Effective Hamiltonians for phosphorene and silicene

DOE PAGES

Lew Yan Voon, L. C.; Lopez-Bezanilla, A.; Wang, J.; ...

2015-02-04

Here, we derived the effective Hamiltonians for silicene and phosphorene with strain, electric field and magnetic field using the method of invariants. Our paper extends the work on silicene, and on phosphorene. Our Hamiltonians are compared to an equivalent one for graphene. For silicene, the expression for band warping is obtained analytically and found to be of different order than for graphene.We prove that a uniaxial strain does not open a gap, resolving contradictory numerical results in the literature. For phosphorene, it is shown that the bands near the Brillouin zone center only have terms in even powers of themore » wave vector.We predict that the energies change quadratically in the presence of a perpendicular external electric field but linearly in a perpendicular magnetic field, as opposed to those for silicene which vary linearly in both cases. Preliminary ab initio calculations for the intrinsic band structures have been carried out in order to evaluate some of the k · p parameters.« less

Hamiltonian purification

DOE Office of Scientific and Technical Information (OSTI.GOV)

Orsucci, Davide; Burgarth, Daniel; Facchi, Paolo

The problem of Hamiltonian purification introduced by Burgarth et al. [Nat. Commun. 5, 5173 (2014)] is formalized and discussed. Specifically, given a set of non-commuting Hamiltonians (h{sub 1}, …, h{sub m}) operating on a d-dimensional quantum system ℋ{sub d}, the problem consists in identifying a set of commuting Hamiltonians (H{sub 1}, …, H{sub m}) operating on a larger d{sub E}-dimensional system ℋ{sub d{sub E}} which embeds ℋ{sub d} as a proper subspace, such that h{sub j} = PH{sub j}P with P being the projection which allows one to recover ℋ{sub d} from ℋ{sub d{sub E}}. The notions of spanning-set purificationmore » and generator purification of an algebra are also introduced and optimal solutions for u(d) are provided.« less

Fernbank Science Center Forest Teacher's Guide-1967.

ERIC Educational Resources Information Center

Cherry, Jim; And Others

This guide is designed primarily to familiarize teachers with the types of programs available through the Fernback Science Center. Instructional programs involving the use of the Fernbank Forest are outlined. Programs for secondary students include Plant Taxonomy, Field Ecology, Winter Taxonomy of Plants, and Climax Forest Succession. Elementary…

Variational symplectic algorithm for guiding center dynamics in the inner magnetosphere

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li Jinxing; Pu Zuyin; Xie Lun

Charged particle dynamics in magnetosphere has temporal and spatial multiscale; therefore, numerical accuracy over a long integration time is required. A variational symplectic integrator (VSI) [H. Qin and X. Guan, Phys. Rev. Lett. 100, 035006 (2008) and H. Qin, X. Guan, and W. M. Tang, Phys. Plasmas 16, 042510 (2009)] for the guiding-center motion of charged particles in general magnetic field is applied to study the dynamics of charged particles in magnetosphere. Instead of discretizing the differential equations of the guiding-center motion, the action of the guiding-center motion is discretized and minimized to obtain the iteration rules for advancing themore » dynamics. The VSI conserves exactly a discrete Lagrangian symplectic structure and has better numerical properties over a long integration time, compared with standard integrators, such as the standard and adaptive fourth order Runge-Kutta (RK4) methods. Applying the VSI method to guiding-center dynamics in the inner magnetosphere, we can accurately calculate the particles'orbits for an arbitrary long simulating time with good conservation property. When a time-independent convection and corotation electric field is considered, the VSI method can give the accurate single particle orbit, while the RK4 method gives an incorrect orbit due to its intrinsic error accumulation over a long integrating time.« less

Branched Hamiltonians and supersymmetry

DOE PAGES

Curtright, Thomas L.; Zachos, Cosmas K.

2014-03-21

Some examples of branched Hamiltonians are explored both classically and in the context of quantum mechanics, as recently advocated by Shapere and Wilczek. These are in fact cases of switchback potentials, albeit in momentum space, as previously analyzed for quasi-Hamiltonian chaotic dynamical systems in a classical setting, and as encountered in analogous renormalization group flows for quantum theories which exhibit RG cycles. In conclusion, a basic two-worlds model, with a pair of Hamiltonian branches related by supersymmetry, is considered in detail.

