4,805 research outputs found

    Recurrence relations and vector equilibrium problems arising from a model of non-intersecting squared Bessel paths

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    In this paper we consider the model of nn non-intersecting squared Bessel processes with parameter α\alpha, in the confluent case where all particles start, at time t=0t=0, at the same positive value x=ax=a, remain positive, and end, at time T=tT=t, at the position x=0x=0. The positions of the paths have a limiting mean density as n→∞n\to\infty which is characterized by a vector equilibrium problem. We show how to obtain this equilibrium problem from different considerations involving the recurrence relations for multiple orthogonal polynomials associated with the modified Bessel functions. We also extend the situation by rescaling the parameter α\alpha, letting it increase proportionally to nn as nn increases. In this case we also analyze the recurrence relation and obtain a vector equilibrium problem for it.Comment: 28 pages, 10 figure

    Weakly-entangled states are dense and robust

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    Motivated by the mathematical definition of entanglement we undertake a rigorous analysis of the separability and non-distillability properties in the neighborhood of those three-qubit mixed states which are entangled and completely bi-separable. Our results are not only restricted to this class of quantum states, since they rest upon very general properties of mixed states and Unextendible Product Bases for any possible number of parties. Robustness against noise of the relevant properties of these states implies the significance of their possible experimental realization, therefore being of physical -and not exclusively mathematical- interest.Comment: 4 pages, final version, accepted for publication in PR

    A geometrical analysis of the field equations in field theory

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    In this review paper we give a geometrical formulation of the field equations in the Lagrangian and Hamiltonian formalisms of classical field theories (of first order) in terms of multivector fields. This formulation enables us to discuss the existence and non-uniqueness of solutions, as well as their integrability.Comment: 14 pages. LaTeX file. This is a review paper based on previous works by the same author

    Numerical study of the hard-core Bose-Hubbard Model on an Infinite Square Lattice

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    We present a study of the hard-core Bose-Hubbard model at zero temperature on an infinite square lattice using the infinite Projected Entangled Pair State algorithm [Jordan et al., Phys. Rev. Lett. 101, 250602 (2008)]. Throughout the whole phase diagram our values for the ground state energy, particle density and condensate fraction accurately reproduce those previously obtained by other methods. We also explore ground state entanglement, compute two-point correlators and conduct a fidelity-based analysis of the phase diagram. Furthermore, for illustrative purposes we simulate the response of the system when a perturbation is suddenly added to the Hamiltonian.Comment: 8 pages, 6 figure

    Enhancement of entanglement in one-dimensional disordered systems

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    The pairwise quantum entanglement of sites in disordered electronic one-dimensional systems (rings) is studied. We focus on the effect of diagonal and off diagonal disorder on the concurrence CijC_{ij} between electrons on neighbor and non neighbor sites i,ji,j as a function of band filling. In the case of diagonal disorder, increasing the degree of disorder leads to a decrease of the concurrence with respect to the ordered case. However, off-diagonal disorder produces a surprisingly strong enhancement of entanglement. This remarkable effect occurs near half filling, where the concurrence becomes up to 15% larger than in the ordered system.Comment: 21 pages, 9 figure
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