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Journal Cover Reviews in Mathematical Physics
  [SJR: 1.092]   [H-I: 36]   [0 followers]  Follow
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 0129-055X - ISSN (Online) 1793-6659
   Published by World Scientific Homepage  [118 journals]
  • On weakly conformally symmetric pseudo-Riemannian manifolds
    • Authors: Carlo Alberto Mantica, Young Jin Suh
      Abstract: Reviews in Mathematical Physics, Ahead of Print.
      In this paper, we study the properties of weakly conformally symmetric pseudo- Riemannian manifolds focusing particularly on the [math]-dimensional Lorentzian case. First, we provide a new proof of an important result found in literature; then several new others are stated. We provide a decomposition for the conformal curvature tensor in [math]. Moreover, some important identities involving two particular covectors are stated; for example, it is proven that under certain conditions the Ricci tensor and other tensors are Weyl compatible. Topological properties involving the vanishing of the first Pontryagin form are then stated. Further, we study weakly conformally symmetric 4-dimensional Lorentzian manifolds (space-times): it is proven that one of the previously defined covectors is null and unique up to a scaling. Moreover, it is shown that under certain conditions, the same vector is an eigenvector of the Ricci tensor and its integral curves are geodesics. Finally, it is stated that such space-time is of Petrov type N with respect to the same vector.
      Citation: Reviews in Mathematical Physics
      PubDate: 2017-01-26T09:11:03Z
      DOI: 10.1142/S0129055X17500076
  • A cut-off tubular geometry of loop space
    • Authors: Partha Mukhopadhyay
      Abstract: Reviews in Mathematical Physics, Ahead of Print.
      Motivated by the computation of loop space quantum mechanics as indicated in [14], here we seek a better understanding of the tubular geometry of loop space [math] corresponding to a Riemannian manifold [math] around the submanifold of vanishing loops. Our approach is to first compute the tubular metric of [math] around the diagonal submanifold, where [math] is the Cartesian product of [math] copies of [math] with a cyclic ordering. This gives an infinite sequence of tubular metrics such that the one relevant to [math] can be obtained by taking the limit [math]. Such metrics are computed by adopting an indirect method where the general tubular expansion theorem of [21] is crucially used. We discuss how the complete reparametrization isometry of loop space arises in the large-[math] limit and verify that the corresponding Killing equation is satisfied to all orders in tubular expansion. These tubular metrics can alternatively be interpreted as some natural Riemannian metrics on certain bundles of tangent spaces of [math] which, for [math], is the tangent bundle [math].
      Citation: Reviews in Mathematical Physics
      PubDate: 2017-01-17T10:09:27Z
      DOI: 10.1142/S0129055X17500064
  • Surface superconductivity in presence of corners
    • Authors: Michele Correggi, Emanuela L. Giacomelli
      Abstract: Reviews in Mathematical Physics, Ahead of Print.
      We consider an extreme type-II superconducting wire with non-smooth cross section, i.e. with one or more corners at the boundary, in the framework of the Ginzburg–Landau theory. We prove the existence of an interval of values of the applied field, where superconductivity is spread uniformly along the boundary of the sample. More precisely, the energy is not affected to leading order by the presence of corners and the modulus of the Ginzburg–Landau minimizer is approximately constant along the transversal direction. The critical fields delimiting this surface superconductivity regime coincide with the ones in absence of boundary singularities.
      Citation: Reviews in Mathematical Physics
      PubDate: 2017-01-17T10:09:27Z
      DOI: 10.1142/S0129055X17500052
  • Wannier functions and [math] invariants in time-reversal symmetric
           topological insulators
    • Authors: Horia D. Cornean, Domenico Monaco, Stefan Teufel
      Abstract: Reviews in Mathematical Physics, Ahead of Print.
      We provide a constructive proof of exponentially localized Wannier functions and related Bloch frames in 1- and 2-dimensional time-reversal symmetric (TRS) topological insulators. The construction is formulated in terms of periodic TRS families of projectors (corresponding, in applications, to the eigenprojectors on an arbitrary number of relevant energy bands), and is thus model-independent. The possibility to enforce also a TRS constraint on the frame is investigated. This leads to a topological obstruction in dimension 2, related to [math] topological phases. We review several proposals for [math] indices that distinguish these topological phases, including the ones by Fu–Kane [16], Prodan [33], Graf–Porta [24] and Fiorenza–Monaco–Panati [27]. We show that all these formulations are equivalent. In particular, this allows to prove a geometric formula for the [math] invariant of 2-dimensional TRS topological insulators, originally indicated in [16], which expresses it in terms of the Berry connection and the Berry curvature.
      Citation: Reviews in Mathematical Physics
      PubDate: 2017-01-10T09:04:06Z
      DOI: 10.1142/S0129055X17300011
  • Chern number modification in crossing the boundary between different band
           structures: Three-band models with cubic symmetry
    • Authors: T Iwai, B. Zhilinskii
      Abstract: Reviews in Mathematical Physics, Ahead of Print.
      A family of [math] Hermitian matrix Hamiltonians defined on the sphere [math] and depending on extra control parameters in the presence of a finite subgroup of [math] as a symmetry group are studied with eigen-line bundles which are constructed by piecing together locally-defined eigenvectors. The condition for degeneracy in eigenvalues splits in general the space of control parameters into distinct iso-Chern domains on each of which the Chern numbers of the associated eigen-line bundles are constant. A Chern number modification or a delta-Chern occurs when crossing the boundary from one iso-Chern domain to another. The present article provides a formula for the delta-Chern on the model of a two-parameter family of [math] Hermitian matrix Hamiltonians with cubic symmetry together with the whole sets of Chern numbers on respective iso-Chern domains.
      Citation: Reviews in Mathematical Physics
      PubDate: 2017-01-10T09:04:02Z
      DOI: 10.1142/S0129055X17500040
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