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Calculation of positron observables using a finite-element-based approach

Description: We report the development of a new method for calculating positron observables using a finite-element approach for the solution of the Schrodinger equation. This method combines the advantages of both basis-set and real-space-grid approaches. The strict locality in real space of the finite element basis functions results in a method that is well suited for calculating large systems of a thousand or more atoms, as required for calculations of extended defects such as dislocations. In addition, the method is variational in nature and its convergence can be controlled systematically. The calculation of positron observables is straightforward due to the real-space nature of this method. We illustrate the power of this method with positron lifetime calculations on defects and defect-free materials, using overlapping atomic charge densities.
Date: November 4, 1998
Creator: Klein, B. M.; Pask, J. E. & Sterne, P.
Partner: UNT Libraries Government Documents Department

A general formula for Rayleigh-Schroedinger perturbation energy utilizing a power series expansion of the quantum mechanical Hamiltonian

Description: Perturbation theory has long been utilized by quantum chemists as a method for approximating solutions to the Schroedinger equation. Perturbation treatments represent a system`s energy as a power series in which each additional term further corrects the total energy; it is therefore convenient to have an explicit formula for the nth-order energy correction term. If all perturbations are collected into a single Hamiltonian operator, such a closed-form expression for the nth-order energy correction is well known; however, use of a single perturbed Hamiltonian often leads to divergent energy series, while superior convergence behavior is obtained by expanding the perturbed Hamiltonian in a power series. This report presents a closed-form expression for the nth-order energy correction obtained using Rayleigh-Schroedinger perturbation theory and a power series expansion of the Hamiltonian.
Date: February 1, 1997
Creator: Herbert, J.M.
Partner: UNT Libraries Government Documents Department

Dirac charge dynamics in graphene by infrared spectroscopy

Description: A remarkable manifestation of the quantum character of electrons in matter is offered by graphene, a single atomic layer of graphite. Unlike conventional solids where electrons are described with the Schrödinger equation, electronic excitations in graphene are governed by the Dirac hamiltonian. Some of the intriguing electronic properties of graphene, such as massless Dirac quasiparticles with linear energy-momentum dispersion, have been confirmed by recent observations. Here, we report an infrared spectromicroscopy study of charge dynamics in graphene integrated in gated devices. Our measurements verify the expected characteristics of graphene and, owing to the previously unattainable accuracy of infrared experiments, also uncover significant departures of the quasiparticle dynamics from predictions made for Dirac fermions in idealized, free-standing graphene. Several observations reported here indicate the relevance of many-body interactions to the electromagnetic response of graphene.
Date: April 29, 2008
Creator: Martin, Michael C.; Li, Z. Q.; Henriksen, E. A.; Jiang, Z.; Hao, Z.; Martin, Michael C et al.
Partner: UNT Libraries Government Documents Department

On Ideal Stability of Cylindrical Localized Interchange Modes

Description: Stability of cylindrical localized ideal pressure-driven interchange plasma modes is revisited. Converting the underlying eigenvalue problem into the form of the Schroedinger equation gives a new simple way of deriving the Suydam stability criterion and calculating the growth rates of unstable modes. Near the marginal stability limit the growth rate is exponentially small and the mode has a double-peak structure.
Date: May 15, 2007
Creator: Umansky, M V
Partner: UNT Libraries Government Documents Department

