Wigner function for a particle in an infinite lattice

We study the Wigner function for a quantum system with a discrete, infinite dimensional Hilbert space, such as a spinless particle moving on a one dimensional infinite lattice. We discuss the peculiarities of this scenario and of the associated phase space construction, propose a meaningful definition of the Wigner function in this case, and characterize the set of pure states for which it is non-negative. We propose a measure of non-classicality for states in this system which is consistent with the continuum limit. The prescriptions introduced here are illustrated by applying them to localized and Gaussian states, and to their superpositions.Comment: 19 pages (single column), 7 figure

A study of Wigner functions for discrete-time quantum walks

We perform a systematic study of the discrete time Quantum Walk on one dimension using Wigner functions, which are generalized to include the chirality (or coin) degree of freedom. In particular, we analyze the evolution of the negative volume in phase space, as a function of time, for different initial states. This negativity can be used to quantify the degree of departure of the system from a classical state. We also relate this quantity to the entanglement between the coin and walker subspaces.Comment: 16 pages, 8 figure

A Study on Dialog Act Recognition using Character-Level Tokenization

Dialog act recognition is an important step for dialog systems since it reveals the intention behind the uttered words. Most approaches on the task use word-level tokenization. In contrast, this paper explores the use of character-level tokenization. This is relevant since there is information at the sub-word level that is related to the function of the words and, thus, their intention. We also explore the use of different context windows around each token, which are able to capture important elements, such as affixes. Furthermore, we assess the importance of punctuation and capitalization. We performed experiments on both the Switchboard Dialog Act Corpus and the DIHANA Corpus. In both cases, the experiments not only show that character-level tokenization leads to better performance than the typical word-level approaches, but also that both approaches are able to capture complementary information. Thus, the best results are achieved by combining tokenization at both levels.Comment: 11 pages, 2 figures, 4 tables, AIMSA 201

Periodically rippled graphene: growth and spatially resolved electronic structure

We studied the growth of an epitaxial graphene monolayer on Ru(0001). The graphene monolayer covers uniformly the Ru substrate over lateral distances larger than several microns reproducing the structural defects of the Ru substrate. The graphene is rippled with a periodicity dictated by the difference in lattice parameter between C and Ru. The theoretical model predict inhomogeneities in the electronic structure. This is confirmed by measurements in real space by means of scanning tunnelling spectroscopy. We observe electron pockets at the higher parts of the ripples.Comment: 5 page

Periodically modulated geometric and electronic structure of graphene on Ru(0001)

We report here on a method to fabricate and characterize highly perfect, periodically rippled graphene monolayers and islands, epitaxially grown on single crystal metallic substrates under controlled UHV conditions. The periodicity of the ripples is dictated by the difference in lattice parameters of graphene and substrate, and, thus, it is adjustable. We characterize its perfection at the atomic scale by means of STM and determine its electronic structure in the real space by local tunnelling spectroscopy. There are periodic variations in the geometric and electronic structure of the graphene monolayer. We observe inhomogeneities in the charge distribution, i.e a larger occupied Density Of States at the higher parts of the ripples. Periodically rippled graphene might represent the physical realization of an ordered array of coupled graphene quantum dots. The data show, however, that for rippled graphene on Ru(0001) both the low and the high parts of the ripples are metallic. The fabrication of periodically rippled graphene layers with controllable characteristic length and different bonding interactions with the substrate will allow a systematic experimental test of this fundamental problem.Comment: 12 pages. Contribution to the topical issue on graphene of Semiconductor Science and Technolog

Wigner formalism for a particle on an infinite lattice: dynamics and spin

The recently proposed Wigner function for a particle in an infinite lattice (Hinarejos M, Banuls MC and Perez A 2012 New J. Phys. 14 103009) is extended here to include an internal degree of freedom as spin. This extension is made by introducing a Wigner matrix. The formalism is developed to account for dynamical processes, with or without decoherence. We show explicit solutions for the case of Hamiltonian evolution under a position-dependent potential, and for evolution governed by a master equation under some simple models of decoherence, for which the Wigner matrix formalism is well suited. Discrete processes are also discussed. Finally, we discuss the possibility of introducing a negativity concept for the Wigner function in the case where the spin degree of freedom is included

Helium reflectivity and Debye temperature of graphene grown epitaxially on Ru(0001)

It is shown that the surface of an epitaxial graphene monolayer grown on Ru(0001) could be used as a quite efficient external mirror for He-atom microscopy, with a specular reflectivity of 20% of the incident beam. Furthermore, the system is stable up to 1150 K, and the He reflectivity remains almost unchanged after exposure to air. Additionally, the high reflectivity for H2 molecules (11%) opens up the development of a H2 microprobe suitable for lithography. The Debye temperature for this epitaxial graphene monolayer has been determined from a study of the temperature dependence of the He specular intensity as a function of incident parameters. A value of 1045 K has been obtained, which is much higher than the 590 K reported for graphite under similar conditions, and close to the value of 1287 K calculated for isolated grapheneThis work was supported by the Ministerio de Educación y Ciencia through the program CONSOLIDER-INGENIO on Molecular Nanoscience (Project No. CSD 2007-00010), Project No. FIS2010-18847, and a Juan de la Cierva grant (A.P.), and by Comunidad de Madrid through the program NANOBIOMAGNE

Electronic and Geometric Corrugation of Periodically Rippled, Self-nanostructured Graphene Epitaxially Grown on Ru(0001)

Graphene epitaxially grown on Ru(0001) displays a remarkably ordered pattern of hills and valleys in Scanning Tunneling Microscopy (STM) images. To which extent the observed "ripples" are structural or electronic in origin have been much disputed recently. A combination of ultrahigh resolution STM images and Helium Atom diffraction data shows that i) the graphene lattice is rotated with respect to the lattice of Ru and ii) the structural corrugation as determined from He diffraction is substantially smaller (0.015 nm) than predicted (0.15 nm) or reported from X-Ray Diffraction or Low Energy Electron Diffraction. The electronic corrugation, on the contrary, is strong enough to invert the contrast between hills and valleys above +2.6 V as new, spatially localized electronic states enter the energy window of the STM. The large electronic corrugation results in a nanostructured periodic landscape of electron and holes pockets.Comment: 16 pages, 6 figure

Periodically modulated geometric and electronic structure of graphene on Ru(0001)

We report here on a method to fabricate and characterize highly perfect, periodically rippled graphene monolayers and islands, epitaxially grown on single crystal metallic substrates under controlled UHV conditions. The periodicity of the ripples is dictated by the difference in lattice parameters of graphene and substrate, and, thus, it is adjustable. We characterize its perfection at the atomic scale by means of STM and determine its electronic structure in the real space by local tunnelling spectroscopy. There are periodic variations in the geometric and electronic structure of the graphene monolayer. We observe inhomogeneities in the charge distribution, i.e a larger occupied Density Of States at the higher parts of the ripples. Periodically rippled graphene might represent the physical realization of an ordered array of coupled graphene quantum dots. The data show, however, that for rippled graphene on Ru(0001) both the low and the high parts of the ripples are metallic. The fabrication of periodically rippled graphene layers with controllable characteristic length and different bonding interactions with the substrate will allow a systematic experimental test of this fundamental problem.Comment: 12 pages. Contribution to the topical issue on graphene of Semiconductor Science and Technolog