Gauge invariance, massless modes and topology of gauge fields in multi-band superconductors

Multi-phase physics is a new physics of multi-gap superconductors. Multi-band superconductors exhibit many interesting and novel properties. We investigate the dynamics of the phase-difference mode and show that this mode yields a new excitation mode. The phase-difference mode is represented as an abelian vector field. There are massless modes when the number of gaps is greater than three and the Josephson term is frustrated. The fluctuation of phase-difference modes with non-trivial topology leads to the existence of a fractional-quantum flux vortex in a magnetic field. A superconductor with a fractional-quantum flux vortex is regarded as a topological superconductor with the integer Chern number.Comment: Proceedings of the 12th Asia and Pacific Physics Conference (2013

Systematic solution-generation of five-dimensional black holes

Solitonic solution-generating methods are powerful tools to construct nontrivial black hole solutions of the higher-dimensional Einstein equations systematically. In five dimensions particularly, the solitonic methods can be successfully applied to the construction of asymptotically Minkowski spacetimes with multiple horizons. We review the solitonic methods applicable to higher-dimensional vacuum spacetimes and present some five-dimensional examples derived from the methods.Comment: Invited review for Prog. Theor. Phys. Suppl., 33 pages, 13 figures. v2: References added v3: published versio

Traversability and connectivity of the middle graph of a graph

AbstractWe define a graph M(G) as an intersection graph Ω(F) on the point set V(G) of any graph G. Let X(G) be the line set of G and F = V′(G) ∪ X(G), where V′(G) indicates the family of all one point subsets of the set V(G). Let M(G) = Ω(F). M(G) is called the middle graph of G. The following theorems result: 1.Theorem 1. Let G be any graph and G+ be a graph constructed from G. Then we have L(G+)≅M(G), where L(G+) is the line graphof G+2.Theorem 2. Let G be a graph. The middle graph M(G) of G is hamiltonian if and only if G contains a closed spanning trail.3.Theorem 3. If a graph G is eulerian, then the middle graph m(G) of G is eulerian and hamiltonian.4.Theorem 4. If M(G) is eulerian, then G is eulerian and M(G) is hamiltonian.5.Theorem 5. Let G be a graph. The middle graph M(G) of G contains a closed spanning trail if and only if G is connected and without points of degree ⩽ 1.6.Theorem 6. If a graph G is n-line connected, then the middle graph M(G) is n-connected