SEARCH · Search NASA

Results for “quantum formalism”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 91 records · Page 5

All sources NASA NTRS DOE OSTI

NASA NTRS1992

Non-scalar uncertainty: Uncertainty in dynamic systems

The following point is stated throughout the paper: dynamic systems are usually subject to uncertainty, be it the unavoidable quantic uncertainty when working with sufficiently small scales or when working in large scales uncertainty can be allowed by the researcher in order to simplify the problem, or it can be introduced by nonlinear interactions. Even though non-quantic uncertainty can generally be dealt with by using the ordinary probability formalisms, it can also be studied with the proposed non-scalar formalism. Thus, non-scalar uncertainty is a more general theoretical framework giving insight into the nature of uncertainty and providing a practical tool in those cases in which scalar uncertainty is not enough, such as when studying highly nonlinear dynamic systems. This paper's specific contribution is the general concept of non-scalar uncertainty and a first proposal for a methodology. Applications should be based upon this methodology. The advantage of this approach is to provide simpler mathematical models for prediction of the system states. Present conventional tools for dealing with uncertainty prove insufficient for an effective description of some dynamic systems. The main limitations are overcome abandoning ordinary scalar algebra in the real interval (0, 1) in favor of a tensor field with a much richer structure and generality. This approach gives insight into the interpretation of Quantum Mechanics and will have its most profound consequences in the fields of elementary particle physics and nonlinear dynamic systems. Concepts like 'interfering alternatives' and 'discrete states' have an elegant explanation in this framework in terms of properties of dynamic systems such as strange attractors and chaos. The tensor formalism proves especially useful to describe the mechanics of representing dynamic systems with models that are closer to reality and have relatively much simpler solutions. It was found to be wise to get an approximate solution to an accurate model than to get a precise solution to a model constrained by simplifying assumptions. Precision has a very heavy cost in present physical models, but this formalism allows the trade between uncertainty and simplicity. It was found that modeling reality sometimes requires that state transition probabilities should be manipulated as nonscalar quantities, finding at the end that there is always a transformation to get back to scalar probability.

Martinez, Salvador Gutierrez↗

NASA NTRS2009

Multispectrum Analysis of 12CH4 in the v4 Band: I. Air-Broadened Half Widths, Pressure-Induced Shifts, Temperature Dependences and Line Mixing

Lorentz air-broadened half widths, pressure-induced shifts and their temperature dependences have been measured for over 430 transitions (allowed and forbidden) in the v4 band of (CH4)-12 over the temperature range 210 to 314 K. A multispectrum non linear least squares fitting technique was used to simultaneously fit a large number of high-resolution (0.006 to 0.01/cm) absorption spectra of pure methane and mixtures of methane diluted with dry air. Line mixing was detected for pairs of A-, E-, and F-species transitions in the P- and R-branch manifolds and quantified using the off-diagonal relaxation matrix elements formalism. The measured parameters are compared to air- and N2-broadened values reported in the literature for the v4 and other bands. The dependence of the various spectral line parameters upon the tetrahedral symmetry species and rotational quantum numbers of the transitions is discussed. All data used in the present work were recorded using the McMath-Pierce Fourier transform spectrometer located at the National Solar Observatory on Kitt Peak.

Smith, MaryAnn H.↗

NASA NTRS1978

A semiclassical approach to collisional ionization with application to the Ar-He system

A semiclassical approach based on the propagation of classical trajectories on potential surfaces analytically continued into the complex plane, together with a discretization procedure, has been developed for the problem of collisional ionization. Based on Franck-Condon considerations the formalism is reduced to that of the two-state approximation. Preionization loss and tunnelling beyond turning points have not been considered. Calculated partial ionization cross sections for the Ar-He system show good agreement with a fully quantum mechanical treatment.

Lam, K.-S.↗

NASA NTRS1987

Effective propagation constants in dense random media under effective medium approximation

The effective medium approximation is applied to study the effective propagation constants in a dense random medium. The dyadic Green's function is introduced to establish the effective medium approximation formalism for electromagnetic waves. The multiple scattering equations and the Lippmann-Schwinger equations for the transition operator are obtained in the configuration average form. The dispersion equations of multiple scattering is derived by using a standard method in quantum mechanics. To obtain an expression for the effective propagation constants the matrix elements of the configuration average dyadic transiton operator are calculated in momentum representation. Numerical illustations are carried out to demonstrate the difference in the effective propagation constants between the use of this approximation and the well-known quasi-crystalline approximation. A comparison is made with measured loss tangent in dry snow.

