Showing papers in "Physical Review A in 1983"

Estimation of the Kolmogorov entropy from a chaotic signal

Abstract: A new method for estimating the Kolmogorov entropy directly from a time signal is proposed and tested on examples. The method should prove valuable for characterizing experimental chaotic signals.

Variational approach to nonlinear pulse propagation in optical fibers

Abstract: The problem of nonlinear pulse propagation in optical fibers, as governed by the nonlinear Schr\"odinger equation, is reformulated as a variational problem. By means of Gaussian trial functions and a Ritz optimization procedure, approximate solutions are obtained for the evolution during propagation of pulse width, pulse amplitude, and nonlinear frequency chirp. Comparisons with results from inverse-scattering theory and/or numerically obtained solutions show very good agreement.

Random close packing of hard spheres and disks

Abstract: A simple definition of random close packing of hard spheres is presented, and the consequences of this definition are explored According to this definition, random close packing occurs at the minimum packing fraction $\ensuremath{\eta}$ for which the median nearest-neighbor radius equals the diameter of the spheres Using the radial distribution function at more dilute concentrations to estimate median nearest-neighbor radii, lower bounds on the critical packing fraction ${\ensuremath{\eta}}_{\mathrm{RCP}}$ are obtained and the value of ${\ensuremath{\eta}}_{\mathrm{RCP}}$ is estimated by extrapolation Random close packing is predicted to occur for ${\ensuremath{\eta}}_{\mathrm{RCP}}=064\ifmmode\pm\else\textpm\fi{}002$ in three dimensions and ${\ensuremath{\eta}}_{\mathrm{RCP}}=082\ifmmode\pm\else\textpm\fi{}002$ in two dimensions Both of these predictions are shown to be consistent with the available experimental data

New approach to the one-particle Green's function for finite Fermi systems

Abstract: A new approach to the one-particle Green's functions $\mathit{G}$ for finite electronic systems is presented. This approach is based on the diagrammatic perturbation expansions of the Green's function and of the dynamic self-energy part $\mathit{M}$ related to $\mathit{G}$ via the Dyson equation. The exact summation of the latter expansion is reformulated in terms of a simple algebraic form referred to as algebraic diagrammatic construction (ADC). The ADC defines in a systematical way a set of approximation schemes ($n\mathrm{th}$-order ADC schemes) that represent infinite partial summations for $\mathit{M}$ and (via the Dyson equation) for $\mathit{G}$ being complete through $n\mathrm{th}$ order of perturbation theory. The corresponding mathematical procedures are essentially Hermitian eigenvalue problems in restricted configuration spaces of unperturbed ionic configurations. Explicit equations for the second-, third-, and fourth-order ADC schemes are derived and analyzed. While the second- and third-order schemes can be viewed as systematic rederivations of previous approximation schemes, the fourth-order ADC scheme represents a complete fourth-order approximation for the self-energy and the one-particle Green's function which was hitherto not available.

Diffusion-controlled cluster formation in 2—6-dimensional space

Abstract: Diffusion-controlled cluster formation has been simulated on lattices of dimensionality 2-6. For the case of a sticking probability of 1.0 at nearest-neighbor sites, we find that the radius of gyration (${R}_{g}$) of the cluster is related to the number of particles ($N$) by ${R}_{g}\ensuremath{\sim}{N}^{\ensuremath{\beta}}$ (for large $N$). The exponent $\ensuremath{\beta}$ is given by $\frac{\ensuremath{\beta}\ensuremath{\sim}6}{5d}$, where $d$ is the classical (Euclidean) dimensionality of the lattice. These results indicate that the Hausdorff (fractal) dimensionality ($D$) is related to the Euclidean dimensionality ($d$) by $D\ensuremath{\approx}\frac{5d}{6}$ ($d=2\ensuremath{-}6$). Similar results can be obtained from the density-density correlation function in two-dimensional simulations. Nonlattice simulations have also been carried out in two- and three-dimensional space. The radius-of-gyration exponents ($\ensuremath{\beta}$) obtained from these simulations are essentially equal to those obtained in the lattice model simulations. We have also investigated the effects of sticking probabilities ($S$) less than 1.0 on diffusion-limited cluster formation on two- and three-dimensional lattices. While smaller sticking probabilities do lead to the formation of denser clusters, the radius-of-gyration exponents are insensitive to sticking coefficients over the range $0.1\ensuremath{\le}S\ensuremath{\le}1.0$.

