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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

Kinetic and interaction components of the exact time-dependent correlation potential

The exact exchange-correlation (xc) potential of time-dependent density functional theory has been shown to have striking features. For example, step and peak features are generically found when the system is far from its ground-state, and these depend nonlocally on the density in space and time. We analyze the xc potential by decomposing it into kinetic and interaction components and comparing each with their exact-adiabatic counterparts, for a range of dynamical situations in model one-dimensional two-electron systems. We find that often, but not always, the kinetic contribution is largely responsible for these features that are missed by the adiabatic approximation. The adiabatic approximation often makes a smaller error for the interaction component, which we write in two parts, one being the Coulomb potential due to the time-dependent xc hole. Non-adiabatic features of the kinetic component were also larger than those of the interaction component in cases that we studied when there is negligible step structure. In ground-state situations, step and peak structures arise in cases of static correlation, when more than one determinant is essential to describe the interacting state. We investigate the time-dependent natural orbital occupation numbers and find the corresponding relation between these and the dynamical step is more complex than for the ground-state case.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Developing new and understanding old approximations in TDDFT

When a system has evolved far from a ground-state, the adiabatic approximations commonly used in time-dependent density functional theory calculations completely fail in some applications, while giving qualitatively good predictions in others, and sometimes even quantitative predictions. It is not clearly understood why this is so, and developing practical approximations going beyond the adiabatic approximation remains a challenge. This paper explores three different lines of investigation. First, an expression for the exact time-dependent exchange–correlation potential suggests that the accuracy of an adiabatic approximation is intimately related to the deviation between the natural orbital occupation numbers of the physical system and those of the Kohn–Sham system, and we explore this on some exactly-solvable model systems. The exact expression further suggests a path to go beyond the adiabatic approximations, and in the second part we discuss a newly proposed class of memory-dependent approximations developed in this way. Finally, we derive a new expression for the exact exchange–correlation potential from a coupling-constant path integration.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1984

Cross-tail ion drift in a realistic model magnetotail

By integrating the exact equations of motion, particle orbits have been followed in a good model magnetospheric field consisting of a planetary dipole, forward magnetosphere, and magnetotail current system. Proton energies from 2 eV to 20 keV were used for the full range of equatorial pitch angles and phase. Despite considerable pitch angle scattering in the equatorial plane crossings, it is found, first, that the bounce-averaged cross-tail drift velocity is approximately independent of pitch angle. Second, it is found that, averaged over initial gyrophase, the drift velocity (due to field curvature and gradient) is proportional to proton energy and is given to good approximation by adiabatic approximations, even up to 20 keV, despite the extreme lack of meeting the adiabatic criteria.

Propp, K.↗
NASA NTRS1973

A rigorous cosmic-ray transport equation with no restrictions on particle energy.

A new transport equation for the cosmic-ray omnidirectional intensity is obtained. This equation follows exactly from the coupled pair of differential moment equations we presented earlier. It can be characterized as a nonlocal convection-diffusion equation in which the usual transport coefficients are replaced by time integral operators. The nonlocal equation is shown to reduce to the standard convection-diffusion form if the adiabatic approximation can be applied. In general, the adiabatic approximation does not apply; however, by going to the limits of infinite and zero gyroradius and, in addition, applying the adiabatic approximation, the large- and small-gyroradius transport theories due originally to Jokipii are regained. The validity of these theories as asymptotic limits and as approximate theories in the interplanetary magnetic field is discussed.

Klimas, A. J.↗
DOE OSTI2016

Constructing diabatic representations using adiabatic and approximate diabatic data – Coping with diabolical singularities