Zhu, P. Y.↗

NASA NTRS2014

Kuang's Semi-Classical Formalism for Calculating Electron Capture Cross Sections: A Space- Physics Application

Accurate estimates of electroncapture cross sections at energies relevant to the modeling of the transport, acceleration, and interaction of energetic neutral atoms (ENA) in space (approximately few MeV per nucleon) and especially for multi-electron ions must rely on detailed, but computationally expensive, quantum-mechanical description of the collision process. Kuang's semi-classical approach is an elegant and efficient way to arrive at these estimates. Motivated by ENA modeling efforts for apace applications, we shall briefly present this approach along with sample applications and report on current progress.

Barghouty, A. F.↗

NASA NTRS1972

The last Balmer line and H gamma in model B stars

Profiles of the last few Balmer lines (H12-H27) and the full profiles of the H gamma line were computed for a grid of hydrogen line blanketed model atmospheres. The use of the last hydrogen line and the equivalent width of H gamma provide a quick means of estimating the effective temperature and surface gravity of B stars. Regression curves relating the quantum number of the last hydrogen line to the electron density in the model atmosphere are given. Futhermore, it is shown that the difference in the gravity determination deduced from H gamma equivalent widths using the Edmonds-Schuter-Wells formalism and the Griem wing formulae is, at worst, 0.18 in the common logarithm.

Fischel, D.↗

NASA NTRS1991

Transverse conductivity of a relativistic plasma in oblique electric and magnetic fields

Resistive tearing in a primary candidate for flares occurring in stressed magnetic fields. Its possible application to the strongly magnetized environments (Hz about 10 to the 12th G) near the surface of neutron stars, particularly as a mechanism for generating the plasma heating and particle acceleration leading to gamma-ray bursts, has motivated a quantum treatment of this process, which requires knowledge of the electrical conductivity sigma of a relativistic gas in a new domain (i.e., that of a low-density n/e/) plasma in oblique electric and magnetic fields. This paper discusses the mathematical formalism for calculating sigma and present numerical results for a wide range of parameter values. The results indicate that sigma depends very strongly on both the applied electric and magnetic fields.

Melia, Fulvio↗

NASA NTRS1975

Use of the Wigner representation in scattering problems

The basic equations of quantum scattering were translated into the Wigner representation, putting quantum mechanics in the form of a stochastic process in phase space, with real valued probability distributions and source functions. The interpretative picture associated with this representation is developed and stressed and results used in applications published elsewhere are derived. The form of the integral equation for scattering as well as its multiple scattering expansion in this representation are derived. Quantum corrections to classical propagators are briefly discussed. The basic approximation used in the Monte-Carlo method is derived in a fashion which allows for future refinement and which includes bound state production. Finally, as a simple illustration of some of the formalism, scattering is treated by a bound two body problem. Simple expressions for single and double scattering contributions to total and differential cross-sections as well as for all necessary shadow corrections are obtained.

Bemler, E. A.↗

NASA NTRS1995

Covariant harmonic oscillators and coupled harmonic oscillators

It is shown that the system of two coupled harmonic oscillators shares the basic symmetry properties with the covariant harmonic oscillator formalism which provides a concise description of the basic features of relativistic hadronic features observed in high-energy laboratories. It is shown also that the coupled oscillator system has the SL(4,r) symmetry in classical mechanics, while the present formulation of quantum mechanics can accommodate only the Sp(4,r) portion of the SL(4,r) symmetry. The possible role of the SL(4,r) symmetry in quantum mechanics is discussed.

Han, Daesoo↗

NASA NTRS1982

Large numbers hypothesis. I - Classical formalism

A self-consistent formulation of physics at the classical level embodying Dirac's large numbers hypothesis (LNH) is developed based on units covariance. A scalar 'field' phi(x) is introduced and some fundamental results are derived from the resultant equations. Some unusual properties of phi are noted such as the fact that phi cannot be the correspondence limit of a normal quantum scalar field.

