25,879 research outputs found

    Surface spectral function in the superconducting state of a topological insulator

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    We discuss the surface spectral function of superconductors realized from a topological insulator, such as the copper-intercalated Bi2_{2}Se3_{3}. These functions are calculated by projecting bulk states to the surface for two different models proposed previously for the topological insulator. Dependence of the surface spectra on the symmetry of the bulk pairing order parameter is discussed with particular emphasis on the odd-parity pairing. Exotic spectra like an Andreev bound state connected to the topological surface states are presented.Comment: 12 pages, 9 figures, 1 tabl

    Relativistic DNLS and Kaup-Newell Hierarchy

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    By the recursion operator of the Kaup-Newell hierarchy we construct the relativistic derivative NLS (RDNLS) equation and the corresponding Lax pair. In the nonrelativistic limit cc \rightarrow \infty it reduces to DNLS equation and preserves integrability at any order of relativistic corrections. The compact explicit representation of the linear problem for this equation becomes possible due to notions of the qq-calculus with two bases, one of which is the recursion operator, and another one is the spectral parameter

    Bandwidth theorem for random graphs

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    A graph GG is said to have \textit{bandwidth} at most bb, if there exists a labeling of the vertices by 1,2,...,n1,2,..., n, so that ijb|i - j| \leq b whenever {i,j}\{i,j\} is an edge of GG. Recently, B\"{o}ttcher, Schacht, and Taraz verified a conjecture of Bollob\'{a}s and Koml\'{o}s which says that for every positive r,Δ,γr,\Delta,\gamma, there exists β\beta such that if HH is an nn-vertex rr-chromatic graph with maximum degree at most Δ\Delta which has bandwidth at most βn\beta n, then any graph GG on nn vertices with minimum degree at least (11/r+γ)n(1 - 1/r + \gamma)n contains a copy of HH for large enough nn. In this paper, we extend this theorem to dense random graphs. For bipartite HH, this answers an open question of B\"{o}ttcher, Kohayakawa, and Taraz. It appears that for non-bipartite HH the direct extension is not possible, and one needs in addition that some vertices of HH have independent neighborhoods. We also obtain an asymptotically tight bound for the maximum number of vertex disjoint copies of a fixed rr-chromatic graph H0H_0 which one can find in a spanning subgraph of G(n,p)G(n,p) with minimum degree (11/r+γ)np(1-1/r + \gamma)np.Comment: 29 pages, 3 figure
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