«Ode to Psyche», de John Keats.

Esta traducción de Dde to Psyche de Johnn Keats sigue el original verso a verso, si bien es libre en lo referente a metro y rima.This transiation of Keatss Ode to Psyche into Spanish foilows the original verse by verse, but it is free with regards to metre and rhyme

Quadratic vector fields with a weak focus of third order

We study phase portraits of quadratic vector fields with a weak focus of third order at the origin. We show numerically the existence of at least 20 different global phase portraits for such vector fields coming from exactly 16 different local phase portraits available for these vector fields. Among these 20 phase portraits, 17 have no limit cycles and three have at least one limit cycle

Quasi-elastic peak lineshapes in adsorbate diffusion on nearly flat surfaces at low coverages: the motional narrowing effect in Xe on Pt(111)

Quasi-elastic helium atom scattering measurements have provided clear evidence for a two-dimensional free gas of Xe atoms on Pt(111) at low coverages. Increasing the friction due to the surface, a gradual change of the shape of the quasi-elastic peak is predicted and analyzed for this system in terms of the so-called motional narrowing effect. The type of analysis presented here for the quasi-elastic peak should be prior to any deconvolution procedure carried out in order to better extract information from the process, e.g. diffusion coefficients and jump distributions. Moreover, this analysis also provides conditions for the free gas regime different than those reported earlier.Comment: 12 pages, 4 figures (revised version

The Electron-Phonon Coupling Constant for Single-Layer Graphene on Metal Substrates Determined from He Atom Scattering

Recent theory has demonstrated that the value of the electron-phonon coupling strength $\lambda$ can be extracted directly from the thermal attenuation (Debye-Waller factor) of Helium atom scattering reflectivity. This theory is here extended to multivalley semimetal systems and applied to the case of graphene on different metal substrates and graphite. It is shown that $\lambda$ rapidly increases for decreasing graphene-substrate binding strength. Two different calculational models are considered which produce qualitatively similar results for the dependence of $\lambda$ on binding strength. These models predict, respectively, values of $\lambda_{HAS} = 0.89$ and 0.32 for a hypothetical flat free-standing single-layer graphene with cyclic boundary conditions. The method is suitable for analysis and characterization of not only the graphene overlayers considered here, but also other layered systems such as twisted graphene bilayers.Comment: 25 pages, 3 figures, 1 tabl

The electron-phonon coupling strength at metal surfaces directly determined from the Helium atom scattering Debye-Waller factor

A new quantum-theoretical derivation of the elastic and inelastic scattering probability of He atoms from a metal surface, where the energy and momentum exchange with the phonon gas can only occur through the mediation of the surface free-electron density, shows that the Debye-Waller exponent is directly proportional to the electron-phonon mass coupling constant $\lambda$. The comparison between the values of $\lambda$ extracted from existing data on the Debye-Waller factor for various metal surfaces and the $\lambda$ values known from literature indicates a substantial agreement, which opens the possibility of directly extracting the electron-phonon coupling strength in quasi-2D conducting systems from the temperature or incident energy dependence of the elastic Helium atom scattering intensities.Comment: 14 pages, 2 figures, 1 tabl

A generalized Chudley-Elliott vibration-jump model in activated atom surface diffusion

Here the authors provide a generalized Chudley-Elliott expression for activated atom surface diffusion which takes into account the coupling between both low-frequency vibrational motion (namely, the frustrated translational modes) and diffusion. This expression is derived within the Gaussian approximation framework for the intermediate scattering function at low coverage. Moreover, inelastic contributions (arising from creation and annihilation processes) to the full width at half maximum of the quasi-elastic peak are also obtained.Comment: (5 pages, 2 figures; revised version

Kramers' turnover theory for diffusion of Na atoms on a Cu(001) surface measured by He scattering

12 pages, 7 figures.The diffusion of adatoms and molecules on a surface at low coverage can be measured by helium scattering. The experimental observable is the dynamic structure factor. In this article, we show how Kramers' turnover theory can be used to infer physical properties of the diffusing particle from the experiment. Previously, Chudley and Elliot showed, under reasonable assumptions, that the dynamic structure factor is determined by the hopping distribution of the adsorbed particle. Kramers' theory determines the hopping distribution in terms of two parameters only. These are an effective frequency and the energy loss of the particle to the bath as it traverses from one barrier to the next. Kramers' theory, including finite barrier corrections, is tested successfully against numerical Langevin equation simulations, using both separable and nonseparable interaction potentials. Kramers' approach, which really is a steepest descent estimate for the rate, based on the Langevin equation, involves closed analytical expressions and so is relatively easy to implement. Diffusion of Na atoms on a Cu(001) surface has been chosen as an example to illustrate the application of Kramers' theory.This work has been supported in part by DGICYT (Spain) under Contract No. BFM2001-2179. R.G. and J.L.V. thank the Minister of Science and Technology (Spain) for a Ramón y Cajal Contract and a predoctoral F.P.I. grant. This work has also been supported by grants from the Israel Science Foundation, the Minerva Foundation (Munich), and the Volkswagen Foundation.Peer reviewe

Quantum Zeno and anti-Zeno effects in surface diffusion of interacting adsorbates

Surface diffusion of interacting adsorbates is here analyzed within the context of two fundamental phenomena of quantum dynamics, namely the quantum Zeno effect and the anti-Zeno effect. The physical implications of these effects are introduced here in a rather simple and general manner within the framework of non-selective measurements and for two (surface) temperature regimes: high and very low (including zero temperature). The quantum intermediate scattering function describing the adsorbate diffusion process is then evaluated for flat surfaces, since it is fully analytical in this case. Finally, a generalization to corrugated surfaces is also discussed. In this regard, it is found that, considering a Markovian framework and high surface temperatures, the anti-Zeno effect has already been observed, though not recognized as such.Comment: 17 pages, 1 figur

Hamiltonian theory for vibrational line shapes of atoms adsorbed on surfaces

An analytical theory which was based on a Hamiltonian equivalent of the generalized Langevin equation, for the line shape, temperature-dependent shift and broadening of the translational or T-mode peak is presented. The theory can be used to infer physical parameters of the adatom-surface interaction. For the line shape a first-order perturbative solution of the normal-mode coordinates was used. For the shift and broadening, a perturbative expansion in the instantaneous system frequency was employed.This work has been supported in part by DGICYT (Spain) under Contract No. BFM2001-2179. R.G. and J.L.V. thank the Ministry of Science and Technology (Spain) for a Ramón y Cajal Contract and a predoctoral F.P.I. grant, respectively. This work has also been supported by grants from the Israel Science Foundation, the Minerva Foundation (Munich) and the Volkswagen Foundation.Peer Reviewe

Line Shape Broadening in Surface Diffusion of Interacting Adsorbates with Quasielastic He Atom Scattering

The experimental line shape broadening observed in adsorbate diffusion on metal surfaces with increasing coverage is usually related to the nature of the adsorbate-adsorbate interaction. Here we show that this broadening can also be understood in terms of a fully stochastic model just considering two noise sources: (i) a Gaussian white noise accounting for the surface friction, and (ii) a shot noise replacing the physical adsorbate-adsorbate interaction potential. Furthermore, contrary to what could be expected, for relatively weak adsorbate-substrate interactions the opposite effect is predicted: line shapes get narrower with increasing coverage.Comment: 4 pages, 2 figures (slightly revised version