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At least 109 records · Page 6

Energetics and Dynamics of GaAs Epitaxial Growth via Quantum Wave Packet Studies

The dynamics of As(sub 2) molecule incorporation into the flat Ga-terminated GaAs(100) surface is studied computationally. The time-dependent Schrodinger equation is solved on a two-dimensional potential energy surface obtained using density functional theory calculations. The probabilities of trapping and subsequent dissociation of the molecular As(sub 2) bond are calculated as a function of beam translational energy and vibrational quantum number of As(sub 2).

Dzegilenko, Fedor N.↗

Multi-Dimensional Quantum Effect Simulation Using a Density-Gradient Model and Script-Level Programming Techniques

A density-gradient (DG) model is used to calculate quantum-mechanical corrections to classical carrier transport in MOS (Metal Oxide Semiconductor) inversion/accumulation layers. The model is compared to measured data and to a fully self-consistent coupled Schrodinger and Poisson equation (SCSP) solver. Good agreement is demonstrated for MOS capacitors with gate oxide as thin as 21 A. It is then applied to study carrier distribution in ultra short MOSFETs (Metal Oxide Semiconductor Field Effect Transistor) with surface roughness. This work represents the first implementation of the DG formulation on multidimensional unstructured meshes. It was enabled by a powerful scripting approach which provides an easy-to-use and flexible framework for solving the fourth-order PDEs (Partial Differential Equation) of the DG model.

Rafferty, Connor S.↗

Calculation of Scattering Amplitude Without Partial Analysis: Inclusion of Exchange - II

There was a method for calculating the whole scattering amplitude, f(Omega(sub k)), directly. The idea was to calculate the complete wave function Psi numerically, and use it in an integral expression for f, which can be reduced to a 2 dimensional quadrature. The original application was for e-H scattering without exchange. There the Schrodinger reduces a 2-d partial differential equation (pde), which was solved using the finite element method (FEM). Here we extend the method to the exchange approximation. The S.E. can be reduced to a pair of coupled pde's, which are again solved by the FEM. The formal expression for f(Omega(sub k)) consists two integrals, f+/- = f(sub d) +/- f(sub e); f(sub d) is formally the same integral as the no-exchange f. We have also succeeded in reducing f(sub e) to a 2-d integral. Results will be presented at the meeting.

Temkin, Aaron↗

Backscattering and Nonparaxiality Arrest Collapse of Damped Nonlinear Waves

The critical nonlinear Schrodinger equation (NLS) models the propagation of intense laser light in Kerr media. This equation is derived from the more comprehensive nonlinear Helmholtz equation (NLH) by employing the paraxial approximation and neglecting the backscattered waves. It is known that if the input power of the laser beam (i.e., L(sub 2) norm of the initial solution) is sufficiently high, then the NLS model predicts that the beam will self-focus to a point (i.e.. collapse) at a finite propagation distance. Mathematically, this behavior corresponds to the formation of a singularity in the solution of the NLS. A key question which has been open for many years is whether the solution to the NLH, i.e., the 'parent' equation, may nonetheless exist and remain regular everywhere, in particular for those initial conditions (input powers) that lead to blowup in the NLS. In the current study, we address this question by introducing linear damping into both models and subsequently comparing the numerical solutions of the damped NLH (boundary-value problem) with the corresponding solutions of the damped NLS (initial-value problem). Linear damping is introduced in much the same way as done when analyzing the classical constant-coefficient Helmholtz equation using the limiting absorption principle. Numerically, we have found that it provides a very efficient tool for controlling the solutions of both the NLH and NHS. In particular, we have been able to identify initial conditions for which the NLS solution does become singular. whereas the NLH solution still remains regular everywhere. We believe that our finding of a larger domain of existence for the NLH than that for the NLS is accounted for by precisely those mechanisms, that have been neglected when deriving the NLS from the NLH, i.e., nonparaxiality and backscattering.

