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Towards bulk based preconditioning for quantum dotcomputations

Description: This article describes how to accelerate the convergence of Preconditioned Conjugate Gradient (PCG) type eigensolvers for the computation of several states around the band gap of colloidal quantum dots. Our new approach uses the Hamiltonian from the bulk materials constituent for the quantum dot to design an efficient preconditioner for the folded spectrum PCG method. The technique described shows promising results when applied to CdSe quantum dot model problems. We show a decrease in the number of iteration steps by at least a factor of 4 compared to the previously used diagonal preconditioner.
Date: May 25, 2006
Creator: Dongarra, Jack; Langou, Julien; Tomov, Stanimire; Channing,Andrew; Marques, Osni; Vomel, Christof et al.
Partner: UNT Libraries Government Documents Department

Multiple Valley Couplings in Nanometer Si MOSFETs

Description: We investigate the couplings between different energy band valleys in a MOSFET device using self-consistent calculations of million-atom Schroedinger-Poisson Equations. Atomistic empirical pseudopotentials are used to describe the device Hamiltonian and the underlying bulk band structure. The MOSFET device is under nonequilibrium condition with a source-drain bias up to 2V, and a gate potential close to the threshold potential. We find that all the intervalley couplings are small, with the coupling constants less than 3 meV. As a result, the system eigenstates derived from different bulk valleys can be calculated separately. This will significantly reduce the simulation time, because the diagonalization of the Hamiltonian matrix scales as the third power of the total number of basis functions.
Date: July 11, 2008
Creator: Wang, Lin-Wang; Deng, Hui-Xiong; Jiang, Xiang-Wei; Luo, Jun-Wei; Li, Shu-Shen; Xia, Jian-Bai et al.
Partner: UNT Libraries Government Documents Department

LR: Compact connectivity representation for triangle meshes

Description: We propose LR (Laced Ring) - a simple data structure for representing the connectivity of manifold triangle meshes. LR provides the option to store on average either 1.08 references per triangle or 26.2 bits per triangle. Its construction, from an input mesh that supports constant-time adjacency queries, has linear space and time complexity, and involves ordering most vertices along a nearly-Hamiltonian cycle. LR is best suited for applications that process meshes with fixed connectivity, as any changes to the connectivity require the data structure to be rebuilt. We provide an implementation of the set of standard random-access, constant-time operators for traversing a mesh, and show that LR often saves both space and traversal time over competing representations.
Date: January 28, 2011
Creator: Gurung, T; Luffel, M; Lindstrom, P & Rossignac, J
Partner: UNT Libraries Government Documents Department

A Hamiltonian-Free Description of Single Particle Dynamics for Hopelessly Complex Periodic Systems

Description: We develop a picture of periodic systems which does not rely on the Hamiltonian of the system but on maps between a finite number of time locations. Moser or Deprit-like normalizations are done directly on the maps thereby avoiding the complex time-dependent theory. We redefine linear and nonlinear Floquet variables entirely in terms of maps. This approach relies heavily on the Lie representation of maps introduced by Dragt and Finn. One might say that although we do not use the Hamiltonian in the normalization transformation, we are using Lie operators which are themselves, in some sense, pseudo-Hamiltonians for the maps they represent. Our techniques find application in accelerator dynamics or in any field where the Hamiltonian is periodic but hopelessly complex, such as magnetic field design in stellarators.
Date: January 1, 1990
Creator: Forest, E.
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

Quantum adiabatic computation with a constant gap is not useful in one dimension

Description: We show that it is possible to use a classical computer to efficiently simulate the adiabatic evolution of a quantum system in one dimension with a constant spectral gap, starting the adiabatic evolution from a known initial product state. The proof relies on a recently proven area law for such systems, implying the existence of a good matrix product representation of the ground state, combined with an appropriate algorithm to update the matrix product state as the Hamiltonian is changed. This implies that adiabatic evolution with such Hamiltonians is not useful for universal quantum computation. Therefore, adiabatic algorithms which are useful for universal quantum computation either require a spectral gap tending to zero or need to be implemented in more than one dimension (we leave open the question of the computational power of adiabatic simulation with a constant gap in more than one dimension).
Date: January 1, 2009
Creator: Hastings, Matthew
Partner: UNT Libraries Government Documents Department

