Mixed type Hermite-Padé approximation inspired by the Degasperis-Procesi equation

In this work we present new results on the convergence of diagonal sequences of certain mixed type Hermite-Padé approximants of a Nikishin system. The study is motivated by a mixed Hermite-Padé approximation scheme used in the construction of solutions of a Degasperis-Procesi peakon problem and germane to the analysis of the inverse spectral problem for the discrete cubic string.This author [G.L.L] was supported by research grant MTM2015-65888-C4-2-P of Ministerio de Economía, Industria y Competitividad. This author [S.M.P.] received support from research grant CONICYT Fondecyt/Postdoctorado/ Proyecto 3170112. [J.S] Partially supported by NSERC

Spin polarization induced by decoherence in a tunneling one-dimensional Rashba model

Basic questions on the nature of spin polarization in two terminal systems and the way in which decoherence breaks Time-Reversal Symmetry (TRS) are analyzed. We exactly solve several one-dimensional models of tunneling electrons and show the interplay of spin precession and decay of the wavefunction in either a U(1) magnetic field or an effective Spin-Orbit (SO) magnetic field. Spin polarization is clearly identified as the emergence of a spin component parallel to either magnetic field. We show that Onsager's reciprocity is fulfilled when time reversal symmetry is present and no spin polarization arises, no matter the barrier parameters or the SO strength. Introducing a Buttiker's decoherence probe, that preserves unitarity of time evolution, we show that breaking of TRS results in a strong spin polarization for realistic SO, and barrier strengths. We discuss the significance of these results as a very general scenario for the onset of the Chiral-Induced Spin Selectivity effect (CISS), now possibly matching experiments in a quantitative manner.Comment: 24 pages, 14 figure

On the convergence of multi-level Hermite-Pad\'e approximants

In the present paper we prove a Stieltjes type theorem on the convergence of a sequence of rational functions associated with a mixed type Hermite-Pad\'e approximation problem of a Nikishin system of functions and analyze the ratio asymptotic of the corresponding Hermite-Pad\'e polynomials.Comment: 24 page