46 research outputs found
Quantum and classical localisation, the spin quantum Hall effect and generalisations
We consider network models for localisation problems belonging to symmetry
class C. This symmetry class arises in a description of the dynamics of
quasiparticles for disordered spin-singlet superconductors which have a
Bogoliubov - de Gennes Hamiltonian that is invariant under spin rotations but
not under time-reversal. Our models include but also generalise the one studied
previously in the context of the spin quantum Hall effect. For these systems we
express the disorder-averaged conductance and density of states in terms of
sums over certain classical random walks, which are self-avoiding and have
attractive interactions. A transition between localised and extended phases of
the quantum system maps in this way to a similar transition for the classical
walks. In the case of the spin quantum Hall effect, the classical walks are the
hulls of percolation clusters, and our approach provides an alternative
derivation of a mapping first established by Gruzberg, Read and Ludwig, Phys.
Rev. Lett. 82, 4254 (1999).Comment: 11 pages, 5 figure
Complete solutions to the metric of spherically collapsing dust in an expanding spacetime with a cosmological constant
We present semi-analytical solutions to the background equations describing
the Lema\^itre-Tolman-Bondi (LTB) metric as well as the homogeneous Friedmann
equations, in the presence of dust, curvature and a cosmological constant
Lambda. For none of the presented solutions any numerical integration has to be
performed. All presented solutions are given for expanding and collapsing
phases, preserving continuity in time and radius. Hence, these solutions
describe the complete space time of a collapsing spherical object in an
expanding universe. In the appendix we present for completeness a solution of
the Friedmann equations in the additional presence of radiation, only valid for
the Robertson-Walker metric.Comment: 23 pages, one figure. Numerical module for evaluation of the
solutions released at
http://web.physik.rwth-aachen.de/download/valkenburg/ColLambda/ Matches
published version, published under Open Access. Note change of titl
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