Three-Nucleon Electroweak Capture Reactions

Description: Recent advances in the study of the p-d radiative and mu-3he weak capture processes are presented and discussed. The three-nucleon bound and scattering states are obtained using the correlated-hyperspherical-harmonics method, with realistic Hamiltonians consisting of the Argonne v14 or Argonne v18 two-nucleon and Tucson-Melbourne or Urbana IX three-nucleon interactions. The electromagnetic and weak transition operators include one- and two-body contributions. The theoretical accuracy achieved in these calculations allows for interesting comparisons with experimental data.
Date: October 1, 2002
Creator: Marcucci, L.E.; Viviani, M.; Kievsky, A.; Rosati, S. & Schiavilla, R.
Partner: UNT Libraries Government Documents Department

b {r_arrow} sl{sup +}l{sup {minus}} in the left-right symmetric model

Description: We begin to analyze and contrast the predictions for the decay b {r_arrow} sl{sup +}l{sup {minus}} in the Left-Right Symmetric Model (LMR) with those of the Standard Model (SM). In particular, we show that the forward-backward asymmetry of the lepton spectrum can be used to distinguish the SM from the simplest manifestation of the LRM.
Date: May 1, 1997
Creator: Rizzo, T.G.
Partner: UNT Libraries Government Documents Department

Methods of beam cooling

Description: Diverse methods which are available for particle beam cooling are reviewed. They consist of some highly developed techniques such as radiation damping, electron cooling, stochastic cooling and the more recently developed, laser cooling. Methods which have been theoretically developed, but not yet achieved experimentally, are also reviewed. They consist of ionization cooling, laser cooling in three dimensions and stimulated radiation cooling.
Date: February 1, 1996
Creator: Sessler, A.M.
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

The n-particle picture and the calculation of the electronic structure of atoms, molecules, and solids

Description: The works referred to above indicate the usefulness of viewing an N-particle system from a higher-dimensional perspective. In doing so, one should attempt to strike a balance between conceptual clarity and computational efficiency, which mitigates against considering calculations in 3n-dimensional space except for rather small values of n. It appears that such a procedure may be profitably employed if a system of N particles were to be considered as consisting of a collection of units or sets, (I{sub k}), each containing n{sub k} particles so that {Sigma}{sub k} n{sub k} = N. The resulting problem associated with these sets of particles that interact with one another is obviously formally identical to the original one. However, it possesses the formal advantage of allowing, in principle, the systematic approach to an exact solution by treating the entire system as a single unit. The operative words here are in principle, as practical applications do not seem to be possible but for the smallest number of particles in a unit, say n = 2 or n = 3. However, in such an implementation, the interparticle correlation is treated directly and explicitly within a unit, resulting in a more accurate treatment of the system the larger the number of particle in a unit.
Date: August 1, 1997
Creator: Gonis, A.; Turchi, P.E.A.; Schulthess, T.C. & Ek, J. van
Partner: UNT Libraries Government Documents Department

SYMMETRY, HAMILTONIAN PROBLEMS AND WAVELETS IN ACCELERATOR PHYSICS

Description: In this paper the authors consider applications of methods from wavelet analysis to nonlinear dynamical problems related to accelerator physics. In this approach they take into account underlying algebraical, geometrical and topological structures of corresponding problems.
Date: March 31, 2000
Creator: FEDOROVA,A.; ZEITLIN,M. & PARSA,Z.
Partner: UNT Libraries Government Documents Department

The algebras of large N matrix mechanics

Description: Extending early work, we formulate the large N matrix mechanics of general bosonic, fermionic and supersymmetric matrix models, including Matrix theory: The Hamiltonian framework of large N matrix mechanics provides a natural setting in which to study the algebras of the large N limit, including (reduced) Lie algebras, (reduced) supersymmetry algebras and free algebras. We find in particular a broad array of new free algebras which we call symmetric Cuntz algebras, interacting symmetric Cuntz algebras, symmetric Bose/Fermi/Cuntz algebras and symmetric Cuntz superalgebras, and we discuss the role of these algebras in solving the large N theory. Most important, the interacting Cuntz algebras are associated to a set of new (hidden!) local quantities which are generically conserved only at large N. A number of other new large N phenomena are also observed, including the intrinsic nonlocality of the (reduced) trace class operators of the theory and a closely related large N field identification phenomenon which is associated to another set (this time nonlocal) of new conserved quantities at large N.
Date: September 16, 1999
Creator: Halpern, M.B. & Schwartz, C.
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