Electronically Nonadiabatic Dynamics via Semiclassical Initial Value Methods

Description: In the late 1970's Meyer and Miller (MM) [J. Chem. Phys. 70, 3214 (1979)] presented a classical Hamiltonian corresponding to a finite set of electronic states of a molecular system (i.e., the various potential energy surfaces and their couplings), so that classical trajectory simulations could be carried out treating the nuclear and electronic degrees of freedom (DOF) in an equivalent dynamical framework (i.e., by classical mechanics), thereby describing non-adiabatic dynamics in a more unified manner. Much later Stock and Thoss (ST) [Phys. Rev. Lett. 78, 578 (1997)] showed that the MM model is actually not a 'model', but rather a 'representation' of the nuclear-electronic system; i.e., were the MMST nuclear-electronic Hamiltonian taken as a Hamiltonian operator and used in the Schroedinger equation, the exact (quantum) nuclear-electronic dynamics would be obtained. In recent years various initial value representations (IVRs) of semiclassical (SC) theory have been used with the MMST Hamiltonian to describe electronically non-adiabatic processes. Of special interest is the fact that though the classical trajectories generated by the MMST Hamiltonian (and which are the 'input' for an SC-IVR treatment) are 'Ehrenfest trajectories', when they are used within the SC-IVR framework the nuclear motion emerges from regions of non-adiabaticity on one potential energy surface (PES) or another, and not on an average PES as in the traditional Ehrenfest model. Examples are presented to illustrate and (hopefully) illuminate this behavior.
Date: December 11, 2008
Creator: Miller, William H.
Partner: UNT Libraries Government Documents Department

The evolution of consciousness

Description: It is argued that the principles of classical physics are inimical to the development of an adequate science of consciousness. The problem is that insofar as the classical principles are valid consciousness can have no effect on the behavior, and hence on the survival prospects, of the organisms in which it inheres. Thus within the classical framework it is not possible to explain in natural terms the development of consciousness to the high-level form found in human beings. In quantum theory, on the other hand, consciousness can be dynamically efficacious: quantum theory does allow consciousness to influence behavior, and thence to evolve in accordance with the principles of natural selection. However, this evolutionary requirement places important constraints upon the details of the formulation of the quantum dynamical principles.
Date: August 16, 1996
Creator: Stapp, H.P.
Partner: UNT Libraries Government Documents Department

Symbolic derivation of high-order Rayleigh-Schroedinger perturbation energies using computer algebra: Application to vibrational-rotational analysis of diatomic molecules

Description: Rayleigh-Schroedinger perturbation theory is an effective and popular tool for describing low-lying vibrational and rotational states of molecules. This method, in conjunction with ab initio techniques for computation of electronic potential energy surfaces, can be used to calculate first-principles molecular vibrational-rotational energies to successive orders of approximation. Because of mathematical complexities, however, such perturbation calculations are rarely extended beyond the second order of approximation, although recent work by Herbert has provided a formula for the nth-order energy correction. This report extends that work and furnishes the remaining theoretical details (including a general formula for the Rayleigh-Schroedinger expansion coefficients) necessary for calculation of energy corrections to arbitrary order. The commercial computer algebra software Mathematica is employed to perform the prohibitively tedious symbolic manipulations necessary for derivation of generalized energy formulae in terms of universal constants, molecular constants, and quantum numbers. As a pedagogical example, a Hamiltonian operator tailored specifically to diatomic molecules is derived, and the perturbation formulae obtained from this Hamiltonian are evaluated for a number of such molecules. This work provides a foundation for future analyses of polyatomic molecules, since it demonstrates that arbitrary-order perturbation theory can successfully be applied with the aid of commercially available computer algebra software.
Date: July 1, 1997
Creator: Herbert, J.M.
Partner: UNT Libraries Government Documents Department

Spectrum of the ballooning Schroedinger equation

Description: The ballooning Schroedinger equation (BSE) is a model equation for investigating global modes that can, when approximated by a Wentzel-Kramers-Brillouin (WKB) ansatz, be described by a ballooning formalism locally to a field line. This second order differential equation with coefficients periodic in the independent variable {theta}{sub k} is assumed to apply even in cases where simple WKB quantization conditions break down, thus providing an alternative to semiclassical quantization. Also, it provides a test bed for developing more advanced WKB methods: e.g. the apparent discontinuity between quantization formulae for {open_quotes}trapped{close_quotes} and {open_quotes}passing{close_quotes} modes, whose ray paths have different topologies, is removed by extending the WKB method to include the phenomena of tunnelling and reflection. The BSE is applied to instabilities with shear in the real part of the local frequency, so that the dispersion relation is inherently complex. As the frequency shear is increased, it is found that trapped modes go over to passing modes, reducing the maximum growth rate by averaging over {theta}{sub k}.
Date: January 1, 1997
Creator: Dewar, R.L.
Partner: UNT Libraries Government Documents Department