Understanding nuclear motions in molecules: Derivation of Eckart frame ro-vibrational Hamiltonian operators via a gateway Hamiltonian operator

DOE Office of Scientific and Technical Information (OSTI.GOV)

Szalay, Viktor, E-mail: szalay.viktor@wigner.mta.hu

A new ro-vibrational Hamiltonian operator, named gateway Hamiltonian operator, with exact kinetic energy term, T-hat, is presented. It is in the Eckart frame and it is of the same form as Watson’s normal coordinate Hamiltonian. However, the vibrational coordinates employed are not normal coordinates. The new Hamiltonian is shown to provide easy access to Eckart frame ro-vibrational Hamiltonians with exact T-hat given in terms of any desired set of vibrational coordinates. A general expression of the Eckart frame ro-vibrational Hamiltonian operator is given and some of its properties are discussed.

Perspective: Quantum Hamiltonians for optical interactions

NASA Astrophysics Data System (ADS)

Andrews, David L.; Jones, Garth A.; Salam, A.; Woolley, R. Guy

2018-01-01

The multipolar Hamiltonian of quantum electrodynamics is extensively employed in chemical and optical physics to treat rigorously the interaction of electromagnetic fields with matter. It is also widely used to evaluate intermolecular interactions. The multipolar version of the Hamiltonian is commonly obtained by carrying out a unitary transformation of the Coulomb gauge Hamiltonian that goes by the name of Power-Zienau-Woolley (PZW). Not only does the formulation provide excellent agreement with experiment, and versatility in its predictive ability, but also superior physical insight. Recently, the foundations and validity of the PZW Hamiltonian have been questioned, raising a concern over issues of gauge transformation and invariance, and whether observable quantities obtained from unitarily equivalent Hamiltonians are identical. Here, an in-depth analysis of theoretical foundations clarifies the issues and enables misconceptions to be identified. Claims of non-physicality are refuted: the PZW transformation and ensuing Hamiltonian are shown to rest on solid physical principles and secure theoretical ground.

Hamiltonian thermostats fail to promote heat flow

NASA Astrophysics Data System (ADS)

Hoover, Wm. G.; Hoover, Carol G.

2013-12-01

Hamiltonian mechanics can be used to constrain temperature simultaneously with energy. We illustrate the interesting situations that develop when two different temperatures are imposed within a composite Hamiltonian system. The model systems we treat are ϕ4 chains, with quartic tethers and quadratic nearest-neighbor Hooke's-law interactions. This model is known to satisfy Fourier's law. Our prototypical problem sandwiches a Newtonian subsystem between hot and cold Hamiltonian reservoir regions. We have characterized four different Hamiltonian reservoir types. There is no tendency for any of these two-temperature Hamiltonian simulations to transfer heat from the hot to the cold degrees of freedom. Evidently steady heat flow simulations require energy sources and sinks, and are therefore incompatible with Hamiltonian mechanics.

On the domain of the Nelson Hamiltonian

NASA Astrophysics Data System (ADS)

Griesemer, M.; Wünsch, A.

2018-04-01

The Nelson Hamiltonian is unitarily equivalent to a Hamiltonian defined through a closed, semibounded quadratic form, the unitary transformation being explicitly known and due to Gross. In this paper, we study the mapping properties of the Gross-transform in order to characterize the regularity properties of vectors in the form domain of the Nelson Hamiltonian. Since the operator domain is a subset of the form domain, our results apply to vectors in the domain of the Hamiltonian as well. This work is a continuation of our previous work on the Fröhlich Hamiltonian.

