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Results for “SEMICLASSICAL APPROXIMATION”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1974

Vibration-translation energy transfer in anharmonic diatomic molecules. 1: A critical evaluation of the semiclassical approximation

The semiclassical approximation is applied to anharmonic diatomic oscillators in excited initial states. Multistate numerical solutions giving the vibrational transition probabilities for collinear collisions with an inert atom are compared with equivalent, exact quantum-mechanical calculations. Several symmetrization methods are shown to correlate accurately the predictions of both theories for all initial states, transitions, and molecular types tested, but only if coupling of the oscillator motion and the classical trajectory of the incident particle is considered. In anharmonic heteronuclear molecules, the customary semiclassical method of computing the classical trajectory independently leads to transition probabilities with anomalous low-energy resonances. Proper accounting of the effects of oscillator compression and recoil on the incident particle trajectory removes the anomalies and restores the applicability of the semiclassical approximation.

Mckenzie, R. L.↗
NASA NTRS1975

Vibration-translation energy transfer in anharmonic diatomic molecules. I - A comparative evaluation of the semiclassical approximation

The semiclassical approximation (quantum oscillator, classical path) is applied to anharmonic diatomic oscillators in excited initial states. Multistate numerical solutions giving the vibrational transition probabilities for collinear collisions with an inert atom are compared with equivalent, exact quantum-mechanical calculations. Several symmetrization methods are shown to correlate accurately the predictions of both theories for all initial states, transitions, and molecular types tested, but only if coupling of the oscillator motion and the classical trajectory of the incident particle is considered. In anharmonic heteronuclear molecules, the customary semiclassical method of computing the classical trajectory independently leads to transition probabilities with anomalous low-energy resonances. Proper accounting of the effects of oscillator compression and recoil on the incident particle trajectory removes the anomalies and restores the applicability of the semiclassical approximation.

Mckenzie, R. L.↗
NASA NTRS1993

Semiclassical approximation for electron impact excitation of hydrogenic ions

The threshold behavior of the electron impact excitation cross sections for hydrogenic ions is investigated using the semiclassical approximation with the hyperbolic orbit for the projectile path, rather than the straight line path. The symmetric approximation is applied to modify the ordinary hyperbolic orbit. The modification factor due to the hyperbolic orbit approximation produces the correct energy dependence of the cross section near the excitation threshold. This result is very similar to that of the quantum mechanical case. The semiclassical enhancement factor due to this simple modification corresponds to the Coulomb focusing factor in the Born-Bethe approximation. In the high-energy limit, the semiclassical cross sections approach the Born-Bethe cross sections, with a finite cutoff in the momentum transfer for dipole transitions.

Jung, Young-Dae↗
DOE OSTI2020

Charge transfer rate constants for the carotenoid-porphyrin-C 60 molecular triad dissolved in tetrahydrofuran: The spin-boson model vs the linearized semiclassical approximation

Charge transfer rate constants were calculated for the carotenoid-porphyrin-C 60 (CPC 60 ) molecular triad dissolved in explicit tetrahydrofuran. The calculation was based on mapping the all-atom anharmonic Hamiltonian of this system onto the spin-boson Hamiltonian. The mapping was based on discretizing the spectral density from the time correlation function of the donor–acceptor potential energy gap, as obtained from all-atom molecular dynamics simulations. Different spin-boson Hamiltonians were constructed for each of the possible transitions between the three excited electronic states in two different triad conformations. The rate constants of three possible transitions were calculated via the quantum-mechanically exact Fermi’s golden rule (FGR), as well as a progression of more approximate expressions that lead to the classical Marcus expression. The advantage of the spin-boson approach is that once the mapping is established, the quantum-mechanically exact FGR and the hierarchy of approximations are known in closed form. The classical Marcus charge transfer rate constants obtained with the spin-boson Hamiltonians were found to reproduce those obtained from all-atom simulations with the linearized semiclassical approximation, thereby confirming the equivalence of the two approaches for this system. Furthermore, within the spin-boson Hamiltonian, we also found that the quantum-mechanically exact FGR rate constants were significantly enhanced compared to the classical Marcus theory rate constants for two out of three transitions in one of the two conformations under consideration. The results confirm that mapping to the spin-boson model can yield accurate predictions for charge transfer rate constants in a system as complex as CPC 60 dissolved in tetrahydrofuran.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1995