HIGH-ENERGY COLLIDING CRYSTALS - A THEORETICAL STUDY

Description: Recent theoretical investigations of beam crystallization using computer modeling based on the method of molecular dynamics (MD) and analytical approach based on the phonon theory are motivated by the study of colliding crystalline beams [4]. Analytical study of crystal stability in an alternating-gradient (AG) focusing ring was previously limited to the smooth approximation. In a typical ring, results obtained under such approximation largely agrees with that obtained with the MD simulation. However, as we explore ring lattices appropriate for beam crystallization at high energies (Lorentz factor y much larger than the transverse tunes v,, vy) [5], this approximation fails. Here, we present a newly developed phonon theory in a time-dependent Hamiltonian system representing the actual AG-focusing ring and predict the stability of 1D crystals at high energies. Luminosity enhancement is illustrated in examples of rare-ion colliders based on ordered 1D strings of ions.
Date: September 10, 2007
Creator: WEI,J.
Partner: UNT Libraries Government Documents Department

An Algebraic Approach to the Evolution of Emittances upon Crossing the Linear Coupling Difference Resonance

Description: One of the hallmarks of linear coupling is the resonant exchange of oscillation amplitude between the horizontal and vertical planes when the difference between the unperturbed tunes is close to an integer. The standard derivation of this phenomenon (known as the difference resonance) can be found, for example, in the classic papers of Guignard [1, 2]. One starts with an uncoupled lattice and adds a linear perturbation that couples the two planes. The equations of motion are expressed in hamiltonian form. As the difference between the unperturbed tunes approaches an integer, one finds that the perturbing terms in the hamiltonian can be divided into terms that oscillate slowly and ones that oscillate rapidly. The rapidly oscillating terms are discarded or transformed to higher order with an appropriate canonical transformation. The resulting approximate hamiltonian gives equations of motion that clearly exhibit the exchange of oscillation amplitude between the two planes. If, instead of the hamiltonian, one is given the four-by-four matrix for one turn around a synchrotron, then one has the complete solution for the turn-by-turn (TBT) motion. However, the conditions for the phenomenon of amplitude exchange are not obvious from a casual inspection of the matrix. These conditions and those that give rise to the related sum resonance are identified in this report. The identification is made using the well known formalism of Edwards and Teng [3, 4, 5] and, in particular, the normalized coupling matrix of Sagan and Rubin [6]. The formulae obtained are general in that no particular hamiltonian or coupling elements are assumed. The only assumptions are that the one-turn matrix is symplectic and that it has distinct eigenvalues on the unit circle in the complex plane. Having identified the conditions of the one-turn matrix that give rise to the resonances, we focus on the difference resonance ...
Date: September 1, 2008
Creator: Gardner,C.
Partner: UNT Libraries Government Documents Department

Transverse Mode Coupling Instability in a Double RF System

Description: The equations for transverse mode coupling in a storage ring with a double rf system are derived from a Hamiltonian formalism. The resulting integral equation is expanded into a set of orthogonal polynomials, and the expansion coefficients are then given by the solution of an infinite determinant. Truncation of this determinant permits solution of the problem on a computer, and a code has been written which finds the complex mode frequencies. The stability limits of LEP with a third harmonic are determined by equating the imaginary part of the solution to the radiation damping rate.
Date: February 1, 1993
Creator: Chin, Y.-H.
Partner: UNT Libraries Government Documents Department

S-matrix Calculations of Energy Levels of the Lithium Isoelectronic Sequence

Description: A QED approach to the calculation of the spectra of the lithium isoelectronic sequence is implemented. A modified Furry representation based on the Kohn-Sham potential is used to evaluate all one- and two-photon diagrams with the exception of the two-loop Lamb shift. Three-photon diagrams are estimated with Hamiltonian methods. After incorporating recent calculations of the two-loop Lamb shift and recoil corrections a comprehensive tabulation of the 2s, 2p{sub 1/2} and 2p{sub 3/2} energy levels as well as the 2s - 2p{sub 1/2} and 2s - 2p{sub 3/2} transition energies for Z = 10 - 100 is presented.
Date: November 2, 2010
Creator: sapirstein, J & Cheng, K T
Partner: UNT Libraries Government Documents Department

Mesoscale modeling of irreversible volume growth in powders of anisotropic crystals