We have recently introduced a diabatization scheme, which simultaneously fits and diabatizes adiabatic ab initio electronic wave functions, Zhu and Yarkony J. Chem. Phys. 140, 024112 (2014). The algorithm uses derivative couplings in the defining equations for the diabatic Hamiltonian, H{sup d}, and fits all its matrix elements simultaneously to adiabatic state data. This procedure ultimately provides an accurate, quantifiably diabatic, representation of the adiabatic electronic structure data. However, optimizing the large number of nonlinear parameters in the basis functions and adjusting the number and kind of basis functions from which the fit is built, which provide the essential flexibility, has proved challenging. In this work, we introduce a procedure that combines adiabatic state and diabatic state data to efficiently optimize the nonlinear parameters and basis function expansion. Further, we consider using direct properties based diabatizations to initialize the fitting procedure. To address this issue, we introduce a systematic method for eliminating the debilitating (diabolical) singularities in the defining equations of properties based diabatizations. We exploit the observation that if approximate diabatic data are available, the commonly used approach of fitting each matrix element of H{sup d} individually provides a starting point (seed) from which convergence of the full H{sup d} construction algorithm is rapid. The optimization of nonlinear parameters and basis functions and the elimination of debilitating singularities are, respectively, illustrated using the 1,2,3,4{sup 1}A states of phenol and the 1,2{sup 1}A states of NH{sub 3}, states which are coupled by conical intersections.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

TeV Cosmic-Ray Anisotropy from the Magnetic Field at the Heliospheric Boundary

In this study, we performed numerical calculations to test the suggestion by Desiati and Lazarian that the anisotropies of TeV cosmic rays may arise from their interactions with the heliosphere. For this purpose, we used a magnetic field model of the heliosphere and performed direct numerical calculations of particle trajectories. Unlike earlier papers testing the idea, we did not employ time-reversible techniques that are based on Liouville's theorem. We showed numerically that for scattering by the heliosphere, the conditions of Liouville's theorem are not satisfied, and the adiabatic approximation and time-reversibility of the particle trajectories are not valid. Finally, our results indicate sensitivity to the magnetic structure of the heliospheric magnetic field, and we expect that this will be useful for probing this structure in future research.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1976

Test particle propagation in magnetostatic turbulence. 1. Failure of the diffusion approximation

The equation which governs the quasi-linear approximation to the ensemble and gyro-phase averaged one-body probability distribution function is constructed from first principles. This derived equation is subjected to a thorough investigation in order to calculate the possible limitations of the quasi-linear approximation. It is shown that the reduction of this equation to a standard diffusion equation in the Markovian limit can be accomplished through the application of the adiabatic approximation. A numerical solution of the standard diffusion equation in the Markovian limit is obtained for the narrow parallel beam injection. Comparison of the diabatic and adiabatic results explicitly demonstrates the failure of the Markovian description of the probability distribution function. Through the use of a linear time-scale extension the failure of the adiabatic approximation, which leads to the Markovian limit, is shown to be due to mixing of the relaxation and interaction time scales in the presence of the strong mean field.

Klimas, A. J.↗
DOE OSTI2015

Modeling of different scenarios of thin current sheet equilibria in the Earth’s magnetotail

The Earth’s magnetosphere is an open dynamic system permanently interacting with the solar wind, i.e., the plasma flow from the Sun. Some plasma processes in the magnetosphere are of spontaneous explosive character, while others develop rather slowly as compared to the characteristic times of plasma particle motion in it. The large-scale current sheet in the magnetotail can be in an almost equilibrium state both in quiet periods and during geomagnetic perturbations, and its variations can be considered quasistatic. Thus, under some conditions, the magnetotail current sheet can be described as an equilibrium plasma system. Its state depends on various parameters, in particular, on those determining the dynamics of charged particles. Knowing the main governing parameters, one can study the structure and properties of the current sheet equilibrium. This work is devoted to the self-consistent modeling of the equilibrium thin current sheet (TCS) of the Earth’s magnetotail, the thickness of which is comparable with the ion gyroradius. The main objective of this work is to examine how the TCS structure depends on the parameters characterizing the particle dynamics and magnetic field geometry. A numerical hybrid self-consistent TCS model in which the tension of magnetic field lines is counterbalanced by the inertia of ions moving through the sheet is constructed. The ion dynamics is considered in the quasi-adiabatic approximation, while the electron motion, in the conductive fluid approximation. Depending on the values of the adiabaticity parameter κ (which determines the character of plasma particle motion) and the dimensionless normal component of the magnetic field b{sub z}, the following two scenarios are considered: (A) the adiabaticity parameter is proportional to the particle energy and b{sub z} = const and (B) the particle energy is fixed and the adiabaticity parameter is proportional to b{sub z}. The structure of the current sheet and particle dynamics in it are studied as functions of the parameters κ and b{sub z}. It is shown that, in scenario A, the current sheet thickness decreases with increasing adiabaticity parameter due to a decrease in the ion gyroradius. Accordingly, the radius of curvature of magnetic field lines decreases, which leads to an increase in the contribution of electron drift currents near the neutral plane z = 0. Numerical simulations demonstrate that current equilibria can exist if the adiabaticity parameter lies in the range 0.05 ≤ κ ≤ 0.7. At κ ∼ 0.7, the contribution of electron drift currents to the total current density is much larger than the contribution of ions and the ion motion becomes chaotic. At larger values of the adiabaticity parameter, no equilibrium solutions were found in the framework of the given one-dimensional model. Therefore, the value κ = 0.7 corresponds to the upper applicability limit of the quasi-adiabatic model of the current sheet. In scenario B, an increase in the parameter κ leads to the appearance of a large number of quasi-trapped ions in the current sheet, due to which the current sheet thickens and the amplitude of the current density decreases. As a result, equilibrium solutions exist in a much narrower range of the adiabaticity parameter, 0.05≤ κ ≤ 0.25. Consequences of the existence of parametric boundaries of equilibrium solutions for the TCS under actual geomagnetic conditions are discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Fermi’s Golden Rule Rate Expression for Transitions Due to Nonadiabatic Derivative Couplings in the Adiabatic Basis