Fibich, G.↗

Calculation of the Full Scattering Amplitude without Partial Wave Decomposition II: Inclusion of Exchange

As is well known, the full scattering amplitude can be expressed as an integral involving the complete scattering wave function. We have shown that the integral can be simplified and used in a practical way. Initial application to electron-hydrogen scattering without exchange was highly successful. The Schrodinger equation (SE), which can be reduced to a 2d partial differential equation (pde), was solved using the finite element method. We have now included exchange by solving the resultant SE, in the static exchange approximation, which is reducible to a pair of coupled pde's. The resultant scattering amplitudes, both singlet and triplet, calculated as a function of energy are in excellent agreement with converged partial wave results.

Shertzer, Janine↗

Calculation of the Full Scattering Amplitude without Partial Wave Decomposition II

As is well known, the full scattering amplitude can be expressed as an integral involving the complete scattering wave function. We have shown that the integral can be simplified and used in a practical way. Initial application to electron-hydrogen scattering without exchange was highly successful. The Schrodinger equation (SE) can be reduced to a 2d partial differential equation (pde), and was solved using the finite element method. We have now included exchange by solving the resultant SE, in the static exchange approximation. The resultant equation can be reduced to a pair of coupled pde's, to which the finite element method can still be applied. The resultant scattering amplitudes, both singlet and triplet, as a function of angle can be calculated for various energies. The results are in excellent agreement with converged partial wave results.

Shertzer, J.↗

Coherence Phenomena in Coupled Optical Resonators

We predict a variety of photonic coherence phenomena in passive and active coupled ring resonators. Specifically, the effective dispersive and absorptive steady-state response of coupled resonators is derived, and used to determine the conditions for coupled-resonator-induced transparency and absorption, lasing without gain, and cooperative cavity emission. These effects rely on coherent photon trapping, in direct analogy with coherent population trapping phenomena in atomic systems. We also demonstrate that the coupled-mode equations are formally identical to the two-level atom Schrodinger equation in the rotating-wave approximation, and use this result for the analysis of coupled-resonator photon dynamics. Notably, because these effects are predicted directly from coupled-mode theory, they are not unique to atoms, but rather are fundamental to systems of coherently coupled resonators.

Smith, D. D.↗

Soliton resonance in bose-einstein condensate

A new phenomenon in nonlinear dispersive systems, including a Bose-Einstein Condensate (BEC), has been described. It is based upon a resonance between an externally induced soliton and 'eigen-solitons' of the homogeneous cubic Schrodinger equation. There have been shown that a moving source of positive /negative potential induces bright /dark solitons in an attractive / repulsive Bose condensate.

Bose-Einstein Condensate BEC nonlinear dispersive ↗

Nonlinear Evolution of Alfvenic Wave Packets

Alfven waves are a ubiquitous feature of the solar wind. One approach to studying the evolution of such waves has been to study exact solutions to approximate evolution equations. Here we compare soliton solutions of the Derivative Nonlinear Schrodinger evolution equation (DNLS) to solutions of the compressible MHD equations.

nonlinear evolution alfvenic wave packets solar wi↗

Nonlinear Optics and Applications

Nonlinear optics is the result of laser beam interaction with materials and started with the advent of lasers in the early 1960s. The field is growing daily and plays a major role in emerging photonic technology. Nonlinear optics play a major role in many of the optical applications such as optical signal processing, optical computers, ultrafast switches, ultra-short pulsed lasers, sensors, laser amplifiers, and many others. This special review volume on Nonlinear Optics and Applications is intended for those who want to be aware of the most recent technology. This book presents a survey of the recent advances of nonlinear optical applications. Emphasis will be on novel devices and materials, switching technology, optical computing, and important experimental results. Recent developments in topics which are of historical interest to researchers, and in the same time of potential use in the fields of all-optical communication and computing technologies, are also included. Additionally, a few new related topics which might provoke discussion are presented. The book includes chapters on nonlinear optics and applications; the nonlinear Schrodinger and associated equations that model spatio-temporal propagation; the supercontinuum light source; wideband ultrashort pulse fiber laser sources; lattice fabrication as well as their linear and nonlinear light guiding properties; the second-order EO effect (Pockels), the third-order (Kerr) and thermo-optical effects in optical waveguides and their applications in optical communication; and, the effect of magnetic field and its role in nonlinear optics, among other chapters.