Dynamics of structural transitions in liquids

Abstract: The \"inherent structures\" which underlie the liquid state are those stable particle packings (potential minima) which can be reached by a steepest-descent quench on the potential-energy hypersurface. This paper explores the dynamics of transition between distinct inherent structures for a simple classical model of monatomic substances. Molecular-dynamics calculations with 32 and 108 particles have been carried out with running construction of the mapping to potential minima. This determines the distribution of stable packings according to their potential energy and shows how transition rates between alternative structures vary with total system energy. Melting and freezing events have been monitored in this manner. %'e observe occasional transitions in localized \"twostate\" (bistable) systems in strongly supercooled amorphous states. Transitions in fIuid states display a peculiar intermittency that may have relevance to self-diffusion and viscous flow.

Nonlinear asymmetric self-phase modulation and self-steepening of pulses in long optical waveguides

Abstract: For nonlinear short-pulse propagation in long optical fibers, the conventional static approximation of the nonlinear terms in the wave equation must be extended to include the derivative of the pulse envelope. As a result, an initially symmetric pulse will develop an asymmetric self-phase modulation and a self-steepening, which ultimately lead to shock formation unless balanced by dispersion. This effect may be responsible for the pulse asymmetries observed in recent experiments.

Nonequilibrium molecular dynamics via Gauss's principle of least constraint

Abstract: Gauss's principle of least constraint is used to develop nonequilibrium molecular-dynamics algo­ rithms for systems SUbject to constraints. The treatment not only includes "nonholonomic" constraints-those involving velocities-but it also provides a basis for simulating nonequilibrium steady states. We describe two applications of this new use of Gauss's principle. The first of these examples, the isothermal molecular dynamics of a three-particle chain, can be treated analytically. The second, the steady-state diffusiort~of a Lennard-Jones liquid, near its triple point, is studied nu­ merically. The measured diffusion coefficient agrees with inaependent estimates from eqUilibrium fluctuation theory and from Hamiltonian external fields. I. INTRODUCTION

Multiply charged ions induced by multiphoton absorption in rare gases at 0.53 \mu{}m

Abstract: Up to quadruply charged ions are induced in Xe atoms by a 50-psec laser pulse at 0.53 \ensuremath{\mu}m in the ${10}^{12}$ W ${\mathrm{cm}}^{\ensuremath{-}2}$ range. The mechanism of the formation of ${\mathrm{Xe}}^{2+}$ ions is elucidated. In the lowest intensity range, ${\mathrm{Xe}}^{2+}$ ions are produced by direct 15-photon absorption from the ground state of the atoms, while at a higher intensity ${\mathrm{Xe}}^{2+}$ ions are produced by a stepwise process via ${\mathrm{Xe}}^{+}$ ions. These two processes take place at distinctly different intensities. A kinetic model using rate equations affords a good fit with experimental results. Moreover, for the first time it was possible to obtain the multiphoton ionization cross sections related to the two-electron removal from Xe atoms, as well as the one-electron removal from ${\mathrm{Xe}}^{+}$ ions.

Determination of molecular orientation of monolayer adsorbates by optical second-harmonic generation

Abstract: Optical second-harmonic generation has been used to deduce the average arrangement and orientation of $p$-nitrobenzoic acid molecules adsorbed at air-silica and ethanol-silica interfaces. An adsorption isotherm for the liquid-solid interface has also been obtained.

Diffusion-controlled cluster formation in two, three, and four dimensions

Abstract: Diffusion-controlled cluster formation has been simulated in two-, three-, and four- dimensional space. The radii of gyration (${R}_{g}$) of the resulting clusters have a power-law dependence on the number of particles in the cluster $(N) {R}_{g}={N}^{\ensuremath{\beta}}$. The corresponding Hausdorff dimensionality ($D=\frac{1}{\ensuremath{\beta}}$) is related to the Euclidean dimensionality $d$ by the relationship $D\ensuremath{\sim}\frac{5}{6}d$ for $d=3$ and 4. For the two-dimensional case we find that $\frac{D}{d}$ has a value about 2% smaller (0.847 \ifmmode\pm\else\textpm\fi{} 0.01). However, a value of $\frac{5}{6}$ (0.833) is only just outside the 95% confidence limits and cannot be completely ruled out. In the two-dimensional simulations $\ensuremath{\beta}$ is insensitive to lattice details and in both two- and three-dimensional simulations $\ensuremath{\beta}$ is insensitive to the sticking coefficient ($S$) over the range $1.0\ensuremath{\ge}S\ensuremath{\ge}0.1$.