Quantum mechanics from an equivalence principle

Description: The authors show that requiring diffeomorphic equivalence for one-dimensional stationary states implies that the reduced action S{sub 0} satisfies the quantum Hamilton-Jacobi equation with the Planck constant playing the role of a covariantizing parameter. The construction shows the existence of a fundamental initial condition which is strictly related to the Moebius symmetry of the Legendre transform and to its involutive character. The universal nature of the initial condition implies the Schroedinger equation in any dimension.
Date: May 15, 1997
Creator: Faraggi, A. E. & Matone, M.
Partner: UNT Libraries Government Documents Department

The equivalence principle of quantum mechanics: Uniqueness theorem

Description: Recently the authors showed that the postulated diffeomorphic equivalence of states implies quantum mechanics. This approach takes the canonical variables to be dependent by the relation p = {partial_derivative}{sub q}S{sub 0} and exploits a basic GL(2,C)-symmetry which underlies the canonical formalism. In particular, they looked for the special transformations leading to the free system with vanishing energy. Furthermore, they saw that while on the one hand the equivalence principle cannot be consistently implemented in classical mechanics, on the other it naturally led to the quantum analogue of the Hamilton-Jacobi equation, thus implying the Schroedinger equation. In this letter they show that actually the principle uniquely leads to this solution. The authors also express the canonical and Schroedinger equations by means of the brackets recently introduced in the framework of N = 2 SYM. These brackets are the analogue of the Poisson brackets with the canonical variables taken as dependent.
Date: October 28, 1997
Creator: Faraggi, A.E. & Matone, M.
Partner: UNT Libraries Government Documents Department

Vortex dynamics and correlated disorder in high-{Tc} superconductors

Description: We develop a theory for the vortex motion in the presence of correlated disorder in the form of the twin boundaries and columnar defects. Mapping vortex trajectories onto boson world lines enables us to establish the duality of the vortex transport in the systems with correlated disorder and hopping conductivity of charged particles in 2D systems. A glassy-like dynamics of the vortex lines with zero linear-resistivity and strongly nonlinear current-voltage behavior as V {proportional_to} exp[{minus} const/J{sup {mu}}] in a Bose glass state is predicted.
Date: August 1, 1993
Creator: Vinokur, V.M.
Partner: UNT Libraries Government Documents Department

Quantum transformations

Description: We show that the quantum Hamilton-Jacobi equation can be written in the classical form with the spatial derivative {partial_derivative}{sub q} replaced by {partial_derivative}{sub q} with dq = dq/{radical}1{minus}{beta}{sup 2}(q), where {beta}{sup 2}(q) is strictly related to the quantum potential. This can be seen as the opposite of the problem of finding the wave function representation of classical mechanics as formulated by Schiller and Rosen. The structure of the above {open_quotes}quantum transformation{close_quotes}, related to the recently formulated equivalence principle, indicates that the potential deforms space geometry. In particular, a result by Flanders implies that both W(q) = V(q) {minus} E and the quantum potential Q are proportional to the curvatures {kappa}{sub W} and {kappa}{sub Q} which arise as natural invariants in an equivalence problem for curves in the projective line. In this formulation the Schroedinger equation takes the geometrical form ({partial_derivative}{sub q}{sup 2} + {kappa}{sub W}){psi} = 0.
Date: January 9, 1998
Creator: Faraggi, A.E. & Matone, M.
Partner: UNT Libraries Government Documents Department

Adiabatic theory of Wannier threshold laws and ionization cross sections

Description: The Wannier threshold law for three-particle fragmentation is reviewed. By integrating the Schroedinger equation along a path where the reaction coordinate R is complex, anharmonic corrections to the simple power law are obtained. These corrections are found to be non-analytic in the energy E, in contrast to the expected analytic dependence upon E.
Date: December 31, 1994
Creator: Macek, J.H. & Ovchinnikov, S.Yu.
Partner: UNT Libraries Government Documents Department

