Surface embedding, topology and dualization for spin networks

Spin networks are graphs derived from 3nj symbols of angular momentum. The surface embedding, the topology and dualization of these networks are considered. Embeddings into compact surfaces include the orientable sphere S^2 and the torus T, and the not orientable projective space P^2 and Klein's bottle K. Two families of 3nj graphs admit embeddings of minimal genus into S^2 and P^2. Their dual 2-skeletons are shown to be triangulations of these surfaces.Comment: LaTeX 17 pages, 6 eps figures (late submission to arxiv.org

Energetics and stability of dangling-bond silicon wires on H passivated Si(100)

We evaluate the electronic, geometric and energetic properties of quasi 1-D wires formed by dangling bonds on Si(100)-H (2 x 1). The calculations are performed with density functional theory (DFT). Infinite wires are found to be insulating and Peierls distorted, however finite wires develop localized electronic states that can be of great use for molecular-based devices. The ground state solution of finite wires does not correspond to a geometrical distortion but rather to an antiferromagnetic ordering. For the stability of wires, the presence of abundant H atoms in nearby Si atoms can be a problem. We have evaluated the energy barriers for intradimer and intrarow diffusion finding all of them about 1 eV or larger, even in the case where a H impurity is already sitting on the wire. These results are encouraging for using dangling-bond wires in future devices.Comment: 8 pages, 6 figure

The discretised harmonic oscillator: Mathieu functions and a new class of generalised Hermite polynomials

We present a general, asymptotical solution for the discretised harmonic oscillator. The corresponding Schr\"odinger equation is canonically conjugate to the Mathieu differential equation, the Schr\"odinger equation of the quantum pendulum. Thus, in addition to giving an explicit solution for the Hamiltonian of an isolated Josephon junction or a superconducting single-electron transistor (SSET), we obtain an asymptotical representation of Mathieu functions. We solve the discretised harmonic oscillator by transforming the infinite-dimensional matrix-eigenvalue problem into an infinite set of algebraic equations which are later shown to be satisfied by the obtained solution. The proposed ansatz defines a new class of generalised Hermite polynomials which are explicit functions of the coupling parameter and tend to ordinary Hermite polynomials in the limit of vanishing coupling constant. The polynomials become orthogonal as parts of the eigenvectors of a Hermitian matrix and, consequently, the exponential part of the solution can not be excluded. We have conjectured the general structure of the solution, both with respect to the quantum number and the order of the expansion. An explicit proof is given for the three leading orders of the asymptotical solution and we sketch a proof for the asymptotical convergence of eigenvectors with respect to norm. From a more practical point of view, we can estimate the required effort for improving the known solution and the accuracy of the eigenvectors. The applied method can be generalised in order to accommodate several variables.Comment: 18 pages, ReVTeX, the final version with rather general expression

Inelastic current-voltage characteristics of atomic and molecular junctions

We report first-principles calculations of the inelastic current-voltage (I-V) characteristics of a gold point contact and a molecular junction in the nonresonant regime. Discontinuities in the I-V curves appear in correspondence to the normal modes of the structures. Due to the quasi-one-dimensional nature of these systems, specific modes with large longitudinal component dominate the inelastic I-V curves. In the case of the gold point contact, our results are in good agreement with recent experimental data. For the molecular junction, we find that the inelastic I-V curves are quite sensitive to the structure of the contact between the molecule and the electrodes thus providing a powerful tool to extract the bonding geometry in molecular wires.Comment: 4 pages, 3 figure

Electron transport via local polarons at interface atoms

Electronic transport is profoundly modified in the presence of strong electron-vibration coupling. We show that in certain situations, the electron flow takes place only when vibrations are excited. By controlling the segregation of boron in semiconducting Si(111)-3√×3√R30° surfaces, we create a type of adatom with a dangling-bond state that is electronically decoupled from any other electronic state. However, probing this state with scanning tunnelling microscopy at 5 K yields high currents. These findings are rationalized by ab-initio calculations that show the formation of a local polaron in the transport process

