4,805 research outputs found
Recurrence relations and vector equilibrium problems arising from a model of non-intersecting squared Bessel paths
In this paper we consider the model of non-intersecting squared Bessel
processes with parameter , in the confluent case where all particles
start, at time , at the same positive value , remain positive, and
end, at time , at the position . The positions of the paths have a
limiting mean density as 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 , letting it
increase proportionally to as 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
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
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
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
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 between electrons on
neighbor and non neighbor sites 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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