Parametric oscillator in a Kerr medium: evolution of coherent states

We study the temporal evolution of a coherent state under the action of a parametric oscillator and a nonlinear Kerr-like medium. We make use of the interaction picture representation and use an exact time evolution operator for the time independent part of the Hamiltonian. We approximate the interaction picture Hamiltonian in such a way as to make it a member of a Lie algebra. The corresponding time evolution operator behaves like a squeezing operator due to the temporal dependence of the oscillator's frequency. We analyze the probability amplitude and the auto correlation function for different Hamiltonian parameters and we find a very good agreement between our approximate results and converged numerical calculations.Comment: 11 pages, 3 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

Efficient implementation of a van der Waals density functional: Application to double-wall carbon nanotubes

We present an efficient implementation of the van der Waals density functional of Dion et al [Phys. Rev. Lett. 92, 246401 (2004)], which expresses the nonlocal correlation energy as a double spacial integral. We factorize the integration kernel and use fast Fourier transforms to evaluate the selfconsistent potential, total energy, and atomic forces, in N log(N) operations. The resulting overhead in total computational cost, over semilocal functionals, is very moderate for medium and large systems. We apply the method to calculate the binding energies and the barriers for relative translation and rotation in double-wall carbon nanotubes.Comment: 4 pages, 1 figure, 1 tabl

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

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 $C_{ij}$ between electrons on neighbor and non neighbor sites $i,j$ 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