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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

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 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

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

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

Notes on lie algebraic analysis of achromats

Description: Normal form technique is a powerful method to analyze the achromat problem. Assume the one cell map M{sub cell} = ARe{sup :h{sub 3}}:{sub e}{sup :h{sub 4}}: A{sup {minus}1}, where h{sub 3},h{sub 4} are the normal forms of the generators of the unit cell map, and A is the nonlinear transformation that brings M{sub cell} into its normal form; then the map of the whole system is M{sub N} = M{sub cell}{sup N} = AR{sup N} A{sup {minus}1} = I, provided that we can set e{sup :h{sub 3}}:, e{sup :h{sub 4}}, and R{sup N} to the identity (or only {delta} dependent) maps. Therefore, the conditions to form an achromat are h{sub 3} and h{sub 4} equal to zero (or {delta} dependent only) and the total linear map is identity. In this report, we will apply these conditions to a FODO array (a simple model system) to make it an achromat. We will start from Hamiltonians and work all the way up to obtain the analytical expressions of the required sextupole and octupole strengths.
Date: January 1, 1995
Creator: Wang, Chunxi & Chao, A.
Partner: UNT Libraries Government Documents Department

Theory of gain in group-III nitride lasers

Description: A microscopic theory of gain in a group-III nitride quantum well laser is presented. The approach, which treats carrier correlations at the level of quantum kinetic theory, gives a consistent account of plasma and excitonic effects in an inhomogeneously broadened system.
Date: June 1, 1997
Creator: Chow, W.W.; Wright, A.F. & Girndt, A.
Partner: UNT Libraries Government Documents Department

Towards a next-to-leading logarithmic result in B {r_arrow} X{sub s}{gamma}

Description: The calculation of the O ({alpha}{sub s}) virtual corrections to the matrix element of the inclusive decay b {r_arrow} s{gamma} is reported. These contributions drastically reduce the large renormalization scale dependence of the leading logarithmic calculation. Combining these results with the preliminary result for the Wilson coefficient C{sub {gamma}} (m{sub b}) calculated recently by Chetyrkin, Misiak, and Muenz, we estimate the branching ratio to be BR(B {r_arrow} X{sub s} {gamma}) = (3.25 {plus_minus} 0.50) x 10{sup {minus}4}.
Date: August 1, 1996
Creator: Greub, C. & Hurth, T.
Partner: UNT Libraries Government Documents Department

Paraxial expansion of a static magnetic field in a ring accelerator

Description: In the paraxial approximation, trajectories of beam particles in a ring accelerator are computed expanded in powers of lateral displacements and slopes from a closed reference orbit. To do this, one needs first the expanded expressions of the magnetic field and potentials producing the particle motion. This is derived here in a most general form.
Date: June 1, 1995
Creator: Teng, L.C.
Partner: UNT Libraries Government Documents Department

No strings attached potential vs. interaction energy in QCD

Description: In infrared-stable fixed-point field theories, the interaction energy of a test particle is proportional to the non-relativistic (heavy source) coordinate-space potential derived from the field strength produced by that source. This is no longer true in ultraviolet-stable fixed-point field theories (UVSFPFT) as they may not have a finite infrared fixed point. This leads to the possibility that UVSFPFTs may have quite conventional field strength distributions despite the unusual spatial dependence expected for the interaction energy.
Date: October 20, 1996
Creator: Goldman, T.
Partner: UNT Libraries Government Documents Department

The second-order tune shift with amplitude for octupole-induced resonances in storage ring

Description: The purpose of this note is to analyze the octupole-induced resonances, to lowest order, in a synchrotron and storage ring. When the Hamiltonian with octupole term is transformed to action-angle variables, it is found that the amplitude-dependent tune shift terms are composed of two types: terms of second-order in betatron oscillation amplitude of a particle and terms of fourth-order in oscillation amplitude. Obtaining fourth-order terms requires complicated analysis even with the first-order perturbation theory employed. Treatment of this analysis will be the subject of a subsequent note. Second-order terms are straightforward and simple to calculate, and therefore they treat them here first.
Date: September 1, 1988
Creator: Yoon, M.
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

Crab crossing in a large hadron collider

Description: Since its invention by Palmer in 1988, crab crossing has been explored by many people for both linear and storage ring collides to allow for an angle crossing without a loss of luminosity. Various crab crossing scenarios have been incorporated in the design of newly proposed linear collides and {Beta}-factory projects. For a hadron collider, this scheme can also be employed to lower {Beta}* at the interaction point for a higher luminosity. In this paper, we first review the principle and operational requirements of various crab crossing schemes for storage ring collides. A Hamiltonian formalism is developed to study the dynamics of crab crossing and the related synchro-betatron coupling. Requirements are obtained for the operational voltage and frequency of the crab cavities, and for the accuracy of voltage matching and phase matching of the cavities. For the recently proposed high-field hadron collider, a deflection crabbing scheme can be used to reduce {Beta}* from 0. 1 m to 0.05 m and below, without a loss of luminosity due to angle crossing. The required voltage of the storage rf system is reduced from 100 MV to below 10 MV. With the same frequency of 379 MHz operating in a transverse mode, the required voltage of the crab cavities is about 3.2{approximately}4.4 MV. The required accuracy of voltage and betatron-phase matching is about 1 %.
Date: December 1, 1996
Creator: Wei, Jie
Partner: UNT Libraries Government Documents Department