No abstract

The problem of consistency of smoothed particle hydrodynamics (SPH) has demanded considerable attention in the past few years due to the ever increasing number of applications of the method in many areas of science and engineering. A loss of consistency leads to an inevitable loss of approximation accuracy. In this paper, we revisit the issue of SPH kernel and particle consistency and demonstrate that SPH has a limiting second-order convergence rate. Numerical experiments with suitably chosen test functions validate this conclusion. In particular, we find that when using the root mean square error as a model evaluation statistics, well-known corrective SPH schemes, which were thought to converge to second, or even higher order, are actually firstorder accurate, or at best close to second order. We also find that observing * Corresponding author Email addresses: leonardo.sigalotti@gmail.com (Leonardo Di G. Sigalotti), jaime.klapp@inin.gob.mx (Jaime Klapp), ottorendon@gmail.com (Otto Rendón), carlosvax@gmail.com (Carlos A. Vargas), franklin.pena@gmail.com (Franklin Peña-Polo) Preprint submitted to Journal of Applied Numerical MathematicsMay 18, 2016 the joint limit when N → ∞, h → 0, and n → ∞, as was recently proposed by Zhu et al., where N is the total number of particles, h is the smoothing length, and n is the number of neighbor particles, standard SPH restores full C 0 particle consistency for both the estimates of the function and its derivatives and becomes insensitive to particle disorder.

We analyze the role of resonances in two-fermion entanglement production for a quasi-one-dimensional two-channel scattering problem. We solve exactly for the problem of a two-fermion antisymmetric product state scattering off a double-␦-well potential. It is shown that the two-particle concurrence of the post-selected state has an oscillatory behavior where the concurrence vanishes at the values of momenta for virtual bound states in the double well. These concurrence zeros are interpreted in terms of the uncertainty in the knowledge of the state of the one-particle subspace-reduced one-particle density matrix. Our results suggest the manipulation of fermion entanglement production through the resonance structure of quantum dots.Entanglement production and quantification have been given much recent attention due to their importance as a resource for quantum information and quantum communication. 1,2 In this direction, there have been recent proposals for producing bipartite fermionic entangled states in the solid-state environment focusing on the role of the direct interaction between particles. Some of these approaches involve direct Coulomb interactions in quantum dots 3 and interference effects, 4 phonon-mediated interactions in superconductors, 5,6 and Kondo-like scattering of conduction electrons. 7 Nevertheless, it has been shown that fermion entanglement can be achieved in the absence of such interactions 8 in the form of particle-hole entanglement even when fermions are injected from thermal reservoirs. In such a setup the orbital degree of freedom is entangled. Other implementations based on the noninteracting scheme have been proposed that entangle the spin degree of freedom and are thus more robust to decoherence 9 because of the weaker coupling of the spin to the environment.In this work we address the problem of entanglement generation for electrons in the context of a two-channel quasione-dimensional conductor, 10 following the scattering matrix formalism of Ref. 8 For the scattering region, we choose a double-␦ potential, separated a distance d. Such a potential is the simplest potential that exhibits resonances and that can be analytically handled. The problem is solved for the concurrence 11,12 exactly for all values of the barrier heights and separation as a function of the incoming electron momenta. The concurrence of the entangled post-selected state is found to oscillate while its envelope decays as a function of electron momentum ͑k i ͒ difference ⌬k = k 2 − k 1 . We find that the concurrence is exactly zero when one or both of the k values hits the resonant states for the potential well. The concurrence zeros are then interpreted in terms of the uncertainty of the state in the one-particle subspace by obtaining the reduced density matrix. We thus determine the role of resonances in the entangling properties of the well, demonstrating new possibilities for fermion entanglement control. We consider in detail the independent channel scenario but quantitative changes due to channel mixing will ...

No abstract