Femtolensing: Beyond the semiclassical approximation

Femtolensoing is a gravitational lensing effect in which the magnification is a function not only of the position and sizes of the source and lens, but also of the wavelength of light. Femtolensing is the only known effect of 10(exp -13) - 10(exp -16) solar mass) dark-matter objects and may possibly be detectable in cosmological gamma-ray burst spectra. We present a new and efficient algorithm for femtolensing calculation in general potentials. The physical optics results presented here differ at low frequencies from the semiclassical approximation, in which the flux is attributed to a finite number of mutually coherent images. At higher frequencies, our results agree well with the semicalssical predictions. Applying our method to a point-mass lens with external shear, we find complex events that have structure at both large and small spectral resolution. In this way, we show that femtolensing may be observable for lenses up to 10(exp -11) solar mass, much larger than previously believed. Additionally, we discuss the possibility of a search femtolensing of white dwarfs in the Large Magellanic Cloud at optical wavelengths.

Ulmer, Andrew↗
NASA NTRS1989

Semiclassical approximations in the coherent-state representation

The semiclassical limit of the stationary Schroedinger equation in the coherent-state representation is analyzed simultaneously for the groups W1, SU(2), and SU(1,1). A simple expression for the first two orders for the wave function and the associated semiclassical quantization rule is obtained if a definite choice for the classical Hamiltonian and expansion parameter is made. The behavior of the modulus of the wave function, which is a distribution function in a curved phase space, is studied for the three groups. The results are applied to the quantum triaxial rotor.

Kurchan, J.↗
NASA NTRS1973

Molecular collisions 21: Semiclassical approximation to atom-symmetric top rotational excitation

A distorted wave approximation to the T matrix for atom-symmetric top scattering was developed. The approximation is correct to first order in the part of the interaction potential responsible for transitions in the component of rotational angular momentum along the symmetry axis of the top. A semiclassical expression for this T matrix is derived by assuming large values of orbital and rotational angular momentum quantum numbers.

Russell, D.↗
NASA NTRS1973

Molecular collisions. 11: Semiclassical approximation to atom-symmetric top rotational excitation

In a paper of this series a distorted wave approximation to the T matrix for atom-symmetric top scattering was developed which is correct to first order in the part of the interaction potential responsible for transitions in the component of rotational angular momentum along the symmetry axis of the top. A semiclassical expression for this T matrix is derived by assuming large values of orbital and rotational angular momentum quantum numbers.

Russell, D.↗
DOE OSTI2020

Computational modeling of charge hopping dynamics along a disordered one-dimensional wire with energy gradients in quantum environments

This computational study investigates the effects of energy gradients on charge hopping dynamics along a one-dimensional chain of discrete sites coupled to quantum bath, which is modeled at the level of Pauli master equation (PME). This study also assesses the performance of different approximations for the hopping rates. Three different methods for solving the PME, a fourth order Runge–Kutta method, numerical diagonalization of the rate matrix followed by analytic propagation, and kinetic Monte Carlo simulation method, are tested and confirmed to produce virtually identical values of time dependent mean square displacement, diffusion constant, and mobility. Five different rate expressions, exact numerical evaluation of Fermi’s Golden Rule (FGR) rate, stationary phase interpolation (SPI) approximation, semiclassical approximation, classical Marcus rate, and Miller–Abrahams rate, are tested to help understand the effects of approximations in representing quantum environments in the presence of energy gradients. The results based on direct numerical evaluation of FGR rate exhibit transition from diffusive to non-diffusive behavior with the increase in the gradient and show that the charge transport in the quantum bath is more sensitive to the magnitude of the gradient and the disorder than in the classical bath. Among all the four approximations for the hopping rates, the SPI approximation is confirmed to work best overall. A comparison of two different methods to calculate the mobility identifies drift motion of the population distribution as the major source of non-diffusive behavior and provides more reliable information on the contribution of quantum bath.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1974

Orientational invariance of the rotational transition probability in the sudden approximation

Semiclassical collisions of an atom with a rigid-rotor molecule are examined in the sudden approximation. The rotational transition probability is shown to be invariant with respect to the choice of orientation for the molecular coordinate system; this fact contradicts recently reported results of a computer analysis. The present analysis may lead to an improved interpretation of recent molecular beam measurements.

Stallcop, J. R.↗
NASA NTRS1972

Semiclassical theory of inelastic collisions. II - Momentum-space formulation.