Abdeldayem, Hossin A.↗

Application of the Finite Element Method in Atomic and Molecular Physics

The finite element method (FEM) is a numerical algorithm for solving second order differential equations. It has been successfully used to solve many problems in atomic and molecular physics, including bound state and scattering calculations. To illustrate the diversity of the method, we present here details of two applications. First, we calculate the non-adiabatic dipole polarizability of Hi by directly solving the first and second order equations of perturbation theory with FEM. In the second application, we calculate the scattering amplitude for e-H scattering (without partial wave analysis) by reducing the Schrodinger equation to set of integro-differential equations, which are then solved with FEM.

Shertzer, Janine↗

Applications of the Hybrid Theory to the Scattering of Electrons from HE+ and Li++ and Resonances in these Systems

Applications of the hybrid theory to the scattering of electrons from Ile+ and Li++ and resonances in these systems, A. K. Bhatia, NASA/Goddard Space Flight Center- The Hybrid theory of electron-hydrogen elastic scattering [I] is applied to the S-wave scattering of electrons from He+ and Li++. In this method, both short-range and long-range correlations are included in the Schrodinger equation at the same time. Phase shifts obtained in this calculation have rigorous lower bounds to the exact phase shifts and they are compared with those obtained using the Feshbach projection operator formalism [2], the close-coupling approach [3], and Harris-Nesbet method [4]. The agreement among all the calculations is very good. These systems have doubly-excited or Feshbach resonances embedded in the continuum. The resonance parameters for the lowest ' S resonances in He and Li+ are calculated and they are compared with the results obtained using the Feshbach projection operator formalism [5,6]. It is concluded that accurate resonance parameters can be obtained by the present method, which has the advantage of including corrections due to neighboring resonances and the continuum in which these resonances are embedded.

Bhatia, Anand K.↗

Calculation of State Specific Rate Coefficients for Non-Equilibrium Hypersonics Applications: from H(Psi) = E(Psi) to k(T) = A *exp(-E(sub a)/RT)

Development of High-Fidelity Physics-Based Models to describe hypersonic flight through the atmospheres of Earth and Mars is underway at NASA Ames Research Center. The goal is to construct chemistry models of the collisional and radiative processes that occur in the bow shock and boundary layers of spacecraft during atmospheric entry that are free of empiricism. In this talk I will discuss our philosophy and describe some of our progress. Topics to be covered include thermochemistry, internal energy relaxation, collisional dissociation and radiative emission and absorption. For this work we start by solving the Schrodinger equation to obtain accurate interaction potentials and radiative properties. Then we invoke classical mechanics to compute state-specific heavy particle collision cross sections and reaction rate coefficients. Finally, phenomenological rate coefficients and relaxation times are determined from master equation solutions.

aerothermodynamics↗

D-Wave Electron-H, -He+, and -Li2+ Elastic Scattering and Photoabsorption in P States of Two-Electron Systems

In previous papers [A. K. Bhatia, Phys. Rev. A 85, 052708 (2012); 86, 032709 (2012); 87, 042705 (2013)] electron-H, -He+, and -Li2+ P-wave scattering phase shifts were calculated using the variational polarized orbital theory. This method is now extended to the singlet and triplet D-wave scattering in the elastic region. The long-range correlations are included in the Schrodinger equation by using the method of polarized orbitals variationally. Phase shifts are compared to those obtained by other methods. The present calculation provides results which are rigorous lower bonds to the exact phase shifts. Using the presently calculated D-wave and previously calculated S-wave continuum functions, photoionization of singlet and triplet P states of He and Li+ are also calculated, along with the radiative recombination rate coefficients at various electron temperatures.