Starting from a general molecular Hamiltonian expressed in the basis of adiabatic electronic and nuclear position states, where a compact and complete expression for the nonadiabatic derivative coupling (NDC) Hamiltonian term is obtained, we provide a general analysis of the Fermi’s golden rule (FGR) rate expression for nonadiabatic transitions between adiabatic states. We then consider a quasi-adiabatic approximation that uses crude adiabatic states and NDC couplings, both evaluated at the minimum potential energy configuration of the initial adiabatic state, for the definition of the zeroth and first-order terms of the Hamiltonian. Although the application of this approximation is rather limited, it allows deriving a general FGR rate expression without further approximation while accounting for non-Condon contribution to the FGR rate arising from momentum operators of NDC terms and its coupling with vibronic displacements. For a generic and widely used model where all nuclear degrees of freedom and environmental effects are represented as linearly coupled harmonic oscillators, we derive a closed-form FGR rate expression that requires only Fourier transform. The resulting rate expression includes quadratic contributions of NDC terms and their couplings to Franck–Condon modes, which require evaluation of two additional bath spectral densities in addition to the conventional one that appears in a typical FGR rate theory based on the Condon approximation. Model calculations for the case where nuclear vibrations consist of both a sharp high-frequency mode and an Ohmic bath spectral density illustrate new features and implications of the rate expression. We then apply our theoretical expression to the nonradiative decay from the first excited singlet state of azulene, which illustrates the utility and implications of our theoretical results.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1990

Electron heating in quasi-perpendicular shocks - A Monte Carlo simulation

To study the problem of electron heating in quasi-perpendicular shocks, under the combined effects of 'reversible' motion, in the shock electric potential and magnetic field, and wave-particle interactions a diffusion equation was derived, in the drift (adiabatic) approximation and it was solved by using a Monte Carlo method. The results show that most of the observations can be explained within this framework. The simulation has also definitively shown that the electron parallel temperature is determined by the dc electromagnetic field and not by any wave particle induced heating. Wave-particle interactions are effective in smoothing out the large gradients in phase space produced by the 'reversible' motion of the electrons, thus producing a 'cooling' of the electrons. Some constraints on the wave-particle interaction process may be obtained from a detailed comparison between the simulation and observations. In particular, it appears that the adiabatic approximation must be violated in order to explain the observed evolution of the perpendicular temperature.

