432 research outputs found
Universal nonequilibrium signatures of Majorana zero modes in quench dynamics
The quantum evolution after a metallic lead is suddenly connected to an
electron system contains information about the excitation spectrum of the
combined system. We exploit this type of "quantum quench" to probe the presence
of Majorana fermions at the ends of a topological superconducting wire. We
obtain an algebraically decaying overlap (Loschmidt echo) for large times after the quench, with
a universal critical exponent =1/4 that is found to be remarkably
robust against details of the setup, such as interactions in the normal lead,
the existence of additional lead channels or the presence of bound levels
between the lead and the superconductor. As in recent quantum dot experiments,
this exponent could be measured by optical absorption, offering a new signature
of Majorana zero modes that is distinct from interferometry and tunneling
spectroscopy.Comment: 9 pages + appendices, 4 figures. v3: published versio
NLC-2 graph recognition and isomorphism
NLC-width is a variant of clique-width with many application in graph
algorithmic. This paper is devoted to graphs of NLC-width two. After giving new
structural properties of the class, we propose a -time algorithm,
improving Johansson's algorithm \cite{Johansson00}. Moreover, our alogrithm is
simple to understand. The above properties and algorithm allow us to propose a
robust -time isomorphism algorithm for NLC-2 graphs. As far as we
know, it is the first polynomial-time algorithm.Comment: soumis \`{a} WG 2007; 12
Pumping conductance, the intrinsic anomalous Hall effect, and statistics of topological invariants
The pumping conductance of a disordered two-dimensional Chern insulator
scales with increasing size and fixed disorder strength to sharp plateau
transitions at well-defined energies between ordinary and quantum Hall
insulators. When the disorder strength is scaled to zero as system size
increases, the "metallic" regime of fluctuating Chern numbers can extend over
the whole band. A simple argument leads to a sort of weighted equipartition of
Chern number over minibands in a finite system with periodic boundary
conditions: even though there must be strong fluctuations between disorder
realizations, the mean Chern number at a given energy is determined by the {\it
clean} Berry curvature distribution expected from the intrinsic anomalous Hall
effect formula for metals. This estimate is compared to numerical results using
recently developed operator algebra methods, and indeed the dominant variation
of average Chern number is explained by the intrinsic anomalous Hall effect. A
mathematical appendix provides more precise definitions and a model for the
full distribution of Chern numbers.Comment: 12 page
A New Perspective on Clustered Planarity as a Combinatorial Embedding Problem
The clustered planarity problem (c-planarity) asks whether a hierarchically
clustered graph admits a planar drawing such that the clusters can be nicely
represented by regions. We introduce the cd-tree data structure and give a new
characterization of c-planarity. It leads to efficient algorithms for
c-planarity testing in the following cases. (i) Every cluster and every
co-cluster (complement of a cluster) has at most two connected components. (ii)
Every cluster has at most five outgoing edges.
Moreover, the cd-tree reveals interesting connections between c-planarity and
planarity with constraints on the order of edges around vertices. On one hand,
this gives rise to a bunch of new open problems related to c-planarity, on the
other hand it provides a new perspective on previous results.Comment: 17 pages, 2 figure
Dependence Logic with Generalized Quantifiers: Axiomatizations
We prove two completeness results, one for the extension of dependence logic
by a monotone generalized quantifier Q with weak interpretation, weak in the
meaning that the interpretation of Q varies with the structures. The second
result considers the extension of dependence logic where Q is interpreted as
"there exists uncountable many." Both of the axiomatizations are shown to be
sound and complete for FO(Q) consequences.Comment: 17 page
Advances in C-Planarity Testing of Clustered Graphs
A clustered graph C=(G,T) consists of an undirected graph G and a rooted tree T in which the leaves of T correspond to the vertices of G=(V,E). Each vertex c in T corresponds to a subset of the vertices of the graph called ''cluster''. C-planarity is a natural extension of graph planarity for clustered graphs, and plays an important role in automatic graph drawing. The complexity status of c-planarity testing is unknown. It has been shown that c-planarity can be tested in linear time for c-connected graphs, i.e., graphs in which the cluster induced subgraphs are connected.
In this paper, we provide a polynomial time algorithm for c-planarity testing for "almost" c-connected clustered graphs, i.e., graphs for which all c-vertices corresponding to the non-c-connected clusters lie on the same path in T starting at the root of T, or graphs in which for each non-connected cluster its super-cluster and all its siblings are connected.
The algorithm uses ideas of the algorithm for subgraph induced planar connectivity augmentation. We regard it as a first step towards general c-planarity testing
Advances on Testing C-Planarity of Embedded Flat Clustered Graphs
We show a polynomial-time algorithm for testing c-planarity of embedded flat
clustered graphs with at most two vertices per cluster on each face.Comment: Accepted at GD '1
Metal--topological-insulator transition in the quantum kicked rotator with Z2 symmetry
The quantum kicked rotator is a periodically driven dynamical system with a
metal-insulator transition. We extend the model so that it includes phase
transitions between a metal and a topological insulator, in the universality
class of the quantum spin Hall effect. We calculate the Z2 topological
invariant using a scattering formulation that remains valid in the presence of
disorder. The scaling laws at the phase transition can be studied efficiently
by replacing one of the two spatial dimensions with a second incommensurate
driving frequency. We find that the critical exponent does not depend on the
topological invariant, in agreement with earlier independent results from the
network model of the quantum spin Hall effect.Comment: 5 figures, 6 page
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