergence is proved, with the natural identification map, as the tube diameters tend to zero.Comment: 19 pages, one figure; introduction amended and some references added, to appear in CM

Duality and Anholonomy in Quantum Mechanics of 1D Contact Interactions

We study systems with parity invariant contact interactions in one dimension. The model analyzed is the simplest nontrivial one --- a quantum wire with a point defect --- and yet is shown to exhibit exotic phenomena, such as strong vs weak coupling duality and spiral anholonomy in the spectral flow. The structure underlying these phenomena is SU(2), which arises as accidental symmetry for a particular class of interactions.Comment: 4 pages ReVTeX with 4 epsf figures. KEK preprint 2000-3. Correction in Eq.(14

Nature of 45 degree vortex lattice reorientation in tetragonal superconductors

The transformation of the vortex lattice in a tetragonal superconductor which consists of its 45 degree reorientation relative to the crystal axes is studied using the nonlocal London model. It is shown that the reorientation occurs as two successive second order (continuous) phase transitions. The transition magnetic fields are calculated for a range of parameters relevant for borocarbide superconductors in which the reorientation has been observed

Z(2)-Singlino Dark Matter in a Portal-Like Extension of the Minimal Supersymmetric Standard Model.

We propose a Z2-stabilized singlino () as a dark matter candidate in extended and R-parity violating versions of the supersymmetric standard model. interacts with visible matter via a heavy messenger field S, which results in a supersymmetric version of the Higgs portal interaction. The relic abundance of can account for cold dark matter if the messenger mass satisfies GeV. Our model can be implemented in many realistic supersymmetric models such as the next-to-minimal supersymmetric (SUSY) standard model and nearly minimal SUSY standard model