The time-dependent equations of the classical picture of inelastic collisions (classical-trajectory equations) are derived using the momentum-space semiclassical approximation. Thereby it is shown that the classical-trajectory equations remain valid in the vicinity of classical turning points provided that (a) the momentum-space semiclassical approximation is valid, (b) the trajectories for elastic scattering in the various internal states differ only slightly, and (c) the slopes of the elastic scattering potentials have the same sign. A brief review of the existing derivations of the classical-trajectory equations is given, and the general conditions for their validity are discussed.

Delos, J. B.↗
DOE OSTI2021

Semi-classical approximation description of static properties of nuclei

In this report, we present recent development in semi-classical description of static properties of nuclei. By employing the Wigner transform, we derive simple semiclassical approximations for evaluating properties of nuclear system. We present results of calculations of static properties, using the energy density functional associated with Skyrme effective nucleon–nucleon interaction. In particular, we consider properties of the Wigner distribution function, line of beta stability, Coulomb and symmetry energies, deformation energies, equation of state, nuclear radii, and single-particle level density.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1991

Relative populations of excited levels within the ground configuration of Si-like Cu, Zn, Ge and Se ions

Populations of 3p2 1D2, 3P1, 3P2 levels in Si-like Cu, Zn, Ge, and Se ions have been deduced from the measurements of absolute intensities of magnetic dipole transitions within the 3s2 3p2 ground configuration. The measured population ratios are compared with theoretical calculations based on the distorted-wave approximation for the electron collisions and a semiclassical approximation for the proton collisions. The observed deviation from the statistical distribution for the excited-level populations within the ground configuration along the silicon isoelectronic sequence is in agreement with theoretical prediction.

Datla, R. U.↗
DOE OSTI2021

The response field and the saddle points of quantum mechanical path integrals

Highlights: • Moyal quantum mechanics and Marinov’s path integral. • Classical and semiclassical limits of Marinov’s path integral. • Oscillating functional integrals. • Instantons of the Marinov’s path integral. In quantum statistical mechanics, Moyal’s equation governs the time evolution of Wigner functions and of more general Weyl symbols that represent the density matrix of arbitrary mixed states. A formal solution to Moyal’s equation is given by Marinov’s path integral. In this paper we demonstrate that this path integral can be regarded as the natural link between several conceptual, geometric, and dynamical issues in quantum mechanics. A unifying perspective is achieved by highlighting the pivotal role which the response field, one of the integration variables in Marinov’s integral, plays for pure states even. The discussion focuses on how the integral’s semiclassical approximation relates to its strictly classical limit; unlike for Feynman type path integrals, the latter is well defined in the Marinov case. The topics covered include a random force representation of Marinov’s integral based upon the concept of “Airy averaging”, a related discussion of positivity-violating Wigner functions describing tunneling processes, and the role of the response field in maintaining quantum coherence and enabling interference phenomena. The double slit experiment for electrons and the Bohm–Aharonov effect are analyzed as illustrative examples. Furthermore, a surprising relationship between the instantons of the Marinov path integral over an analytically continued (“Wick rotated”) response field, and the complex instantons of Feynman-type integrals is found. The latter play a prominent role in recent work towards a Picard–Lefschetz theory applicable to oscillatory path integrals and the resurgence program.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Fluctuation-driven excess noise near superconducting phase transition

We discuss intrinsic mechanisms of nonequilibrium excess noise in superconducting devices and transition edge sensors. In particular, we present an overview of fluctuation-driven contributions to the current noise in the vicinity of the superconducting transition. We argue that sufficiently close to the critical temperature fluctuations of conductivity may become correlated provided that the rate of quasiparticle relaxation is slow as compared to dynamics of superconducting fluctuations. In this regime, fluctuations of conductivity adiabatically follow the fluctuations of the electron distribution. This leads to a substantial enhancement of current noise. Here, the corresponding spectral power density of noise has a Lorentzian shape in the frequency domain while its magnitude scales proportionally to the inelastic relaxation time. It also sensitively depends on the dephasing and Ginzburg–Landau timescales. Further estimates suggest that this mechanism dominates over the conventional temperature fluctuations in the same range of parameters. To describe these effects microscopically, we use the nonequilibrium Keldysh technique in the semiclassical approximation of superconductivity with Boltzmann–Langevin random forces to account for correlations of fluctuations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