Adams, P. J.↗

NASA NTRS1983

Space radiation interaction mechanisms in materials

Models of charged-particle impact under conditions typical of the space environment are reported, with a focus on impact excitation and nuclear reactions, especially for heavy ions. Impact excitation is studied by using a global model for electronic excitation based on formal relations through the classical dielectric function to derive an approximation related to the local plasma (electron density distribution) within the atoms and molecules; and corrections to the model resulting from the nonfluid nature of this plasma are discussed. Nuclear reactions are studied by reducing quantum-mechanical treatment of this general N-body problem to an equivalent two-body problem that is solvable, and by comparing the results with experimental data. The equations for heavy-charged-particle transport are derived and solution techniques demonstrated. Finally, these methods of analysis are applied to study the change in the electrical properties of a GaAs semiconductor for photovoltaic applications; proton damage to GaAs crystals is found to arise from stable replacement defects and to be nonannealable, in contrast to electron-induced damage.

Wilson, J. W.↗

NASA NTRS2023

The Influence of Line Mixing on the j and k Dependencies of Halfwidths and Temperature Exponents in N2-broadening Coefficients of CH3F Spectral Lines

The N2-broadening halfwidths of CH 3 F in the ν 5 and ν 6 perpendicular bands have been calculated, along with their temperature exponents. These calculations utilize a modified and refined version of the Robert-Bonamy formalism, developed by the current authors within a semi-classical line shape framework. Extensive comparisons between the predicted halfwidths from the model and experimental measurements at 296 K and 183 K are presented. Our latest model accurately predicts the dependencies of the halfwidths on both the j and k quantum numbers. Furthermore, by extending our calculations to two additional temperatures, namely 240 K and 350 K, the temperature exponent N is determined for various sub-branches. The dependencies of N on j and k are analyzed, and theoretical explanations are provided to elucidate the predicted behaviors of N.

Methyl fluoride↗

NASA NTRS2005

Bidirectional Classical Stochastic Processes with Measurements and Feedback

A measurement on a quantum system is said to cause the "collapse" of the quantum state vector or density matrix. An analogous collapse occurs with measurements on a classical stochastic process. This paper addresses the question of describing the response of a classical stochastic process when there is feedback from the output of a measurement to the input, and is intended to give a model for quantum-mechanical processes that occur along a space-like reaction coordinate. The classical system can be thought of in physical terms as two counterflowing probability streams, which stochastically exchange probability currents in a way that the net probability current, and hence the overall probability, suitably interpreted, is conserved. The proposed formalism extends the . mathematics of those stochastic processes describable with linear, single-step, unidirectional transition probabilities, known as Markov chains and stochastic matrices. It is shown that a certain rearrangement and combination of the input and output of two stochastic matrices of the same order yields another matrix of the same type. Each measurement causes the partial collapse of the probability current distribution in the midst of such a process, giving rise to calculable, but non-Markov, values for the ensuing modification of the system's output probability distribution. The paper concludes with an analysis of a classical probabilistic version of the so-called grandfather paradox.

Hahne, G. E.↗

NASA NTRS2010

Physical Invariants of Intelligence

A program of research is dedicated to development of a mathematical formalism that could provide, among other things, means by which living systems could be distinguished from non-living ones. A major issue that arises in this research is the following question: What invariants of mathematical models of the physics of systems are (1) characteristic of the behaviors of intelligent living systems and (2) do not depend on specific features of material compositions heretofore considered to be characteristic of life? This research at earlier stages has been reported, albeit from different perspectives, in numerous previous NASA Tech Briefs articles. To recapitulate: One of the main underlying ideas is to extend the application of physical first principles to the behaviors of living systems. Mathematical models of motor dynamics are used to simulate the observable physical behaviors of systems or objects of interest, and models of mental dynamics are used to represent the evolution of the corresponding knowledge bases. For a given system, the knowledge base is modeled in the form of probability distributions and the mental dynamics is represented by models of the evolution of the probability densities or, equivalently, models of flows of information. At the time of reporting the information for this article, the focus of this research was upon the following aspects of the formalism: Intelligence is considered to be a means by which a living system preserves itself and improves its ability to survive and is further considered to manifest itself in feedback from the mental dynamics to the motor dynamics. Because of the feedback from the mental dynamics, the motor dynamics attains quantum-like properties: The trajectory of the physical aspect of the system in the space of dynamical variables splits into a family of different trajectories, and each of those trajectories can be chosen with a probability prescribed by the mental dynamics. From a slightly different perspective, the mechanism of decision-making is feedback from the mental dynamics to the motor dynamics, and this mechanism provides a quantum-like collapse of a random motion into an appropriate deterministic state, such that entropy undergoes a pronounced decrease. The existence of this mechanism is considered to be an invariant of intelligent behavior of living systems, regardless of the origins and material compositions of the systems.

