Dynamical electronic polarizability and the force sum rule

It is shown that a dynamical force sum rule is useful in analyzing the response of a finite electronic system to a uniform electric field that oscillates harmonically in time. The sum rule, which has been used previously in calculations of the response of atoms to electric fields, provides a direct test of electronic polarizability calculations and may lead to useful approximations for the electronic polarizability of metallic microstructures. We apply the sum rule to the case of a small metal sphere in the jellium model, and show that it directly leads to an approximation that is equivalent to the surface-plasmon-pole approximation for the red-shift of the surface plasmon frequency.     

Fixed-Size Quadruples for a New, Hardware-Oriented Representation of the 4D Clifford Algebra

Clifford algebra (geometric algebra) offers a natural and intuitive way to model geometry in fields as robotics, machine vision and computer graphics. This paper proposes a new representation based on fixed-size elements (quadruples) of 4D Clifford algebra and demonstrates that this choice leads to an algorithmic simplification which in turn leads to a simpler and more compact hardware implementation of the algebraic operations. In order to prove the advantages of the new, quadruple-based representation over the classical representation based on homogeneous elements, a coprocessing core supporting the new fixed-size Clifford operands, namely Quad-CliffoSor (Quadruple-based Clifford coprocesSor) was designed and prototyped on an FPGA board. Test results show the potential to achieve a 23× speedup for Clifford products and a 33× speedup for Clifford sums and differences compared to the same operations executed by a software library running on a general-purpose processor.     

Effects of anisotropic scattering on electronic transport properties

The role of anisotropic scattering in transport properties is studied within the framework of the anisotropic relaxation time. The concept of the relaxation time is introduced in a rigorous way, without approximation. Its physical meaning and its connection with linear response theory is discussed. The manner in which electron-impurity scattering and electronphonon scattering influence the relaxation time is considered as well as the role of such anisotropies in the de Haas-van Alphen effect, Hall effect, deviations from Mathiessen's rule, and magnetoresistance. Examples are taken from recent experimental and theoretical work. Some common pitfalls surrounding the use of the anisotropic relaxation time are pointed out.     

Force sum-rule and static electronic polarizability of atoms and microstructures

A sum rule is derived within density functional formalism for the response of an electronic system to a uniform electrostatic field. The sum rule states that the sum of the electrostatic forces on the positive charge background equals zero. The sum rule provides a useful test of electronic polarizability calculations for atoms and microstructures. It also leads to a self-consistency relationship for the induced charge density obtained in image-plane calculations.     

5-GHz repetition-rate dual-wavelength pulse-train generation from an intracavity frequency-modulated Er-Yb:glass laser

We report the experimental demonstration of nearly transform-limited dual-wavelength pulse trains at a 5-GHz repetition rate that were generated by spectral filtering of an intracavity 2.5-GHz frequency-modulated Er-Yb bulk-glass laser operating at the 1533-nm wavelength. Highly stable dual-wavelength pulse trains with ~165-GHz frequency separation, ~48-ps pulse duration, and ~1-mW average single-mode fiber-coupled power were obtained.     

Variational calculation of the work function for small metal spheres

A variational calculation based on the density functional formalism is performed for small metal spheres. The electron density is expressed in terms of two variational parameters chosen to minimize the energy. We find that the work function decreases as the size of the particle increases, approximately in agreement with the classical result for radii greater than a few angstroms.     

The metal-surface selection rule for infrared spectra of molecules adsorbed on small metal particles

The metal-surface selection rule predicts that some infrared absorption bands should be absent from the spectra of molecules adsorbed on metal particles. It predicts that those bands corresponding to molecular vibrations with an oscillating dipole moment parallel to the surface should be suppressed. We calculate that this selection rule should apply to adsorption on metal particles larger than about 20 Å in diameter; for smaller particles the rule is weakened.     

Impurity scattering on the Fermi surface of aluminum

A calculation is described for the anisotropic relaxation time due to impurity scattering on the Fermi surface of aluminum. The Bloch states and the Fermi surface are obtained from Ashcroft's 4-OPW model, while the scattering potentials are obtained from locally re-screened form factors. Numerical results reveal that strong anisotropicsin the electronic lifetime arise for s-like impurities such as Si and Ge. A phase shift model is introduced to explain these anisotropies. The predicted anisotropies appear to be in reasonable agreement with experimental values for the Dingle temperature. The relaxation time for d.c. conductivity is obtained from iterative solution of the Boltzmann equation.