Singular reduction of resonant Hamiltonians

NASA Astrophysics Data System (ADS)

Meyer, Kenneth R.; Palacián, Jesús F.; Yanguas, Patricia

2018-06-01

We investigate the dynamics of resonant Hamiltonians with n degrees of freedom to which we attach a small perturbation. Our study is based on the geometric interpretation of singular reduction theory. The flow of the Hamiltonian vector field is reconstructed from the cross sections corresponding to an approximation of this vector field in an energy surface. This approximate system is also built using normal forms and applying reduction theory obtaining the reduced Hamiltonian that is defined on the orbit space. Generically, the reduction is of singular character and we classify the singularities in the orbit space, getting three different types of singular points. A critical point of the reduced Hamiltonian corresponds to a family of periodic solutions in the full system whose characteristic multipliers are approximated accordingly to the nature of the critical point.

Hamiltonian closures in fluid models for plasmas

NASA Astrophysics Data System (ADS)

Tassi, Emanuele

2017-11-01

This article reviews recent activity on the Hamiltonian formulation of fluid models for plasmas in the non-dissipative limit, with emphasis on the relations between the fluid closures adopted for the different models and the Hamiltonian structures. The review focuses on results obtained during the last decade, but a few classical results are also described, in order to illustrate connections with the most recent developments. With the hope of making the review accessible not only to specialists in the field, an introduction to the mathematical tools applied in the Hamiltonian formalism for continuum models is provided. Subsequently, we review the Hamiltonian formulation of models based on the magnetohydrodynamics description, including those based on the adiabatic and double adiabatic closure. It is shown how Dirac's theory of constrained Hamiltonian systems can be applied to impose the incompressibility closure on a magnetohydrodynamic model and how an extended version of barotropic magnetohydrodynamics, accounting for two-fluid effects, is amenable to a Hamiltonian formulation. Hamiltonian reduced fluid models, valid in the presence of a strong magnetic field, are also reviewed. In particular, reduced magnetohydrodynamics and models assuming cold ions and different closures for the electron fluid are discussed. Hamiltonian models relaxing the cold-ion assumption are then introduced. These include models where finite Larmor radius effects are added by means of the gyromap technique, and gyrofluid models. Numerical simulations of Hamiltonian reduced fluid models investigating the phenomenon of magnetic reconnection are illustrated. The last part of the review concerns recent results based on the derivation of closures preserving a Hamiltonian structure, based on the Hamiltonian structure of parent kinetic models. Identification of such closures for fluid models derived from kinetic systems based on the Vlasov and drift-kinetic equations are presented, and

Hamiltonian approach to slip-stacking dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, S. Y.; Ng, K. Y.

Hamiltonian dynamics has been applied to study the slip-stacking dynamics. The canonical-perturbation method is employed to obtain the second-harmonic correction term in the slip-stacking Hamiltonian. The Hamiltonian approach provides a clear optimal method for choosing the slip-stacking parameter and improving stacking efficiency. The dynamics are applied specifically to the Fermilab Booster-Recycler complex. As a result, the dynamics can also be applied to other accelerator complexes.

Hamiltonian approach to slip-stacking dynamics

DOE PAGES

Lee, S. Y.; Ng, K. Y.

2017-06-29

Hamiltonian dynamics has been applied to study the slip-stacking dynamics. The canonical-perturbation method is employed to obtain the second-harmonic correction term in the slip-stacking Hamiltonian. The Hamiltonian approach provides a clear optimal method for choosing the slip-stacking parameter and improving stacking efficiency. The dynamics are applied specifically to the Fermilab Booster-Recycler complex. As a result, the dynamics can also be applied to other accelerator complexes.

Hamiltonian identifiability assisted by single-probe measurement

NASA Astrophysics Data System (ADS)

Sone, Akira; Cappellaro, Paola; Quantum Engineering Group Team

2017-04-01

We study the Hamiltonian identifiability of a many-body spin- 1 / 2 system assisted by the measurement on a single quantum probe based on the eigensystem realization algorithm (ERA) approach employed in. We demonstrate a potential application of Gröbner basis to the identifiability test of the Hamiltonian, and provide the necessary experimental resources, such as the lower bound in the number of the required sampling points, the upper bound in total required evolution time, and thus the total measurement time. Focusing on the examples of the identifiability in the spin chain model with nearest-neighbor interaction, we classify the spin-chain Hamiltonian based on its identifiability, and provide the control protocols to engineer the non-identifiable Hamiltonian to be an identifiable Hamiltonian.