Solitary excitations in deoxyribonuclei acid (DNA) double helices

Abstract: Dynamical features of solitary excitations in deoxyribonuclei acid (DNA) double helices are described by a revised theory in which the H-bonding energy between complementary base pairs has a more reasonable form Four modes of sine-Gordon solitons which predict the existence of the open states in DNA double helices are found By using the statistical-mechanical formalism which has been established previously, the average soliton number density in DNA double helices is estimated as a function of temperature and compared with the experimental results

Solutions of the reference-hypernetted-chain equation with minimized free energy

Abstract: We use the Rosenfeld-Ashcroft procedure of modeling the bridge function in the reference---hypernetted-chain integral equation with its hard-sphere values, and choose the sphere diameter so that the free energy of the system is minimized. The resulting integral equation is solved for both the long-range Coulomb potential and the short-range Lennard-Jones potential. The results are in excellent agreement with Monte Carlo data for the thermodynamics and structure of both systems. The method provides an entirely first-principles approach to the theory of the structure and thermodynamics of simple classical liquids.

Numerical evaluation of path-integral solutions to Fokker-Planck equations

Abstract: A numerical method, based on the path-integral formalism, is presented to solve nonlinear Fokker-Planck equations with natural boundary conditions. For one-dimensional stochastic processes, several specific examples possessing exact analytic solutions are evaluated numerically for purposes of comparison. Various discretization prescriptions are investigated and found to be equivalent as expected. The numerical method is shown to give accurate results provided the spatial discretization and the time step satisfy certain relationships determined by the drift and the diffusion functions of the nonlinear Fokker-Planck equations. 26 refs., 5 figs.

Applications of the generalized Trotter formula

Abstract: We study the properties of Suzuki's systematic approximations to the exponential operator $\mathrm{exp}(\ensuremath{-}\ensuremath{\beta}H)$ by calculating the thermodynamic functions of three simple quantum models. We demonstrate that the path-integral representation of the partition function obtained from these approximations can be simplified and made more accurate by constructing Hermitian versions of Suzuki's expressions.

Quasifree-scattering model for the imaginary part of the optical potential for electron scattering

Abstract: A relatively simple nonempirical formula for the imaginary part of the optical potential for electron scattering is derived from a quasifree-scattering model with Pauli blocking in which the target is treated as a free-electron gas. The resulting absorption potential is local and energy dependent and is a function of the electron density of the target. This model is tested for electron-helium and electron-neon scattering at 30--3000 eV. For these tests the real part of the potential is also approximated by a local expression, which is partitioned into static, exchange, and polarization terms. Reasonably good agreement with experimental data is obtained for the elastic integral, absorption, and elastic differential cross sections.

Use of l-dependent pseudopotentials in the study of alkali-metal-atom-He systems. The adiabatic molecular potentials

Abstract: Molecular-structure calculations have been performed to obtain the adiabatic potentials for ground state and numerous excited states of alkali-metal--He systems. They use l-dependent pseudopotentials defined from spectroscopy data or scattering data to describe the e/sup -/-M/sup +/ and e/sup -/-He interactions (where M is any alkali-metal atom). Standard variational calculations are made, and a large basis set of Slater-type orbitals is used in order to ensure accuracy and stability of the results. Our results are discussed along with comparisons with other theoretical and experimental data. The overall agreement which has been obtained with all available experimental data indicates that significant improvements in the calculation of the M-He adiabatic potentials have been achieved by using an l-dependent pseudopotential technique.

Cross sections for ionization of gases by 5-4000-keV protons and for electron capture by 5-150-keV protons

Abstract: Using the parallel-plate-capacitor method and a capacitance manometer to determine pressures, total cross sections for the production of positive and negative charges were measured for 5-4000-keV-proton impact on He, Ne, Ar, Kr, ${\mathrm{H}}_{2}$, ${\mathrm{N}}_{2}$, CO, ${\mathrm{O}}_{2}$, C${\mathrm{H}}_{4}$, and C${\mathrm{O}}_{2}$. From these, ionization and electron-capture cross sections were obtained and fitted to semiempirical equations describing the energy dependence in terms of a few parameters. At high energies very good agreement is obtained in the comparison of the ionization cross sections to earlier proton- and electron-impact measurements and with theoretical treatments where they are available, but discrepancies exist for some targets at low energy. Above 10 keV the electron-capture cross sections are in agreement with earlier work for all the targets except CO and C${\mathrm{H}}_{4}$ for which they are (20-40)% higher.

