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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

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

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

The Role of Nuclear Motion in the Photo-Double Ionization ofMolecular Hydrogen

Description: We examine the origin of recently observed variations with internuclear distance (R) of the fully differential cross sections for double ionization of aligned H2 by absorption of a single photon. Using the results of fully converged numerical solutions of the Schroedinger equation, we show that these variations arise primarily from pronounced differences in the R-dependence of the parallel and perpendicular components of the ionization amplitude. We also predict that R-dependences should be readily observable in the asymmetry parameter for photo-double ionization, even in experimental measurements that are not differential in the energy sharings between ejected photo-electrons.
Date: October 26, 2006
Creator: Horner, Daniel A.; Vanroose, Wim; Rescigno, Thomas N.; Martin,Fernando & McCurdy, C. William
Partner: UNT Libraries Government Documents Department

Orbital HP-Clouds for Solving Schr?dinger Equation inQuantum Mechanics

Description: Solving Schroedinger equation in quantum mechanics presents a challenging task in numerical methods due to the high order behavior and high dimension characteristics in the wave functions, in addition to the highly coupled nature between wave functions. This work introduces orbital and polynomial enrichment functions to the partition of unity for solution of Schroedinger equation under the framework of HP-Clouds. An intrinsic enrichment of orbital function and extrinsic enrichment of monomial functions are proposed. Due to the employment of higher order basis functions, a higher order stabilized conforming nodal integration is developed. The proposed methods are implemented using the density functional theory for solution of Schroedinger equation. Analysis of several single and multi-electron/nucleus structures demonstrates the effectiveness of the proposed method.
Date: October 19, 2006
Creator: Chen, J; Hu, W & Puso, M
Partner: UNT Libraries Government Documents Department

Spectral Equations-Of-State Theory for Dense, Partially Ionized Matter

Description: The Schroedinger equation is solved in time and space to implement a finite-temperature equation-of-state theory for dense, partially ionized matter. The time-dependent calculation generates a spectrum of quantum states. Eigenfunctions are calculated from a knowledge of the spectrum and used to calculate the electronic pressure and energy. Results are given for LID and compared with results from the INFERNO model.
Date: May 14, 2004
Creator: Ritchie, A B
Partner: UNT Libraries Government Documents Department

Modeling femtosecond pulse propagation in optical fibers.

Description: Femtosecond pulse propagation in optical fibers requires consideration of higher-order nonlinear effects when implementing the non-linear Schroedinger equation. We show excellent agreement of our model with experimental results both for the temporal and phase features of the pulses. Ultrafast pulse propagation in optical fibers presents a number of challenges given the effect of nonlinearities which become important on such a short time scale. The modeling of femtosecond pulse propagation becomes, consequently, a harder task which has to account for all these effects. In this work, we have included higher order corrections in the non-linear Schroedinger equation and compared the numerical simulation results with experimental data. Our work, besides taking into account the temporal evolution of the pulse, keeps into account also the phase behavior of the electric field, which we compare with experimental results obtained with Frequency Resolved Optical Gating [l]. We also account for self-frequency shift of the pulse and obtain excellent agreement with the experimental results on the Raman shift.
Date: January 1, 2001
Creator: Chung, Y. J. (Yeo-Jin); Schaefer, T. B. (Tobias B.); Gabitov, I. R. (Ildar R.); Omenetto, F. G. (Fiorenzo G.) & Taylor, Antoinette J.,
Partner: UNT Libraries Government Documents Department

Grid-based methods for diatomic quantum scattering problems II: Time-dependent treatment of single- and two-photon ionization of H2+

Description: The time-dependent Schr\"odinger equation for H2+ in a time-varying electromagnetic field is solved in the fixed-nuclei approximation using a previously developed finite-element/ discrete variable representation in prolate spheroidal coordinates. Amplitudes for single- and two-photon ionization are obtained using the method of exterior complex scaling to effectively propagate the field-free solutions from the end of the radiation pulse to infinite times. Cross sections are presented for one-and two-photon ionization for both parallel and perpendicular polarization of the photon field, as well as photoelectron angular distributions for two-photon ionization.
Date: April 20, 2009
Creator: Rescigno, Thomas N.; Tao, L. & McCurdy, C.W.
Partner: UNT Libraries Government Documents Department

Nuclear Recoil Cross Sections from Time-dependent Studies of Two-Photon Double Ionization of Helium

Description: We examine the sensitivity of nuclear recoil cross sections produced by two-photon double ionization of helium to the underlying triple differential cross sections (TDCS) used in their computation. We show that this sensitivity is greatest in the energy region just below the threshold for sequential double ionization. Accurate TDCS, extracted from non-perturbative solutions of the time-dependent Schroedinger equation, are used here in new computations of the nuclear recoil cross section.
Date: December 21, 2009
Creator: Horner, Daniel A.; Rescigno, Thomas N. & McCurdy, C. William
Partner: UNT Libraries Government Documents Department

Long-time solution of the time-dependent Schroedinger equation for an atom in an electromagnetic field using complex coordinate contours

Description: We demonstrate that exterior complex scaling (ECS) can be used to impose outgoing wave boundary conditions exactly on solutions of the time-dependent Schrodinger equation for atoms in intense electromagnetic pulses using finite grid methods. The procedure is formally exact when applied in the appropriate gauge and is demonstrated in a calculation of high harmonic generation in which multiphoton resonances are seen for long pulse durations. However, we also demonstrate that while the application of ECS in this way is formally exact, numerical error can appear for long time propagations that can only be controlled by extending the finite grid. A mathematical analysis of the origins of that numerical error, illustrated with an analytically solvable model, is also given.
Date: September 8, 2009
Creator: Tao, Liang; Vanroose, Wim; Reps, Brian; Rescigno, Thomas N. & McCurdy, C. William
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 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