On the semiclassical approach to cold atomic collisions

We extend the semiclassical description of two-state atomic collisions to low energies for which the impact parameter treatment fails. The problem reduces to solving a system of first-order differential equations with coefficients whose semiclassical asymptotes experience the Stokes phenomenon in the complex coordinate plane. Primitive semiclassical and uniform Airy approximations are discussed.

Semiclassical-quantal approach to the near-threshold ionization of hydrogen

A recent improved version of the semiclassical-quantal approach has been applied to the e(-)-H near-threshold ionization for theta (12) = 180 degrees geometry. It is found, that unlike other sophisticated theoretical methods such as distorted wave theory or convergent close-coupling calculation, the present relatively simpler approach produces correct behavior and numerical values for the triple-differential cross sections. We compare our results with recent absolute measurements and accurate numerical calculations at 2 eV and 4 eV above the threshold at constant theta (12) geometry.

Semiclassical analytical approach to the description of quasimolecular optical transitions

A formula was obtained that describes asymptotically forbidden quasimolecular optical transitions in the frame of the semiclassical approach. It is particularly relevant for the weak extrema in the difference between the ground- and excited- state interaction potentials. When averaged over impact parameters and velocity distribution the formula agreed reasonably well with the recent experimental data for the Ca(4(1)S --> 3(1)D) + He transition.

Semiclassical treatment of Wannier's theory when the exponent diverges

We consider a non-standard application of the Wannier model. A physical example is the single ionization of a hydrogenic beryllium ion with a fully stripped beryllium ion, where the ratio of the charge of the third particle to the charges of the escaping particles is 1/4; we investigate the single ionization by an electron of an atom comprising an electron and a nucleus of charge 1/4. An infinite exponent is obtained suggesting that this process is not tractable within the Wannier model. A modified version of Crothers' uniform semiclassical wavefunction for the outgoing particles has been adopted, since the Wannier exponents and are infinite for an effective charge of Z = 1/4. We use Bessel functions to describe the Peterkop functions u and u and derive a new turning point ?. Since u is well behaved at infinity, there exists only the singularity in u at infinity, thus we employ a one- (rather than two-) dimensional change of dependent variable, ensuring that a uniform solution is obtained that avoids semiclassical breakdown on the Wannier ridge. The regularized final-state asymptotic wavefunction is employed, along with a continuum-distorted-wave approximation for the initial-state wavefunction to obtain total cross sections on an absolute scale. © 2006 IOP Publishing Ltd.

Semiclassical complex angular momentum theory and Pade reconstruction for resonances, rainbows, and reaction thresholds

A semiclassical complex angular momentum theory, used to analyze atom-diatom reactive angular distributions, is applied to several well-known potential (one-particle) problems. Examples include resonance scattering, rainbow scattering, and the Eckart threshold model. Pade reconstruction of the corresponding matrix elements from the values at physical (integral) angular momenta and properties of the Pade approximants are discussed in detail.

Effect of quantization of vibrations on the structural properties of crystals

We study the structural effects produced by the quantization of vibrational degrees of freedom in periodic crystals at zero temperature. To this end we introduce a methodology based on mapping a suitable subspace of the vibrational manifold and solving the Schrödinger equation in it. A number of increasingly accurate approximations ranging from the quasiharmonic approximation (QHA) to the vibrational self-consistent field (VSCF) method and the exact solution are described. A thorough analysis of the approximations is presented for model monatomic and hydrogen-bonded chains, and results are presented for a linear H-F chain where the potential-energy surface is obtained via first-principles electronic structure calculations. We focus on quantum nuclear effects on the lattice constant and show that the VSCF is an excellent approximation, meaning that correlation between modes is not extremely important. The QHA is excellent for covalently bonded mildly anharmonic systems, but it fails for hydrogen-bonded ones. In the latter, the zero-point energy exhibits a nonanalytic behavior at the lattice constant where the H atoms center, which leads to a spurious secondary minimum in the quantum-corrected energy curve. An inexpensive anharmonic approximation of noninteracting modes appears to produce rather good results for hydrogen-bonded chains for small system sizes. However, it converges to the incorrect QHA results for increasing size. Isotope effects are studied for the first-principles H-F chain. We show how the lattice constant and the H-F distance increase with decreasing mass and how the QHA proves to be insufficient to reproduce this behavior.

Systolic array system for vector quantization using transformed sub-band coding.

The use of bit-level systolic arrays in the design of a vector quantized transformed subband coding system for speech signals is described. It is shown how the major components of this system can be decomposed into a small number of highly regular building blocks that interface directly to one another. These include circuits for the computation of the discrete cosine transform, the inverse discrete cosine transform, and vector quantization codebook search.

VLSI architectures for vector quantization

The real time implementation of an efficient signal compression technique, Vector Quantization (VQ), is of great importance to many digital signal coding applications. In this paper, we describe a new family of bit level systolic VLSI architectures which offer an attractive solution to this problem. These architectures are based on a bit serial, word parallel approach and high performance and efficiency can be achieved for VQ applications of a wide range of bandwidths. Compared with their bit parallel counterparts, these bit serial circuits provide better alternatives for VQ implementations in terms of performance and cost. © 1995 Kluwer Academic Publishers.

Semiclassical relativistic fluid theory for electrostatic envelope modes in dense electron-positron-ion plasmas:Modulational instability and rogue waves

A fluid model is used to describe the propagation of envelope structures in an ion plasma under the influence of the action of weakly relativistic electrons and positrons. A multiscale perturbative method is used to derive a nonlinear Schrödinger equation for the envelope amplitude. Criteria for modulational instability, which occurs for small values of the carrier wavenumber (long carrier wavelengths), are derived. The occurrence of rogue waves is briefly discussed. © Cambridge University Press 2013.