On-line construction of position heaps

We propose a simple linear-time on-line algorithm for constructing a position heap for a string [Ehrenfeucht et al, 2011]. Our definition of position heap differs slightly from the one proposed in [Ehrenfeucht et al, 2011] in that it considers the suffixes ordered from left to right. Our construction is based on classic suffix pointers and resembles the Ukkonen's algorithm for suffix trees [Ukkonen, 1995]. Using suffix pointers, the position heap can be extended into the augmented position heap that allows for a linear-time string matching algorithm [Ehrenfeucht et al, 2011].Comment: to appear in Journal of Discrete Algorithm

Localized Entanglement in one-dimensional Anderson model

The entanglement in one-dimensional Anderson model is studied. We show that the pairwise entanglement measured by the average concurrence has a direct relation to the localization length. The numerical study indicates that the disorder significantly reduces the average entanglement, and entanglement distribution clearly displays the entanglement localization. The maximal pairwise entanglement exhibits a maximum as the disorder strength increases,experiencing a transition from increase to decrease. The entanglement between the center of localization and other site decreases exponentially along the spatial direction. Finally,we study effects of disorder on dynamical properties of entanglement.Comment: 5 pages, 6 figure

Entanglement sharing among qudits

Consider a system consisting of n d-dimensional quantum particles (qudits), and suppose that we want to optimize the entanglement between each pair. One can ask the following basic question regarding the sharing of entanglement: what is the largest possible value Emax(n,d) of the minimum entanglement between any two particles in the system? (Here we take the entanglement of formation as our measure of entanglement.) For n=3 and d=2, that is, for a system of three qubits, the answer is known: Emax(3,2) = 0.550. In this paper we consider first a system of d qudits and show that Emax(d,d) is greater than or equal to 1. We then consider a system of three particles, with three different values of d. Our results for the three-particle case suggest that as the dimension d increases, the particles can share a greater fraction of their entanglement capacity.Comment: 4 pages; v2 contains a new result for 3 qudits with d=

A q-deformed nonlinear map

A scheme of q-deformation of nonlinear maps is introduced. As a specific example, a q-deformation procedure related to the Tsallis q-exponential function is applied to the logistic map. Compared to the canonical logistic map, the resulting family of q-logistic maps is shown to have a wider spectrum of interesting behaviours, including the co-existence of attractors -- a phenomenon rare in one dimensional maps.Comment: 17 pages, 19 figure

Grain boundary energies and cohesive strength as a function of geometry

Cohesive laws are stress-strain curves used in finite element calculations to describe the debonding of interfaces such as grain boundaries. It would be convenient to describe grain boundary cohesive laws as a function of the parameters needed to describe the grain boundary geometry; two parameters in 2D and 5 parameters in 3D. However, we find that the cohesive law is not a smooth function of these parameters. In fact, it is discontinuous at geometries for which the two grains have repeat distances that are rational with respect to one another. Using atomistic simulations, we extract grain boundary energies and cohesive laws of grain boundary fracture in 2D with a Lennard-Jones potential for all possible geometries which can be simulated within periodic boundary conditions with a maximum box size. We introduce a model where grain boundaries are represented as high symmetry boundaries decorated by extra dislocations. Using it, we develop a functional form for the symmetric grain boundary energies, which have cusps at all high symmetry angles. We also find the asymptotic form of the fracture toughness near the discontinuities at high symmetry grain boundaries using our dislocation decoration model.Comment: 12 pages, 19 figures, changed titl

A bipartite class of entanglement monotones for N-qubit pure states

We construct a class of algebraic invariants for N-qubit pure states based on bipartite decompositions of the system. We show that they are entanglement monotones, and that they differ from the well know linear entropies of the sub-systems. They therefore capture new information on the non-local properties of multipartite systems.Comment: 6 page

Electromagnetic form factors in the J/\psi mass region: The case in favor of additional resonances

Using the results of our recent analysis of e^+e^- annihilation, we plot the curves for the diagonal and transition form factors of light hadrons in the time-like region up to the production threshold of an open charm quantum number. The comparison with existing data on the decays of J/\psi into such hadrons shows that some new resonance structures may be present in the mass range between 2 GeVand the J/\psi mass. Searching them may help in a better understanding of the mass spectrum in both the simple and a more sophisticated quark models, and in revealing the details of the three-gluon mechanism of the OZI rule breaking in K\bar K channel.Comment: Formulas are added, typo is corrected, the text is rearranged. Replaced to match the version accepted in Phys Rev

Classification of mixed three-qubit states

We introduce a classification of mixed three-qubit states, in which we define the classes of separable, biseparable, W- and GHZ-states. These classes are successively embedded into each other. We show that contrary to pure W-type states, the mixed W-class is not of measure zero. We construct witness operators that detect the class of a mixed state. We discuss the conjecture that all entangled states with positive partial transpose (PPTES) belong to the W-class. Finally, we present a new family of PPTES "edge" states with maximal ranks.Comment: 4 pages, 1 figur