Weak form of Stokes-Dirac structures and geometric discretization of port-Hamiltonian systems

NASA Astrophysics Data System (ADS)

Kotyczka, Paul; Maschke, Bernhard; Lefèvre, Laurent

2018-05-01

We present the mixed Galerkin discretization of distributed parameter port-Hamiltonian systems. On the prototypical example of hyperbolic systems of two conservation laws in arbitrary spatial dimension, we derive the main contributions: (i) A weak formulation of the underlying geometric (Stokes-Dirac) structure with a segmented boundary according to the causality of the boundary ports. (ii) The geometric approximation of the Stokes-Dirac structure by a finite-dimensional Dirac structure is realized using a mixed Galerkin approach and power-preserving linear maps, which define minimal discrete power variables. (iii) With a consistent approximation of the Hamiltonian, we obtain finite-dimensional port-Hamiltonian state space models. By the degrees of freedom in the power-preserving maps, the resulting family of structure-preserving schemes allows for trade-offs between centered approximations and upwinding. We illustrate the method on the example of Whitney finite elements on a 2D simplicial triangulation and compare the eigenvalue approximation in 1D with a related approach.

Constructing Dense Graphs with Unique Hamiltonian Cycles

ERIC Educational Resources Information Center

Lynch, Mark A. M.

2012-01-01

It is not difficult to construct dense graphs containing Hamiltonian cycles, but it is difficult to generate dense graphs that are guaranteed to contain a unique Hamiltonian cycle. This article presents an algorithm for generating arbitrarily large simple graphs containing "unique" Hamiltonian cycles. These graphs can be turned into dense graphs…

Self-Study and Evaluation Guide/1968 Edition. Section D-3: Rehabilitation Centers.

ERIC Educational Resources Information Center

National Accreditation Council for Agencies Serving the Blind and Visually Handicapped, New York, NY.

This self-study and evaluation guide on rehabilitation centers is one of 28 guides designed for organizations undertaking a self-study as part of the process for accreditation from the National Accreditation Council (NAC) for agencies serving the blind and visually handicapped. Provided are lists of standards to be appraised by the self-evaluation…

Worker-Centered Learning: A Union Guide to Workplace Literacy.

ERIC Educational Resources Information Center

Sarmiento, Anthony R.; Kay, Ann

This guide examines organized labor's views on adult literacy. It also describes several union-sponsored workplace education programs and suggests how a union can plan and operate a worker-centered literacy program. The book is organized in three parts. The first part examines workplace literacy in four chapters that cover the following: the…

Hamiltonian quantum simulation with bounded-strength controls

NASA Astrophysics Data System (ADS)

Bookatz, Adam D.; Wocjan, Pawel; Viola, Lorenza

2014-04-01

We propose dynamical control schemes for Hamiltonian simulation in many-body quantum systems that avoid instantaneous control operations and rely solely on realistic bounded-strength control Hamiltonians. Each simulation protocol consists of periodic repetitions of a basic control block, constructed as a modification of an ‘Eulerian decoupling cycle,’ that would otherwise implement a trivial (zero) target Hamiltonian. For an open quantum system coupled to an uncontrollable environment, our approach may be employed to engineer an effective evolution that simulates a target Hamiltonian on the system while suppressing unwanted decoherence to the leading order, thereby allowing for dynamically corrected simulation. We present illustrative applications to both closed- and open-system simulation settings, with emphasis on simulation of non-local (two-body) Hamiltonians using only local (one-body) controls. In particular, we provide simulation schemes applicable to Heisenberg-coupled spin chains exposed to general linear decoherence, and show how to simulate Kitaev's honeycomb lattice Hamiltonian starting from Ising-coupled qubits, as potentially relevant to the dynamical generation of a topologically protected quantum memory. Additional implications for quantum information processing are discussed.