Generalized transport coefficients for hard spheres

Abstract: The wavelength- and frequency-dependent linear transport coefficients and the wavelength-dependent thermodynamic properties have been determined for hard spheres at three different densities and over a region of wavelengths and frequencies that range from the hydrodynamic to the free-streaming regime. The molecular-dynamics calculation involves the evaluation of correlation functions from which the generalized properties can be simply derived consistent with their hydrodynamic definitions. The results are compared with generalized kinetic theory and, except for the viscosity at high density and small wavelength, the predictions of that theory are accurate within a few percent. For the viscosity, mode-coupling theory improves upon the predictions of kinetic theory. A single application is given in which the dependence of the Stokes friction coefficient on the size of the massive Brownian particle is determined using the generalized viscosity. This illustration leads one to believe that generalized hydrodynamics quantitatively applies on the molecular scale.

Diffusion-controlled deposition on fibers and surfaces

Abstract: Monte Carlo simulations have been carried out to investigate the deposition of particles on surfaces and fibers under conditions where the deposition is diffusion controlled. Deposits prepared under diffusion-controlled conditions have a completely different morphology from deposits prepared under conditions where diffusion is not important. For the case of deposition on thin fibers we find that the radius of gyration of the deposit is related to the number of particles in the deposit ($N$) by ${R}_{g}\ensuremath{\sim}{N}^{\ensuremath{\delta}}$ ($\ensuremath{\delta}=0.665\ifmmode\pm\else\textpm\fi{}0.030$) in the limit of large $N$ and long fibers. Consequently, deposits formed on fibers under diffusion-controlled conditions have fractal characteristics similar to those associated with clusters formed under diffusion-controlled conditions. Similar, but less quantitative, results are presented for surface deposits. For two-dimensional deposits grown on a one-dimensional "surface" under diffusion-controlled conditions, the root-mean-square thickness ($T$) of the deposit is related to the number of particles by $T\ensuremath{\sim}{N}^{\ensuremath{\epsilon}}$ ($N\ensuremath{\rightarrow}\ensuremath{\infty}$). The exponent $\ensuremath{\epsilon}$ has the value 1.30\ifmmode\pm\else\textpm\fi{}0.075. Similar results were obtained in three-dimensional simulations of diffusion-controlled deposition on a surface $T\ensuremath{\sim}{N}^{\ensuremath{\epsilon}}$, with ($\ensuremath{\epsilon}=1.70\ifmmode\pm\else\textpm\fi{}0.2$). All of the results reported in this paper were obtained using two- and three-dimensional lattice models. Our results suggest that the structural characteristics of systems grown by diffusion-controlled processes are determined mainly by the dimensionality of the space in which the growth is occurring and are insensitive to geometric variables such as "surface" curvature.

Photon interference and correlation effects produced by independent quantum sources

Abstract: Interference effects produced by independent quantum sources are investigated, when the state of the field is not describable as a simple mixture of coherent states. The results of classical and quantum-mechanical calculations are compared. Whereas correlation effects are predicted both classically and quantum mechanically when the sources have random phases, there are important differences when the number of atoms is small. In particular, when each source consists of just one atom, the joint probability of detecting two photons at two different points in the receiving plane is found to vanish when the distance between them is an odd number of half fringes. Finally it is shown that when the number of atoms of each source is subject to Poisson fluctuations, one recovers the solution given by classical optics for thermal light, no matter how weak the sources may be on the average.

Stark ionization in dc and ac fields: An L2 complex-coordinate approach

Abstract: A finite-dimensional-matrix technique valid for computation of complex eigenvalues and eigenfunctions useful for discussing time evolution in both dc and ac Stark fields is presented. The complex eigenvalue parameters are those of appropriately analytically continued, time-independent Stark Hamiltonians as obtained via the complex scale transformation $r\ensuremath{\rightarrow}r{e}^{i\ensuremath{\theta}}$. Such a transformation distorts the continuous spectrum away from the real axis, exposing the Stark resonances, and also allowing use of finite variational expansions employing ${L}^{2}$ basis functions chosen from a complete discrete basis. The structure of the dc and ac Stark Hamiltonians is discussed and extensive convergence studies performed in both the dc and ac cases to fully document the utility of the method. Sudden and adiabatic dc Stark time evolution is used to illustrate the power of finite-dimensional-matrix methods in describing complex, multiple-time-scale time evolution. The relationship between the ac Stark Hamiltonian used (a time-independent truncated Floquet Hamiltonian) and continued-fraction perturbation theory follows easily via use of matrix partitioning, and provides a particularly straightforward derivation of these results. Finally, some illustrative calculations of off-resonant generalized cross sections are given at low and high intensities, indicating that the method works satisfactorily at intensities the order of internal atomic field strengths. A more detailed discussion of time evolution in two-, three-, and four-photon ionization processes appears in the following paper by Holt, Raymer, and Reinhardt.