Zak, Michail↗

NASA NTRS1994

Simultaneous two component squeezing in generalized q-coherent states

Using a generalization of the q-commutation relations, we develop a formalism in which it is possible to define generalized q-bosonic operators. This formalism includes both types of the usual q-deformed bosons as special cases. The coherent states of these operators show interesting and novel noise reduction properties including simultaneous squeezing in both field components, unlike the conventional case in which squeezing is permitted in only one component. This also contrasts with the usual quantum group deformation which also only permits one component squeezing.

Mcdermott, Roger J.↗

NASA NTRS1986

Isotopic effects in the collinear reactive FHH system

Exact quantum reaction probabilities for a collinear model of the F + HH, HD, DD and DH reactions on the MV potential energy surface have been computed using hyperspherical coordinates. The results, obtained up to a total energy of 1.8 eV, show three main features: (1) resonances, whose positions and widths are analyzed simply in the hyperspherical formalism; (2) a slowly varying background increasing for FHD, decreasing for FDH, and oscillating for FHH and FDD, whose variations are interpreted by classical dynamics; and (3) partial reaction probabilities revealing decreasing vibrational adiabaticity in the order FHH-FDD-FHD-FDH.

Lepetit, B.↗

NASA NTRS1991

Bialgebra deformations and algebras of trees

Let A denote a bialgebra over a field k and let A sub t = A((t)) denote the ring of formal power series with coefficients in A. Assume that A is also isomorphic to a free, associative algebra over k. A simple construction is given which makes A sub t a bialgebra deformation of A. In typical applications, A sub t is neither commutative nor cocommutative. In the terminology of Drinfeld, (1987), A sub t is a quantum group. This construction yields quantum groups associated with families of trees.

Grossman, Robert↗

NASA NTRS2014

An Experimental and Theoretical Study of Nitrogen-Broadened Acetylene Lines

We present experimental nitrogen-broadening coefficients derived from Voigt profiles of isotropic Raman Q-lines measured in the 2 band of acetylene (C2H2) at 150 K and 298 K, and compare them to theoretical values obtained through calculations that were carried out specifically for this work. Namely, full classical calculations based on Gordon's approach, two kinds of semi-classical calculations based on Robert Bonamy method as well as full quantum dynamical calculations were performed. All the computations employed exactly the same ab initio potential energy surface for the C2H2N2 system which is, to our knowledge, the most realistic, accurate and up-to-date one. The resulting calculated collisional half-widths are in good agreement with the experimental ones only for the full classical and quantum dynamical methods. In addition, we have performed similar calculations for IR absorption lines and compared the results to bibliographic values. Results obtained with the full classical method are again in good agreement with the available room temperature experimental data. The quantum dynamical close-coupling calculations are too time consuming to provide a complete set of values and therefore have been performed only for the R(0) line of C2H2. The broadening coefficient obtained for this line at 173 K and 297 K also compares quite well with the available experimental data. The traditional Robert Bonamy semi-classical formalism, however, strongly overestimates the values of half-width for both Qand R-lines. The refined semi-classical Robert Bonamy method, first proposed for the calculations of pressure broadening coefficients of isotropic Raman lines, is also used for IR lines. By using this improved model that takes into account effects from line coupling, the calculated semi-classical widths are significantly reduced and closer to the measured ones.

coefficients↗