Organizing a Successful Family Center in Your School. A Resource Guide. Revised 2005

ERIC Educational Resources Information Center

Wisconsin Department of Public Instruction, 2005

2005-01-01

This booklet was developed to help school staff members, parents, and community leaders understand how family centers can promote family participation and strengthen their schools. It also serves as a guide to establishing family centers. The term, family center, is used throughout this booklet, although many schools prefer to call their center…

Full-field drift Hamiltonian particle orbits in 3D geometry

NASA Astrophysics Data System (ADS)

Cooper, W. A.; Graves, J. P.; Brunner, S.; Isaev, M. Yu

2011-02-01

A Hamiltonian/Lagrangian theory to describe guiding centre orbit drift motion which is canonical in the Boozer coordinate frame has been extended to include full electromagnetic perturbed fields in anisotropic pressure 3D equilibria with nested magnetic flux surfaces. A redefinition of the guiding centre velocity to eliminate the motion due to finite equilibrium radial magnetic fields and the choice of a gauge condition that sets the radial component of the electromagnetic vector potential to zero are invoked to guarantee that the Boozer angular coordinates retain the canonical structure. The canonical momenta are identified and the guiding centre particle radial drift motion and parallel gyroradius evolution are derived. The particle coordinate position is linearly modified by wave-particle interactions. All the nonlinear wave-wave interactions appear explicitly only in the evolution of the parallel gyroradius. The radial variation of the electrostatic potential is related to the binormal component of the displacement vector for MHD-type perturbations. The electromagnetic vector potential projections can then be determined from the electrostatic potential and the radial component of the MHD displacement vector.

Hamiltonian structure of the Lotka-Volterra equations

NASA Astrophysics Data System (ADS)

Nutku, Y.

1990-03-01

The Lotka-Volterra equations governing predator-prey relations are shown to admit Hamiltonian structure with respect to a generalized Poisson bracket. These equations provide an example of a system for which the naive criterion for the existence of Hamiltonian structure fails. We show further that there is a three-component generalization of the Lotka-Volterra equations which is a bi-Hamiltonian system.

Interprofessional education and practice guide no. 2: developing and implementing a center for interprofessional education.

PubMed

Brashers, Valentina; Owen, John; Haizlip, Julie

2015-03-01

The complexity of implementing interprofessional education and practice (IPEP) strategies that extend across the learning continuum requires that institutions create a structure to support effective and organized coordination among interested administrators, faculty and staff. The University of Virginia Center for Academic Strategic Partnerships for Interprofessional Research and Education (UVA Center for ASPIRE) was formally established in 2013 following five years of dramatic growth in interprofessional education at the School of Nursing, School of Medicine and the UVA Health System. This guide briefly describes the steps that led to the creation of the Center and the key lessons learned that can guide other institutions toward establishing their own IPE centers.

The Johnson Space Center management information systems: User's guide to JSCMIS

NASA Technical Reports Server (NTRS)

Bishop, Peter C.; Erickson, Lloyd

1990-01-01

The Johnson Space Center Management Information System (JSCMIS) is an interface to computer data bases at the NASA Johnson Space Center which allows an authorized user to browse and retrieve information from a variety of sources with minimum effort. The User's Guide to JSCMIS is the supplement to the JSCMIS Research Report which details the objectives, the architecture, and implementation of the interface. It is a tutorial on how to use the interface and a reference for details about it. The guide is structured like an extended JSCMIS session, describing all of the interface features and how to use them. It also contains an appendix with each of the standard FORMATs currently included in the interface. Users may review them to decide which FORMAT most suits their needs.

Quasi-Hamiltonian structure and Hojman construction

NASA Astrophysics Data System (ADS)

Carinena, Jose F.; Guha, Partha; Ranada, Manuel F.

2007-08-01

Given a smooth vector field [Gamma] and assuming the knowledge of an infinitesimal symmetry X, Hojman [S. Hojman, The construction of a Poisson structure out of a symmetry and a conservation law of a dynamical system, J. Phys. A Math. Gen. 29 (1996) 667-674] proposed a method for finding both a Poisson tensor and a function H such that [Gamma] is the corresponding Hamiltonian system. In this paper, we approach the problem from geometrical point of view. The geometrization leads to the clarification of several concepts and methods used in Hojman's paper. In particular, the relationship between the nonstandard Hamiltonian structure proposed by Hojman and the degenerate quasi-Hamiltonian structures introduced by Crampin and Sarlet [M. Crampin, W. Sarlet, Bi-quasi-Hamiltonian systems, J. Math. Phys. 43 (2002) 2505-2517] is unveiled in this paper. We also provide some applications of our construction.

