Spectrum of surface-mode contributions to the excitation probability for electron beam interacting with sharp-edged dielectric wedges

The interaction of a nonrelativistic charged particle beam, travelling parallel to the surface of a sharp-edged dielectric wedge is analyzed. The general expressions for excitation probability are obtained for a beam moving along the direction of a symmetry axis, either outside or inside the dielectric wedge. The dielectric function of the medium is assumed to be isotropic, and numerical results are given for the materials of experimental interest.Comment: LaTeX 2.09, 15 pages, 10 figure

Abstract Interpretation of Supermodular Games

Supermodular games find significant applications in a variety of models, especially in operations research and economic applications of noncooperative game theory, and feature pure strategy Nash equilibria characterized as fixed points of multivalued functions on complete lattices. Pure strategy Nash equilibria of supermodular games are here approximated by resorting to the theory of abstract interpretation, a well established and known framework used for designing static analyses of programming languages. This is obtained by extending the theory of abstract interpretation in order to handle approximations of multivalued functions and by providing some methods for abstracting supermodular games, in order to obtain approximate Nash equilibria which are shown to be correct within the abstract interpretation framework

Nonextensive thermodynamic functions in the Schr\"odinger-Gibbs ensemble

Schr\"odinger suggested that thermodynamical functions cannot be based on the gratuitous allegation that quantum-mechanical levels (typically the orthogonal eigenstates of the Hamiltonian operator) are the only allowed states for a quantum system [E. Schr\"odinger, Statistical Thermodynamics (Courier Dover, Mineola, 1967)]. Different authors have interpreted this statement by introducing density distributions on the space of quantum pure states with weights obtained as functions of the expectation value of the Hamiltonian of the system. In this work we focus on one of the best known of these distributions, and we prove that, when considered in composite quantum systems, it defines partition functions that do not factorize as products of partition functions of the noninteracting subsystems, even in the thermodynamical regime. This implies that it is not possible to define extensive thermodynamical magnitudes such as the free energy, the internal energy or the thermodynamic entropy by using these models. Therefore, we conclude that this distribution inspired by Schr\"odinger's idea can not be used to construct an appropriate quantum equilibrium thermodynamics.Comment: 32 pages, revtex 4.1 preprint style, 5 figures. Published version with several changes with respect to v2 in text and reference

Nonlinear energy-loss straggling of protons and antiprotons in an electron gas

The electronic energy-loss straggling of protons and antiprotons moving at arbitrary nonrelativistic velocities in a homogeneous electron gas are evaluated within a quadratic response theory and the random-phase approximation (RPA). These results show that at low and intermediate velocities quadratic corrections reduce significantly the energy-loss straggling of antiprotons, these corrections being, at low-velocities, more important than in the evaluation of the stopping power.Comment: 4 pages, 3 figures, to appear in Phys. Rev.

Ehrenfest dynamics is purity non-preserving: a necessary ingredient for decoherence

We discuss the evolution of purity in mixed quantum/classical approaches to electronic nonadiabatic dynamics in the context of the Ehrenfest model. As it is impossible to exactly determine initial conditions for a realistic system, we choose to work in the statistical Ehrenfest formalism that we introduced in Ref. 1. From it, we develop a new framework to determine exactly the change in the purity of the quantum subsystem along the evolution of a statistical Ehrenfest system. In a simple case, we verify how and to which extent Ehrenfest statistical dynamics makes a system with more than one classical trajectory and an initial quantum pure state become a quantum mixed one. We prove this numerically showing how the evolution of purity depends on time, on the dimension of the quantum state space $D$, and on the number of classical trajectories $N$ of the initial distribution. The results in this work open new perspectives for studying decoherence with Ehrenfest dynamics.Comment: Revtex 4-1, 14 pages, 2 figures. Final published versio

Lifetimes of image-potential states on copper surfaces

The lifetime of image states, which represent a key quantity to probe the coupling of surface electronic states with the solid substrate, have 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. H\"ofer et al, Science 277, 1480 (1997)). We here report theoretical investigations of the lifetime of image states on copper surfaces. We evaluate the lifetimes from the knowledge of the self-energy of the excited quasiparticle, which we compute within the GW approximation of many-body theory. Single-particle wave functions are obtained by solving the Schr\"odinger equation with a realistic one-dimensional model potential, and the screened interaction is evaluated in the random-phase approximation (RPA). Our results are in good agreement with the experimentally determined decay times.Comment: 4 pages, 1 figure, to appear in Phys. Rev. Let

Quadratic electronic response of a two-dimensional electron gas

The electronic response of a two-dimensional (2D) electron system represents a key quantity in discussing one-electron properties of electrons in semiconductor heterojunctions, on the surface of liquid helium and in copper-oxide planes of high-temperature superconductors. We here report an evaluation of the wave-vector and frequency dependent dynamical quadratic density-response function of a 2D electron gas (2DEG), within a self-consistent field approximation. We use this result to find the $Z_1^3$ correction to the stopping power of a 2DEG for charged particles moving at a fixed distance from the plane of the 2D sheet, $Z_1$ being the projectile charge. We reproduce, in the high-density limit, previous full nonlinear calculations of the stopping power of a 2DEG for slow antiprotons, and we go further to calculate the $Z_1^3$ correction to the stopping power of a 2DEG for a wide range of projectile velocities. Our results indicate that linear response calculations are, for all projectile velocities, less reliable in two dimensions than in three dimensions.Comment: 17 pages, 5 figures, to appear in Phys. Rev.

Role of the electric field in surface electron dynamics above the vacuum level

Scanning tunneling spectroscopy (STS) is used to study the dynamics of hot electrons trapped on a Cu(100) surface in field emission resonances (FER) above the vacuum level. Differential conductance maps show isotropic electron interference wave patterns around defects whenever their energy lies within a surface projected band gap. Their Fourier analysis reveals a broad wave vector distribution, interpreted as due to the lateral acceleration of hot electrons in the inhomogeneous tip-induced potential. A line-shape analysis of the characteristic constant-current conductance spectra permits to establish the relation between apparent width of peaks and intrinsic line-width of FERs, as well as the identification of the different broadening mechanisms.Comment: 7 pages, 4 figures, to appear in Phys. Rev.

Time-Dependent Density-Functional Theory for the Stopping Power of an Interacting Electron Gas for Slow Ions

Based on the time-dependent density-functional theory, we have derived a rigorous formula for the stopping power of an {\it interacting} electron gas for ions in the limit of low projectile velocities. If dynamical correlation between electrons is not taken into account, this formula recovers the corresponding stopping power of {\it noninteracting} electrons in an effective Kohn-Sham potential. The correlation effect, specifically the excitonic one in electron-hole pair excitations, however, is found to considerably enhance the stopping power for intermediately charged ions, bringing our theory into good agreement with experiment.Comment: 4 pages, 1 figure, Accepted to Phys. Rev. B (Rapid Communication