Description: Careful thermometric analysis (TMA) on powders of micron-sized triamino-trinitrobenzene (TATB) crystallites are shown to display irreversible growth in volume when subjected to repeated cycles of heating and cooling. Such behavior is counter-intuitive to typical materials response to simulated annealing cycles in atomic-scale molecular dynamics. However, through coarse-grained simulations using a mesoscale Hamiltonian we quantitatively reproduce irreversible growth behavior in such powdered material. We demonstrate that irreversible growth happens only in the presence of intrinsic crystalline anisotropy, and is mediated by particles much smaller than the average crystallite size.
Date: May 5, 2006
Creator: Gee, R; Maiti, A & Fried, L
Partner: UNT Libraries Government Documents Department

Structure of A = 10 - 13 Nuclei with Two- Plus Three-Nucleon Interactions from Chiral Effective Field Theory

Description: Properties of finite nuclei are evaluated with two-nucleon (NN) and three-nucleon (NNN) interactions derived within chiral effective field theory (EFT). The nuclear Hamiltonian is fixed by properties of the A = 2 system, except for two low-energy constants (LECs) that parameterize the short range NNN interaction. We constrain those two LECs by a fit to the A = 3 system binding energy and investigate sensitivity of {sup 4}He, {sup 6}Li, {sup 10,11}B and {sup 12,13}C properties to the variation of the constrained LECs. We identify a preferred choice that gives globally the best description. We demonstrate that the NNN interaction terms significantly improve the binding energies and spectra of mid-p-shell nuclei not just with the preferred choice of the LECs but even within a wide range of the constrained LECs. At the same time, we find that a very high quality description of these nuclei requires further improvements to the chiral Hamiltonian.
Date: January 10, 2007
Creator: Navratil, P; Gueorguiev, V; Vary, J P; Ormand, W E & Nogga, A
Partner: UNT Libraries Government Documents Department

Stochastic Hard-Sphere Dynamics for Hydrodynamics of Non-Ideal Fluids

Description: A novel stochastic fluid model is proposed with a nonideal structure factor consistent with compressibility, and adjustable transport coefficients. This stochastic hard-sphere dynamics (SHSD) algorithm is a modification of the direct simulation Monte Carlo algorithm and has several computational advantages over event-driven hard-sphere molecular dynamics. Surprisingly, SHSD results in an equation of state and a pair correlation function identical to that of a deterministic Hamiltonian system of penetrable spheres interacting with linear core pair potentials. The fluctuating hydrodynamic behavior of the SHSD fluid is verified for the Brownian motion of a nanoparticle suspended in a compressible solvent.
Date: February 26, 2008
Creator: Donev, A; Alder, B J & Garcia, A L
Partner: UNT Libraries Government Documents Department

Relativistic Bound States

Description: The Hamiltonian for Dirac's second-order equation depends nonlinearly on the potential V and the energy E. For this reason the magnetic contribution to the Hamiltonian for s-waves, which has a short range, is attractive for a repulsive Coulomb potential (V > 0) and repulsive for an attractive Coulomb potential (V < 0). Previous studies are confined to the latter case, where strong net attraction near a high-Z nucleus accelerates electrons to velocities close to the speed of light. The Hamiltonian is linear in the product EV/mc{sup 2}. Usually solutions are found in the regime E = mc{sup 2} + {var_epsilon}, where except for high Z, |{var_epsilon}| << mc{sup 2}. Here they show that for V > 0 the attractive magnetic term and the repulsive linear term combine to support a bound state at E = 0.5 mc{sup 2} corresponding to a binding energy E{sub b} = -{var_epsilon} = 0.5 mc{sup 2}.
Date: December 12, 2005
Creator: Ritchie, A B
Partner: UNT Libraries Government Documents Department

RELATIVISTIC EFFECTS ON THE EQUATION OF STATE OF THE LIGHT ACTINIDES

Description: The effect of the relativistic spin-orbit (SO) interaction on the bonding in the early actinides has been investigated by means of electronic-structure calculations. Specifically, the equation of state (EOS) for the face-centered cubic (fcc) model systems of these metals have been calculated from the first-principles density-functional theory (DFT). Traditionally, the SO interaction in electronic-structure methods is implemented as a perturbation to the Hamiltonian that is solved for basis functions that explicitly do not depend on SO coupling. Here this approximation is shown to compare well with the fully relativistic Dirac treatment. It is further shown that SO coupling has a gradually increasing effect on the EOS as one proceeds through the actinides and the effect is diminished as density increases.
Date: November 4, 2005
Creator: Landa, A & Soderlind, P
Partner: UNT Libraries Government Documents Department