Equivalence of Local and Separable Realizations of the Discontinuity-Inducing Contact Interaction and Its Perturbative Renormalizability

We prove that the separable and local approximations of the discontinuity-inducing zero-range interaction in one-dimensional quantum mechanics are equivalent. We further show that the interaction allows the perturbative treatment through the coupling renormalization. Keywords: one-dimensional system, generalized contact interaction, renormalization, perturbative expansion. PACS Nos: 3.65.-w, 11.10.Gh, 31.15.MdComment: ReVTeX 7pgs, doubl column, no figure, See also the website http://www.mech.kochi-tech.ac.jp/cheon

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

Level spacing distribution of pseudointegrable billiard

In this paper, we examine the level spacing distribution $P(S)$ of the rectangular billiard with a single point-like scatterer, which is known as pseudointegrable. It is shown that the observed $P(S)$ is a new type, which is quite different from the previous conclusion. Even in the strong coupling limit, the Poisson-like behavior rather than Wigner-like is seen for $S>1$, although the level repulsion still remains in the small $S$ region. The difference from the previous works is analyzed in detail.Comment: 11 pages, REVTeX file, 3 PostScript Figure

Singlet fermionic dark matter

We propose a renormalizable model of a fermionic dark matter by introducing a gauge singlet Dirac fermion and a real singlet scalar. The bridges between the singlet sector and the standard model sector are only the singlet scalar interaction terms with the standard model Higgs field. The singlet fermion couples to the standard model particles through the mixing between the standard model Higgs and singlet scalar and is naturally a weakly interacting massive particle (WIMP). The measured relic abundance can be explained by the singlet fermionic dark matter as the WIMP within this model. Collider implication of the singlet fermionic dark matter is also discussed. Predicted is the elastic scattering cross section of the singlet fermion into target nuclei for a direct detection of the dark matter. Search of the direct detection of the dark matter provides severe constraints on the parameters of our model.Comment: 12 pages, 7 figure

Periodic Orbits in Polygonal Billiards

We review some properties of periodic orbit families in polygonal billiards and discuss in particular a sum rule that they obey. In addition, we provide algorithms to determine periodic orbit families and present numerical results that shed new light on the proliferation law and its variation with the genus of the invariant surface. Finally, we deal with correlations in the length spectrum and find that long orbits display Poisson fluctuations.Comment: 30 pages (Latex) including 11 figure

Above-Room-Temperature Ferromagnetism in GaSb/Mn Digital Alloys

Digital alloys of GaSb/Mn have been fabricated by molecular beam epitaxy. Transmission electron micrographs showed good crystal quality with individual Mn-containing layers well resolved; no evidence of 3D MnSb precipitates was seen in as-grown samples. All samples studied exhibited ferromagnetism with temperature dependent hysteresis loops in the magnetization accompanied by metallic p-type conductivity with a strong anomalous Hall effect (AHE) up to 400 K (limited by the experimental setup). The anomalous Hall effect shows hysteresis loops at low temperatures and above room temperature very similar to those seen in the magnetization. The strong AHE with hysteresis indicates that the holes interact with the Mn spins above room temperature. All samples are metallic, which is important for spintronics applications. * To whom correspondence should be addressed. E-mail: [email protected]