Exactly solvable one-qubit driving fields generated via non-linear equations

Using the Hubbard representation for $SU(2)$ we write the time-evolution operator of a two-level system in the disentangled form. This allows us to map the corresponding dynamical law into a set of non-linear coupled equations. In order to find exact solutions, we use an inverse approach and find families of time-dependent Hamiltonians whose off-diagonal elements are connected with the Ermakov equation. The physical meaning of the so-obtained Hamiltonians is discussed in the context of the nuclear magnetic resonance phenomeno

Leaky modes of waveguides as a classical optics analogy of quantum resonances

A classical optics waveguide structure is proposed to simulate resonances of short range one-dimensional potentials in quantum mechanics. The analogy is based on the well known resemblance between the guided and radiation modes of a waveguide with the bound and scattering states of a quantum well. As resonances are scattering states that spend some time in the zone of influence of the scatterer, we associate them with the leaky modes of a waveguide, the latter characterized by suffering attenuation in the direction of propagation but increasing exponentially in the transverse directions. The resemblance is complete since resonances (leaky modes) can be interpreted as bound states (guided modes) with definite lifetime (longitudinal shift). As an immediate application we calculate the leaky modes (resonances) associated with a dielectric homogeneous slab (square well potential) and show that these modes are attenuated as they propagate.Comment: The title has been modified to describe better the contents of the article. Some paragraphs have been added to clarify the result

Superpositions of bright and dark solitons supporting the creation of balanced gain and loss optical potentials

Bright and dark solitons of the cubic nonlinear Schrodinger equation are used to construct complex-valued potentials with all-real spectrum. The real part of these potentials is equal to the intensity of a bright soliton while their imaginary part is defined by the product of such soliton with its concomitant, a dark soliton. Considering light propagation in Kerr media, the real part of the potential refers to the self-focusing of the signal and the imaginary one provides the system with balanced gain-and-loss rates.Comment: 6 figures, 17 pages, LaTeX file. The manuscript has been re-organized (abstract, introduction and conclusions rewritten), and it now includes an appendix with detailed calculations of some relevant results reported in the paper. New references were adde

Dynamical Equations, Invariants and Spectrum Generating Algebras of Mechanical Systems with Position-Dependent Mass

We analyze the dynamical equations obeyed by a classical system with position-dependent mass. It is shown that there is a non-conservative force quadratic in the velocity associated to the variable mass. We construct the Lagrangian and the Hamiltonian for this system and find the modifications required in the Euler-Lagrange and Hamilton's equations to reproduce the appropriate Newton's dynamical law. Since the Hamiltonian is not time invariant, we get a constant of motion suited to write the dynamical equations in the form of the Hamilton's ones. The time-dependent first integrals of motion are then obtained from the factorization of such a constant. A canonical transformation is found to map the variable mass equations to those of a constant mass. As particular cases, we recover some recent results for which the dependence of the mass on the position was already unnoticed, and find new solvable potentials of the P\"oschl-Teller form which seem to be new. The latter are associated to either the su(1,1) or the su(2) Lie algebras depending on the sign of the Hamiltonian

Climate variability impacts on coastal dune slack ecohydrology

The hydrological regime of freshwater systems plays a crucial role in shaping the dynamics of the different biological communities that inhabit them. Climate change is expected to cause major alterations in the hydrological regime of dune slacks by producing shifts in temperature, precipitation and evapotranspiration. Across seasons, we explore the controls on common water fleas (Cladocera) and aquatic plant communities relative to water level regime, water chemistry, weather and geomorphological setting, in a slack of the Sheskinmore dune system, Co. Donegal, northwest Ireland. Cladoceran abundance and diversity peak in summer, but also vary inter-annually, and drivers for this and hydrological variability are discussed. Vegetation is likewise affected by hydrology in a spatial sense, where distribution follows wet/dry patches of water. Water chemistry is more variable within the same season than across different years, particularly related to the drying out of the slack. Rainfall through 2016-2017 was lower than average and evapotranspiration showed higher values than average for the same time period. The influence on the slack of this decreased precipitation extended across successive seasons. The water table is the most important driver of slack ecology, with incidence on biological communities expressed by the increased variability inter-annually, as opposed to seasonal variation

Completeness and Nonclassicality of Coherent States for Generalized Oscillator Algebras