Quantum theory of chemical reaction rates

Description: If one wishes to describe a chemical reaction at the most detailed level possible, i.e., its state-to-state differential scattering cross section, then it is necessary to solve the Schroedinger equation to obtain the S-matrix as a function of total energy E and total angular momentum J, in terms of which the cross sections can be calculated as given by equation (1) in the paper. All other physically observable attributes of the reaction can be derived from the cross sections. Often, in fact, one is primarily interested in the least detailed quantity which characterizes the reaction, namely its thermal rate constant, which is obtained by integrating Eq. (1) over all scattering angles, summing over all product quantum states, and Boltzmann-averaging over all initial quantum states of reactants. With the proper weighting factors, all of these averages are conveniently contained in the cumulative reaction probability (CRP), which is defined by equation (2) and in terms of which the thermal rate constant is given by equation (3). Thus, having carried out a full state-to-state scattering calculation to obtain the S-matrix, one can obtain the CRP from Eq. (2), and then rate constant from Eq. (3), but this seems like ``overkill``; i.e., if one only wants the rate constant, it would clearly be desirable to have a theory that allows one to calculate it, or the CRP, more directly than via Eq. (2), yet also correctly, i.e., without inherent approximations. Such a theory is the subject of this paper.
Date: October 1, 1994
Creator: Miller, W. H.
Partner: UNT Libraries Government Documents Department

Quantum leaps in philosophy of mind: Reply to Bourget'scritique

Description: David Bourget has raised some conceptual and technical objections to my development of von Neumann's treatment of the Copenhagen idea that the purely physical process described by the Schroedinger equation must be supplemented by a psychophysical process called the choice of the experiment by Bohr and Process 1 by von Neumann. I answer here each of Bourget's objections.
Date: July 26, 2004
Creator: Stapp, Henry P.
Partner: UNT Libraries Government Documents Department

Excitation and Ionization in H(1s)-H(1s) Collisions

Description: Hydrogen atom - hydrogen atom scattering is a prototype for many of the fundamental principles of atomic collisions. In this work we present an approximation to the H+H system for scattering in the intermediate energy regime of 1 to 100 keV. The approximation ignores electron exchange and two-electron excitation by assuming that one of the atoms is frozen in the 1s state. We allow for the evolution of the active electron by numerically solving the 3D Schroedinger equation. The results capture many features of the problem and are in harmony with recent theoretical studies. Excitation and ionization cross sections are computed and compared to other theory and experiment. New insight into the mechanism of excitation and ionization is inferred from the solutions.
Date: July 15, 1999
Creator: Riley, Merle E. & Ritchie, A. Burke
Partner: UNT Libraries Government Documents Department

Geometric jphases in self-induced transparency

Description: We consider the geometric phases arising in the lossless propagation of light pulses through a medium composed of near resonant two-level atoms. A reformulation of the coupled Maxwell-Schroedinger equations allows us to construct conservation laws in a general context. There exist periodic solutions of these equations which lead to the possibility of cyclical evolution of the state vector and the appearance of a geometric phase. We first show that if the ground state is the initial state of the system, then it acquires a geometric phase after the passage of the soliton pulses of McCall and Hahn. More generally if the initial state is a superposition of the two levels, continuous pulse trains can propagate without appreciable loss. We also find in this case that the state vector develops a geometric phase provided the parameters take on the particular values required for cyclical evolution. In both cases we exhibit the geometric character of the calculated phases by showing that they equal half the solid angle subtended by a closed curve traced by the Bloch, vector on the Bloch sphere. We verify a recent assertion of Anandan and Aharonov that the energy uncertainty in the state is directly related to the speed at which the tip of the Bloch vector moves along the curve on the Bloch sphere (or in more general terms the energy uncertainty is related to the speed in the projective Hilbert space).
Date: May 1, 1991
Creator: Sen, T. & Milovich, J.
Partner: UNT Libraries Government Documents Department

