The band spectrum of periodic potentials with PT-symmetry

A real band condition is shown to exist for one dimensional periodic complex non-hermitian potentials exhibiting PT-symmetry. We use an exactly solvable ultralocal periodic potential to obtain the band structure and discuss some spectral features of the model, specially those concerning the role of the imaginary parameters of the couplings. Analytical results as well as some numerical examples are provided.Comment: 14 pages, 19 included figures (13 coloured). Submitted to J. Phys.

Miura Transformation between two Non-Linear Equations in 2+1 dimensions

A Dispersive Wave Equation in 2+1 dimensions (2LDW) widely discussed by different authors is shown to be nothing but the modified version of the Generalized Dispersive Wave Equation (GLDW). Using Singularity Analysis and techniques based upon the Painleve Property leading to the Double Singular Manifold Expansion we shall find the Miura Transformation which converts the 2LDW Equation into the GLDW Equation. Through this Miura Transformation we shall also present the Lax pair of the 2LDW Equation as well as some interesting reductions to several already known integrable systems in 1+1 dimensions.Comment: 14 pages, latex. Journal of Mathematical Physics (to appear

An amplitude-phase (Ermakov-Lewis) approach for the Jackiw-Pi model of bilayer graphene

In the context of bilayer graphene we use the simple gauge model of Jackiw and Pi to construct its numerical solutions in powers of the bias potential V according to a general scheme due to Kravchenko. Next, using this numerical solutions, we develop the Ermakov-Lewis approach for the same model. This leads us to numerical calculations of the Lewis-Riesenfeld phases that could be of forthcoming experimental interest for bilayer graphene. We also present a generalization of the Ioffe-Korsch nonlinear Darboux transformationComment: FTC, 11 pp, 5 figure

Esquemes argumentatius i coneixement científic. Un estudi sobre la comprensió de la flotabilitat a diferents nivells educatius

Es presenta un estudi sobre les respostes escrites d’estudiants de diversos nivells educatius a una activitat presentada com una narrativa en forma de conte. L’anàlisi es basa en identificar arguments dels estudiants que són estudiats en base a teories d’argumentació. L’estudi dels elements dels arguments ens permet inferir sobre les concepcions científiques i alternatives dels estudiants i trobar esquemes o patrons argumentatius comuns. La comparació entre nivells educatius ens mostra que els tipus d’arguments no varien gaire entre nivells educatius però sí que es troben diferencies quant al tipus d’explicacions que poden ser animistes o que no tenir res a veure amb la física als nivells educatius més baixos

On the shape of spectra for non-self-adjoint periodic Schr\"odinger operators

The spectra of the Schr\"odinger operators with periodic potentials are studied. When the potential is real and periodic, the spectrum consists of at most countably many line segments (energy bands) on the real line, while when the potential is complex and periodic, the spectrum consists of at most countably many analytic arcs in the complex plane. In some recent papers, such operators with complex $\mathcal{PT}$-symmetric periodic potentials are studied. In particular, the authors argued that some energy bands would appear and disappear under perturbations. Here, we show that appearance and disappearance of such energy bands imply existence of nonreal spectra. This is a consequence of a more general result, describing the local shape of the spectrum.Comment: 5 pages, 2 figure

Two-Dimensional Electron Gas in InGaAs/InAlAs Quantum Wells

We designed and performed low temperature DC transport characterization studies on two-dimensional electron gases confined in lattice-matched In$_{0.53}$Ga$_{0.47}$As/In$_{0.52}$Al$_{0.48}$As quantum wells grown by molecular beam epitaxy on InP substrates. The nearly constant mobility for samples with the setback distance larger than 50nm and the similarity between the quantum and transport life-time suggest that the main scattering mechanism is due to short range scattering, such as alloy scattering, with a scattering rate of 2.2 ps$^{-1}$. We also obtain the Fermi level at the In$_{0.53}$Ga$_{0.47}$As/In$_{0.52}$Al$_{0.48}$As surface to be 0.36eV above the conduction band, when fitting our experimental densities with a Poisson-Schr\"odinger model.Comment: Accepted in Applied Physics Letter

On the Lie symmetries of a class of generalized Ermakov systems

The symmetry analysis of Ermakov systems is extended to the generalized case where the frequency depends on the dynamical variables besides time. In this extended framework, a whole class of nonlinearly coupled oscillators are viewed as Hamiltonian Ermakov system and exactly solved in closed form

Dynamical symmetries and the Ermakov invariant

Ermakov systems possessing Noether point symmetry are identified among the Ermakov systems that derive from a Lagrangian formalism and, the Ermakov invariant is shown to result from an associated symmetry of dynamical character. The Ermakov invariant and the associated Noether invariant, are sufficient to reduce these systems to quadratures

Functionalised Poly(Vinyl Alcohol)/Graphene Oxide as Polymer Composite Electrolyte Membranes

[EN] Crosslinked poly(vinyl alcohol) (PVA) based composite films were prepared as polyelectrolyte membranes for low temperature direct ethanol fuel cells (DEFC). The membranes were functionalised by means of the addition of graphene oxide (GO) and sulfonated graphene oxide (SGO) and crosslinked with sulfosuccinic acid (SSA). The chemical structure was corroborated and suitable thermal properties were found. Although the addition of GO and SGO slightly decreased the proton conductivity of the membranes, a significant reduction of the ethanol solution swelling and crossover was encountered, more relevant for those functionalised with SGO. In general, the composite membranes were stable under simulated service conditions. The addition of GO and SGO particles permitted to buffer the loss and almost retain similar proton conductivity than prior to immersion. These membranes are alternative polyelectrolytes, which overcome current concerns of actual commercial membranes such as the high cost or the crossover phenomenon.The authors would like to thank the support of the European Union through the European Regional Development Funds (ERDF). The Spanish Ministry of Economy, Industry and Competitiveness, is thanked for the research project POLYDECARBOCELL (ENE2017-86711-C3-1-R). The Spanish Ministry of Education, Culture and Sports is thanked for the FPU grant for O. Gil-Castell (FPU13/01916).Gil Castell, Ó.; Cerveró, R.; Teruel Juanes, R.; Badia, JD.; Ribes Greus, MD. (2019). Functionalised Poly(Vinyl Alcohol)/Graphene Oxide as Polymer Composite Electrolyte Membranes. Journal of Renewable Materials. 7(7):655-665. https://doi.org/10.32604/jrm.2019.04401S6556657