The lifetime of image states, related to the coupling of surface electronic states with the solid substrate, has been recently determined for quantum numbers $n\le 6$ on Cu(100) by using time-resolved two-photon photoemission in combination with the coherent excitation of several states [U. Höfer et al., Science 277, 1480 (1997)]. We evaluate the lifetimes of image states on copper surfaces from the self-energy of the excited quasiparticle, which we compute within the $\mathrm{GW}$ approximation. Single-particle wave functions are obtained by solving the Schrödinger equation with a realistic one-dimensional model potential, and the screened interaction is evaluated in the random-phase approximation. Our results are in agreement with experimentally determined decay times.

The role of the intrinsic surface state $\mathrm{}(n=0\mathrm{})\mathrm{}$ in the decay of the first image state $\mathrm{}(n=1\mathrm{})\mathrm{}$ at the (111) surface of copper is investigated. Inelastic linewidths are evaluated from the knowledge of the imaginary part of the electron self energy, which we compute, within the GW approximation of the many-body theory, by going beyond a free-electron description of the metal surface. Single-particle wave functions are obtained by solving the Schrödinger equation with a realistic one-dimensional model potential, and departure of the motion along the surface from free-electron behavior is considered through the introduction of the effective mass. The decay of the first image state of Cu(111) into the intrinsic surface state is found to result in a linewidth that represents 40% of the total linewidth. The dependence of linewidths on the momentum of the image state parallel to the surface is also investigated.

We report extensive calculations of the imaginary part of the electron self-energy in the vicinity of the (100) and (111) surfaces of Cu. The quasiparticle self-energy is computed by going beyond a free-electron description of the metal surface, either within the $\mathrm{GW}$ approximation of many-body theory or with inclusion, within the $\mathrm{GW}\Gamma$ approximation, of short-range exchange-correlation effects. Calculations of the decay rate of the first three image states on Cu(100) and the first image state on Cu(111) are also reported, and the impact of both band structure and many-body effects on the electron relaxation process is discussed.

This paper presents an analysis of the dynamic behaviour of constrained layer damping (CLD) beams with thick viscoelastic layer. A homogenised model for the flexural stiffness is formulated using Reddy-Bickford’s quadratic shear in each layer, and it is compared with Ross-Kerwin-Ungar (RKU) classical model, which considers a uniform shear deformation for the viscoelastic core. In order to analyse the efficiency of both models, a numerical application is accomplished and the provided results are compared with those of a 2D model using finite elements, which considers extensional and shear stress and longitudinal, transverse, and rotational inertias. The intermediate viscoelastic material is characterised by a fractional derivative model, with a frequency dependent complex modulus. Eigenvalues and eigenvectors are obtained from an iterative method avoiding the computational problems derived from the frequency dependence of the stiffness matrices. Also, frequency response functions are calculated. The results show that the new model provides better accuracy than the RKU one as the thickness of the core layer increases. In conclusion, a new model has been developed, being able to reproduce the mechanical behaviour of thick CLD beams, reducing storage needs and computational time compared with a 2D model, and improving the results from the RKU model.

Fractional derivative models are widely used to easily characterise more complex damping behaviour than the viscous one, although the underlying properties are not trivial. Several studies about the mathematical properties can be found, but are usually far from the most daily applications. Thus, this paper studies the properties of structural systems whose damping is represented by a fractional model from the point of view of a mechanical engineer. First, a single-degree-of-freedom system with fractional damping is analysed. Specifically, the distribution of the poles and the dynamic response to several excitations is studied for different model parameter values highlighting dissimilarities from systems with conventional viscous damping. In fact, thanks to fractional models, particular behaviours are observed that cannot be reproduced by classical ones. Finally, the dynamics of a machine shaft supported by two bearings presenting fractional damping is analysed. The study is carried out by the Finite Element method, deriving in a system with symmetric matrices. Eigenvalues and eigenvectors are obtained by means of an iterative method, and the effect of damping is visualised on the mode shapes. In addition, the response to a perturbation is computed, revealing the influence of the model parameters on the resulting vibration.