Homogeneous Canonical Formalism and Relativistic Wave Equations

Description: This thesis presents a development of classical canonical formalism and the usual transition schema to quantum dynamics. The question of transition from relativistic mechanics to relativistic quantum dynamics is answered by developing a homogeneous formalism which is relativistically invariant. Using this formalism the Klein-Gordon equation is derived as the relativistic analog of the Schroedinger equation. Using this formalism further, a method of generating other relativistic equations (with spin) is presented.
Date: January 1967
Creator: Jackson, Albert A.
Partner: UNT Libraries

The linear algebraic method for electron-molecule collisions

Description: In order to find numerical solutions to many problems in physics, chemistry and engineering it is necessary to place the equations of motion (classical or quantal) of the variables of dynamical interest on a discrete mesh. The formulation of scattering theory in quantum mechanics is no exception and leads to partial differential or integral equations which may only be solved on digital computers. Typical approaches introduce a numerical grid or basis set expansion of the scattering wavefunction in order to reduce `the problem to the solution of a set of algebraic equations. Often it is more convenient to deal with the scattering matrix or phase amplitude rather than the wavefunction but the essential features of the numerics are unchanged. In this section we will formulate the Linear Algebraic Method (LAM) for electron-atom/molecule scattering for a simple, one-dimensional radial potential. This will illustrate the basic approach and enable the uninitiated reader to follow the subsequent discussion of the general, multi-channel, electron-molecule formulation without undue difficulty. We begin by writing the Schroedinger equation for the s-wave scattering of a structureless particle by a short-range, local potential.
Date: September 1995
Creator: Collins, L. A. & Schneider, B. I.
Partner: UNT Libraries Government Documents Department

Coexistence of coherent and incoherent tunneling in asymmetric double-well potentials

Description: Double-well potentials are widely used to model phenomena in physics and chemistry. The system is assumed to be formed in a metastable state, its dynamical evolution providing the clues for the interpretation of the experimental data. Quantum mechanics predicts coherent oscillations of probability between wells if the double-well potential is nearly symmetric and irreversible exponential decay if the final well has an infinite width. For very asymmetric double-well potentials, these two extreme behaviors are expected to coexist. The purpose of the present paper is to investigate this coexistence and its evolution as a function of the width of (or density of states in) the second well. In this sense, increasing the density of states can be regarded as a mechanism for coherence breakdown. The dynamical evolution of the metastable state can be simulated by solving numerically the time-dependent Schroedinger equation (TDSE). This approach is general, intuitive, and gives access to time scales and dynamical effects. It also allows the inclusion of phenomenological dissipation.
Date: December 1, 1995
Creator: Carjan, N.; Grigorescu, M. & Strottman, D.
Partner: UNT Libraries Government Documents Department

A fully 3D atomistic quantum mechanical study on random dopant induced effects in 25nm MOSFETs

Description: We present a fully 3D atomistic quantum mechanical simulation for nanometered MOSFET using a coupled Schroedinger equation and Poisson equation approach. Empirical pseudopotential is used to represent the single particle Hamiltonian and linear combination of bulk band (LCBB) method is used to solve the million atom Schroedinger's equation. We studied gate threshold fluctuations and threshold lowering due to the discrete dopant configurations. We compared our results with semiclassical simulation results. We found quantum mechanical effects increase the threshold fluctuation while decreases the threshold lowering. The increase of threshold fluctuation is in agreement with previous study based on approximated density gradient approach to represent the quantum mechanical effect. However, the decrease in threshold lowering is in contrast with the previous density gradient calculations.
Date: July 11, 2008
Creator: Wang, Lin-Wang; Jiang, Xiang-Wei; Deng, Hui-Xiong; Luo, Jun-Wei; Li, Shu-Shen; Wang, Lin-Wang et al.
Partner: UNT Libraries Government Documents Department