615 research outputs found
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 , and on the number of classical
trajectories 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 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 correction to the
stopping power of a 2DEG for charged particles moving at a fixed distance from
the plane of the 2D sheet, 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
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.
Nonlinear interaction of charged particles with a free electron gas beyond the random-phase approximation
A nonlinear description of the interaction of charged particles penetrating a
solid has become of basic importance in the interpretation of a variety of
physical phenomena. Here we develop a many-body theoretical approach to the
quadratic decay rate, energy loss, and wake potential of charged particles
moving in an interacting free electron gas. Explicit expressions for these
quantities are obtained either within the random-phase approximation (RPA) or
with full inclusion of short-range exchange and correlation effects. The Z^3
correction to the energy loss of ions is evaluated beyond RPA, in the limit of
low velocities.Comment: 5 pages, 2 figures To appear in Phys. Rev.
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