Veltri, Pierluigi↗
DOE OSTI2016

Range-separated time-dependent density-functional theory with a frequency-dependent second-order Bethe-Salpeter correlation kernel

We present a range-separated linear-response time-dependent density-functional theory (TDDFT) which combines a density-functional approximation for the short-range response kernel and a frequency-dependent second-order Bethe-Salpeter approximation for the long-range response kernel. This approach goes beyond the adiabatic approximation usually used in linear-response TDDFT and aims at improving the accuracy of calculations of electronic excitation energies of molecular systems. A detailed derivation of the frequency-dependent second-order Bethe-Salpeter correlation kernel is given using many-body Green-function theory. Preliminary tests of this range-separated TDDFT method are presented for the calculation of excitation energies of the He and Be atoms and small molecules (H{sub 2}, N{sub 2}, CO{sub 2}, H{sub 2}CO, and C{sub 2}H{sub 4}). The results suggest that the addition of the long-range second-order Bethe-Salpeter correlation kernel overall slightly improves the excitation energies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Exact time-dependent density-functional theory for nonperturbative dynamics of the helium atom

By inverting the time-dependent Kohn-Sham equation for a numerically exact dynamics of the helium atom, we show that the dynamical step and peak features of the exact correlation potential found previously in one-dimensional models persist for real three-dimensional systems. We demonstrate that the Kohn-Sham and true current-densities differ by a rotational component. The results have direct implications for approximate TDDFT calculations of atoms and molecules in strong fields, emphasizing the need to go beyond the adiabatic approximation, and highlighting caution in quantitative use of the Kohn-Sham current.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2013

Magnetic reconnection under anisotropic magnetohydrodynamic approximation

We study the formation of slow-mode shocks in collisionless magnetic reconnection by using one- and two-dimensional collisionless MHD codes based on the double adiabatic approximation and the Landau closure model. We bridge the gap between the Petschek-type MHD reconnection model accompanied by a pair of slow shocks and the observational evidence of the rare occasion of in-situ slow shock observations. Our results showed that once magnetic reconnection takes place, a firehose-sense (p{sub ∥}>p{sub ⊥}) pressure anisotropy arises in the downstream region, and the generated slow shocks are quite weak comparing with those in an isotropic MHD. In spite of the weakness of the shocks, however, the resultant reconnection rate is 10%–30% higher than that in an isotropic case. This result implies that the slow shock does not necessarily play an important role in the energy conversion in the reconnection system and is consistent with the satellite observation in the Earth's magnetosphere.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

A simple method for one-loop renormalization in curved space-time

We present a simple method for deriving the renormalization counterterms from the components of the energy-momentum tensor in curved space-time. This method allows control over the finite parts of the counterterms and provides explicit expressions for each term separately. As an example, the method is used for the self-interacting scalar field in a Friedmann-Robertson-Walker metric in the adiabatic approximation, where we calculate the renormalized equation of motion for the field and the renormalized components of the energy-momentum tensor to fourth adiabatic order while including interactions to one-loop order. Within this formalism the trace anomaly, including contributions from interactions, is shown to have a simple derivation. We compare our results to those obtained by two standard methods, finding agreement with the Schwinger-DeWitt expansion but disagreement with adiabatic subtractions for interacting theories.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1984

Particle transport in planetary magnetospheres

Particle energization in Earth's and Jupiter's magnetospheres is discussed. Understanding of the large scale magnetic and electric fields in which charged particles move is reviewed. Orbit theory in the adiabatic approximation is sketched. General conditions for adiabatic breakdown at each of three levels of periodicity are presented. High energy losses and lower energy sources argue for the existence of magnetospheric accelerations. Nonadiabatic acceleration processes are mentioned. Slow diffusive energization by particle interactions with electromagnetic fluctuations is outlined. This mechanism seems adequate at Earth but, operating alone, is unconvincing for Jupiter. Adding spatial diffusion in the radially distended Jovian magnetodisk may resolve the difficulty.

Birmingham, T. J.↗
DOE OSTI2015

Communication: Creation of molecular vibrational motions via the rotation-vibration coupling

Building on recent advances in the rotational excitation of molecules, we show how the effect of rotation-vibration coupling can be switched on in a controlled manner and how this coupling unfolds in real time after a pure rotational excitation. We present the first examination of the vibrational motions which can be induced via the rotation-vibration coupling after a pulsed rotational excitation. A time-dependent quantum wave packet calculation for the HF molecule shows how a slow (compared to the vibrational period) rotational excitation leads to a smooth increase in the average bond length whereas a fast rotational excitation leads to a non-stationary vibrational motion. As a result, under field-free postpulse conditions, either a stretched stationary bond or a vibrating bond can be created due to the coupling between the rotational and vibrational degrees of freedom. The latter corresponds to a laser-induced breakdown of the adiabatic approximation for rotation-vibration coupling.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