The purposes of this work are (1) to show that the appropriate generalizations of the oscillator algebra permit the construction of a wide set of nonlinear coherent states in unified form; and (2) to clarify the likely contradiction between the nonclassical properties of such nonlinear coherent states and the possibility of finding a classical analog for them since they are P-represented by a delta function. In (1) we prove that a class of nonlinear coherent states can be constructed to satisfy a closure relation that is expressed uniquely in terms of the Meijer G-function. This property automatically defines the delta distribution as the P-representation of such states. Then, in principle, there must be a classical analog for them. Among other examples, we construct a family of nonlinear coherent states for a representation of the su(1,1) Lie algebra that is realized as a deformation of the oscillator algebra. In (2), we use a beam splitter to show that the nonlinear coherent states exhibit properties like anti-bunching that prohibit a classical description for them. We also show that these states lack second order coherence. That is, although the P-representation of the nonlinear coherent states is a delta function, they are not full coherent. Therefore, the systems associated with the generalized oscillator algebras cannot be considered `classical' in the context of the quantum theory of optical coherence.Comment: 26 pages, 10 figures, minor changes, misprints correcte

A new look into the evolution of clusters literature. A bibliometric exercise

In the contemporary globalising knowledge-based economies, local clusters have become crucial elements of regional development, assuming a significant role in both academic and political fields. Although there is an intuitive awareness about the raising importance of the theoretical debate on clusters, there is a substantial lack of empirical support of its precise magnitude and evolution. Moreover, the majority of literature surveys on clusters are exclusively qualitative-based. Aiming at filling this gap, the main purpose of this paper is to provide a quantitative survey of the cluster literature, using bibliometric techniques based on articles. Based on a throughout analysis of all abstracts of articles on clusters published in journals indexed on the Econlit and EBSCO databases, covering the period 1962-2007, our research show that besides their importance in academic fields, the role of clusters has also been widely acknowledged in political spheres. In parallel with the increasing interest in the ‘local’, there has been, as well, an emergent body of literature on global networks and clusters. Moreover, on the basis of the recent boom on clusters literature stands the emergent themes of ‘local networks and social approaches’ and ‘knowledge-based theories’. Literature associated to ‘regional and national innovation systems’ and to ‘institutional approaches’ (local enrooted cultures, governance and customs) has been object of a particular dynamism since the 1990s. Despite the evidence of a clear positive correlation between journals ‘quality’ and formal related research, the evolution of the literature on clusters continues to be mostly appreciative led.Clusters, Industrial Clusters, Industrial Location; Bibliometrics

Position dependent mass Scarf Hamiltonians generated via the Riccati equation

Producción CientíficaThe construction of position dependent mass Scarf Hamiltonians of the trigonometric as well as the hyperbolic types is addressed by means of the factorization method and the Riccati equation. These Hamiltonians are shown to be independent of the ordering parameter of the kinetic term. Additionally, new families of Hamiltonians with the Scarf spectrum are also determined by supersymmetry. Some examples for masses with and without singularities are considered to illustrate our results

Técnicas de estimulación cerebral no invasivas y su aplicación terapéutica en pacientes con afasia

Las Técnicas de Estimulación Cerebral No Invasivas (TECNI) son un grupo de métodos y tecnologías novedosas, entre las que nos encontramos la Estimulación Magnética Transcraneal (EMT) y la Estimulación Transcraneal de Corriente Directa (ETCD), utilizadas como tratamiento rehabilitador en multitud de patologías. En este trabajo nos vamos a centrar plenamente en la aplicación terapéutica en pacientes con afasia. Nos proponemos 5 objetivos entre los cuales se encuentran conocer la efectividad de la estimulación transcraneal en aspectos relacionados con el lenguaje y conocer la efectividad del tratamiento conjunto de estas técnicas asociadas con la terapia logopédica. Metodología: Seleccionamos 26 artículos científicos extraídos de las siguientes bases de datos: Índice Médico Español (IME), Google Académico, Dialnet, Pubmed y Scielo. La mayoría de los estudios aplican la estimulación en pacientes con afasia tras un Accidente Cerebral Vascular (ACV), obteniendo resultados positivos de cara a la recuperación, en aspectos relacionados de forma directa con el lenguaje (sobre todo fluidez verbal y denominación). En ocasiones, se combina la estimulación cerebral con la terapia logopédica, obteniendo resultados favorables en la recuperación del lenguaje, llegando a producir mejoras incluso un año después del tratamiento. Las TECNI y su aplicación terapéutica en el ámbito de la neurorrehabilitación son un campo novedoso y de conocimiento creciente, que necesita un mayor número de estudios, debido a la escasa bibliografía existente. Además, es necesario incluir la terapia logopédica combinada con la estimulación cerebral, ya que se obtienen resultados significativos en la recuperación de la afasia.Grado en Logopedi