Electron-capture for fast highly charged ions in gas targets - an empirical scaling rule

Abstract: A universal empirical scaling rule for electron-capture cross sections is reported for fast, highly charged ions in atomic and molecular targets. Projectiles range in energy from 0.3 to 8.5 MeV/amu, with charge states as high as 59+. This rule permits prediction of electron-capture cross sections for a wide variety of projectile-target combinations.

Optically induced Freedericksz transition and bistability in a nematic liquid crystal

Abstract: An Euler equation, consistent with Maxwell's equations, for describing the optically induced spatial reorientation of the director of a homeotropically oriented nematic liquid crystal is obtained for the case of normal incidence. The exact solution describing the orientation of the director is obtained. By examining the maximum deformation angle near the threshold, the threshold intensity and the criterion for the physical parameters that indicate whether the transition is first- or second-order at the threshold are obtained. The hysteresis accompanying the first-order Freedericksz transition is discussed. By choosing a compound (PAA, $p$-azoxyanisole) with suitable material parameters from known nematic liquid crystals, an experiment is proposed to observe, for the first time, a first-order Freedericksz transition in nematic liquid crystals. The Zel'dovich approach [Sov. Phys.-JETP 54, 32 (1981)] based on the geometrical-optics approximation is shown to be internally inconsistent and also inconsistent with the geometrical-optics approximation. The Euler equation using a self-consistent geometrical-optics approximation is also obtained, and turns out to be identical to our exact Euler equation, but different from the infinite-plane-wave approximation used by Durbin et al. [Phys. Rev. Lett. 47, 1411 (1981)]. Detailed comparisons between our approach and the Durbin approach are made. The dynamics of the transition are discussed and an approximate solution is given. The transient responses to the laser switch-on and switch-off are shown to have exponential time dependence. Finally, the effects of surface interactions on the transition are discussed and the exact solution is given. The procedure for determining the threshold, the saturation, and the parallel-state-maintenance intensities is given. We also discuss the first-order transition and propose experimental methods manifesting the effects of surface interaction. The criterion for the transition to be first order at any intensity is given.

Nonadjustable exchange-correlation model for electron scattering from closed-shell atoms and molecules

Abstract: A nonadjustable-model potential is proposed for electron scattering that includes both electron exchange and correlation effects in a hybridization of local electron-gas theory and the long-range polarization. The model potential energy function consists of the sum of the energy-dependent electron-gas exchange potential (Hara version) and the energy-independent electron-gas correlation potential smoothly joined onto the long-range polarization interaction. Illustrative calculations of elastic scattering phase shifts and cross sections are described for the rare-gas atoms, where reasonable agreement with accurate calculations suggests usefulness of the model for more complex systems.

Momentum-space coupled-channels optical method for electron-atom scattering

Abstract: A complete account is given of a new method for the solution of the problem of electron scattering by a one-electron atom or ion. The method treats all relevant effects explicitly. Reaction channels under consideration are treated by the coupled-channels method in momentum space. Other channels, including the continuum, are treated by adding complex-polarization potentials computed from experimentally tested approximate amplitudes for the relevant reactions. Computational methods are discussed in detail since this is the first successful application of the momentum-space solution to the atomic multichannel problem. The effect of the inclusion of channels outside the coupled space is demonstrated by comparison with three-state close coupling for hydrogen at 54.42 eV.

Measurement of free-free emission from low-energy-electron collisions with Ar

Abstract: The production of free-free radiation in collisions of low-energy electrons with Ar atoms has been measured using the drift-tube technique. The excitation coefficients were obtained from measurements of the absolute intensity of continuum radiation at wavelengths of 500, 650, and 1300 nm. At 650 nm the electric-field---to---gas-density ratio $\frac{E}{N}$ was varied from 0.25\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}21}$ to 10\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}21}$ V ${\mathrm{m}}^{2}$ corresponding to mean electron energies from 1.2 to 5.4 eV. As expected, the emission was proportional to the argon density from 3\ifmmode\times\else\texttimes\fi{}${10}^{24}$ to 15\ifmmode\times\else\texttimes\fi{}${10}^{24}$ atoms/${\mathrm{m}}^{3}$. The experimental excitation coefficients are in good agreement with calculations using theoretical free-free emission cross sections and electron energy distributions and serve to demonstrate the usefulness of simple formulas relating the free-free emission cross section to measured momentum-transfer cross sections.