Persistence in complex systems

Persistence is an important characteristic of many complex systems in nature, related to how long the system remains at a certain state before changing to a different one. The study of complex systems' persistence involves different definitions and uses different techniques, depending on whether short-term or long-term persistence is considered. In this paper we discuss the most important definitions, concepts, methods, literature and latest results on persistence in complex systems. Firstly, the most used definitions of persistence in short-term and long-term cases are presented. The most relevant methods to characterize persistence are then discussed in both cases. A complete literature review is also carried out. We also present and discuss some relevant results on persistence, and give empirical evidence of performance in different detailed case studies, for both short-term and long-term persistence. A perspective on the future of persistence concludes the work.This research has been partially supported by the project PID2020-115454GB-C21 of the Spanish Ministry of Science and Innovation (MICINN). This research has also been partially supported by Comunidad de Madrid, PROMINT-CM project (grant ref: P2018/EMT-4366). J. Del Ser would like to thank the Basque Government for its funding support through the EMAITEK and ELKARTEK programs (3KIA project, KK-2020/00049), as well as the consolidated research group MATHMODE (ref. T1294-19). GCV work is supported by the European Research Council (ERC) under the ERC-CoG-2014 SEDAL Consolidator grant (grant agreement 647423)

Decoherence in elastic and polaronic transport via discrete quantum states

Here we study the effect of decoherence on elastic and polaronic transport via discrete quantum states. The calculations are performed with the help of nonperturbative computational scheme, based on the Green's function theory within the framework of polaron transformation (GFT-PT), where the many-body electron-phonon interaction problem is mapped exactly into a single-electron multi-channel scattering problem. In particular, the influence of dephasing and relaxation processes on the shape of the electrical current and shot noise curves is discussed in detail under the linear and nonlinear transport conditions.Comment: 11 pages, 3 figure

Measurement of the Transverse Beam Spin Asymmetry in Elastic Electron Proton Scattering and the Inelastic Contribution to the Imaginary Part of the Two-Photon Exchange Amplitude

We report on a measurement of the asymmetry in the scattering of transversely polarized electrons off unpolarized protons, A$_\perp$, at two Q$^2$ values of \qsquaredaveragedlow (GeV/c)$^2$ and \qsquaredaveragedhighII (GeV/c)$^2$ and a scattering angle of $30^\circ < \theta_e < 40^\circ$. The measured transverse asymmetries are A$_{\perp}$(Q$^2$ = \qsquaredaveragedlow (GeV/c)$^2$) = (\experimentalasymmetry alulowcorr $\pm$ \statisticalerrorlow$_{\rm stat}$ $\pm$ \combinedsyspolerrorlowalucor$_{\rm sys}$) $\times$ 10$^{-6}$ and A$_{\perp}$(Q$^2$ = \qsquaredaveragedhighII (GeV/c)$^2$) = (\experimentalasymme tryaluhighcorr $\pm$ \statisticalerrorhigh$_{\rm stat}$ $\pm$ \combinedsyspolerrorhighalucor$_{\rm sys}$) $\times$ 10$^{-6}$. The first errors denotes the statistical error and the second the systematic uncertainties. A$_\perp$ arises from the imaginary part of the two-photon exchange amplitude and is zero in the one-photon exchange approximation. From comparison with theoretical estimates of A$_\perp$ we conclude that $\pi$N-intermediate states give a substantial contribution to the imaginary part of the two-photon amplitude. The contribution from the ground state proton to the imaginary part of the two-photon exchange can be neglected. There is no obvious reason why this should be different for the real part of the two-photon amplitude, which enters into the radiative corrections for the Rosenbluth separation measurements of the electric form factor of the proton.Comment: 4 figures, submitted to PRL on Oct.

Evidence for Strange Quark Contributions to the Nucleon's Form Factors at Q2Q^2 = 0.108 (GeV/c)2^2

We report on a measurement of the parity violating asymmetry in the elastic scattering of polarized electrons off unpolarized protons with the A4 apparatus at MAMI in Mainz at a four momentum transfer value of $Q^2$ = \Qsquare (GeV/c)$^2$ and at a forward electron scattering angle of 30$^\circ < \theta_e < 40^\circ$. The measured asymmetry is $A_{LR}(\vec{e}p)$ = (\Aphys $\pm$ \Deltastat$_{stat}$ $\pm$ \Deltasyst$_{syst}$) $\times$ 10$^{-6}$. The expectation from the Standard Model assuming no strangeness contribution to the vector current is A$_0$ = (\Azero $\pm$ \DeltaAzero) $\times$ 10$^{-6}$. We have improved the statistical accuracy by a factor of 3 as compared to our previous measurements at a higher $Q^2$. We have extracted the strangeness contribution to the electromagnetic form factors from our data to be $G_E^s$ + \FakGMs $G_M^s$ = \GEsGMs $\pm$ \DeltaGEsGMs at $Q^2$ = \Qsquare (GeV/c)$^2$. As in our previous measurement at higher momentum transfer for $G_E^s$ + 0.230 $G_M^s$, we again find the value for $G_E^s$ + \FakGMs $G_M^s$ to be positive, this time at an improved significance level of 2 $\sigma$.Comment: 4 pages, 3 figure