D-wave↗

Multi-Domain Routing in Delay Tolerant Networks

The goal of Delay Tolerant Networking (DTN) is to provide the missing ingredient for the ever-growing collection of communicating nodes in our solar system to become a Solar System Internet (SSI). Great strides have been made in modeling particular types of DTNs, such as schedule- or discovery-based. Now, analogously to the Internet, these smaller DTNs can be considered routing domains which must be stitched together to form the overall SSI. In this paper, we propose a framework for cross-domain routing in DTNs as well as methodologies for detecting these sub-domains. Example time-varying networks are given to demonstrate the techniques proposed. A basic component is the mathematical theory of sheaves, which unifies the underlying model of DTN routing algorithms, by giving rise to routing sheaves – these can be defined for the dynamic and scheduled networks as noted above, and can also be used to define the interfaces between these domains in order to route across them. An immediate application would be routing across discovery-based networks connected by scheduled networks. These DTN subdomains remain elusive, however, and need to become well-defined and properly sized for tractable computability. In particular, a balance must be determined between areas that are too large (i.e. large matrix computations) versus areas that are too small (i.e. “many” single-noded domains). Moreover, the connections between the domains should, at least locally, be chosen to optimize data flow and connectivity: we address this in three ways. First, tools from persistent homology are given to understand underlying structures, reminiscent of hierarchies in the Internet Protocol (IP) addressing. Second, we construct a notion of temporal graph curvature based on network geometry to analyze flows induced by dynamical processes on these networks. Finally, Schrodinger Bridges, a tool arising from statistical physics, are proposed as a method of constructing flows on time-evolving networks with desirable properties such as speed, robustness, and load sensitivity. We construct an approach to temporal hypergraphs to simultaneously model unicast, multicast, and broadcast, using the language of scheme theory, and then consider DTN network coding as a way to achieve network-level computation and organization. The paper concludes with a discussion and ideas for future work.

Alan Hylton↗

Focusability in the multi-pump Raman amplification of short laser pulses

Spatially combining multiple strong laser beams is a promising concept for achieving ultrahigh laser intensities. Proof-of-principle experiments have been conducted at the National Ignition Facility to report a combination of up to 20 pulses with high energy conversion efficiency. However, the combination process might damage the seed focusability due to mismatch of the seed and pump wavefronts. Here, we investigate the effect of the finite pump beam size on the focusability of the seed pulse. We propose an approach to retain and even improve the seed focusability by specifically arranging multiple pump beams. The results are demonstrated by the numerical solution of coupled nonlinear Schrödinger equations. Our findings also apply to seed amplification by filamented pump pulses.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

New solutions of nonlocal NLS, mKdV and Hirota equations

In this paper, we provide several novel solutions of the Ablowitz–Musslimani and Yang’s versions of the nonlocal nonlinear Schrödinger (NLS) equation, nonlocal modified Korteweg–de Vries (mKdV) as well as nonlocal Hirota equations. Further, in each case we compare and contrast with the corresponding solutions of the relevant local equation. In addition, we provide new solutions of the local NLS, local mKdV and local Hirota equations which are not the solutions of the corresponding nonlocal equations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

New solutions of coupled nonlocal NLS and coupled nonlocal mKdV equations

In this study, we provide several novel solutions of the coupled Ablowitz–Musslimani (AM) version of the nonlocal nonlinear Schrödinger (NLS) equation and the coupled nonlocal modified Korteweg–de Vries (mKdV) equation. In each case we compare and contrast the corresponding solutions of the relevant coupled local equations. Further, we provide new solutions of the coupled local NLS and coupled local mKdV equations which are not the solutions of the corresponding nonlocal equations. We also show that the nonlocal coupled (as well as uncoupled) mKdV equations have hidden Galilean invariance and admit novel solutions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