Vibroacoustic Payload Environment Prediction System (VAPEPS): VAPEPS management center remote access guide

NASA Technical Reports Server (NTRS)

Fernandez, J. P.; Mills, D.

1991-01-01

A Vibroacoustic Payload Environment Prediction System (VAPEPS) Management Center was established at the JPL. The center utilizes the VAPEPS software package to manage a data base of Space Shuttle and expendable launch vehicle payload flight and ground test data. Remote terminal access over telephone lines to the computer system, where the program resides, was established to provide the payload community a convenient means of querying the global VAPEPS data base. This guide describes the functions of the VAPEPS Management Center and contains instructions for utilizing the resources of the center.

Non-isospectral Hamiltonians, intertwining operators and hidden hermiticity

NASA Astrophysics Data System (ADS)

Bagarello, F.

2011-12-01

We have recently proposed a strategy to produce, starting from a given Hamiltonian h and a certain operator x for which [h,xx]=0 and xx is invertible, a second Hamiltonian h with the same eigenvalues as h and whose eigenvectors are related to those of h by x. Here we extend this procedure to build up a second Hamiltonian, whose eigenvalues are different from those of h, and whose eigenvectors are still related as before. This new procedure is also extended to crypto-hermitian Hamiltonians.

sdg Interacting boson hamiltonian in the seniority scheme

NASA Astrophysics Data System (ADS)

Yoshinaga, N.

1989-03-01

The sdg interacting boson hamiltonian is derived in the seniority scheme. We use the method of Otsuka, Arima and Iachello in order to derive the boson hamiltonian from the fermion hamiltonian. To examine how good is the boson approximation in the zeroth-order, we carry out the exact shell model calculations in a single j-shell. It is found that almost all low-lying levels are reproduced quite well by diagonalizing the sdg interacting boson hamiltonian in the vibrational case. In the deformed case the introduction of g-bosons improves the reproduction of the spectra and of the binding energies which are obtained by diagonalizing the exact shell model hamiltonian. In particular the sdg interacting boson model reproduces well-developed rotational bands.

Dynamical decoupling of unbounded Hamiltonians

NASA Astrophysics Data System (ADS)

Arenz, Christian; Burgarth, Daniel; Facchi, Paolo; Hillier, Robin

2018-03-01

We investigate the possibility to suppress interactions between a finite dimensional system and an infinite dimensional environment through a fast sequence of unitary kicks on the finite dimensional system. This method, called dynamical decoupling, is known to work for bounded interactions, but physical environments such as bosonic heat baths are usually modeled with unbounded interactions; hence, here, we initiate a systematic study of dynamical decoupling for unbounded operators. We develop a sufficient decoupling criterion for arbitrary Hamiltonians and a necessary decoupling criterion for semibounded Hamiltonians. We give examples for unbounded Hamiltonians where decoupling works and the limiting evolution as well as the convergence speed can be explicitly computed. We show that decoupling does not always work for unbounded interactions and we provide both physically and mathematically motivated examples.

Classification of three-state Hamiltonians solvable by the coordinate Bethe ansatz

NASA Astrophysics Data System (ADS)

Crampé, N.; Frappat, L.; Ragoucy, E.

2013-10-01

We classify ‘all’ Hamiltonians with rank 1 symmetry and nearest-neighbour interactions, acting on a periodic three-state spin chain, and solvable through (generalization of) the coordinate Bethe ansatz (CBA). In this way we obtain four multi-parametric extensions of the known 19-vertex Hamiltonians (such as Zamolodchikov-Fateev, Izergin-Korepin and Bariev Hamiltonians). Apart from the 19-vertex Hamiltonians, there exist 17-vertex and 14-vertex Hamiltonians that cannot be viewed as subcases of the 19-vertex ones. In the case of 17-vertex Hamiltonians, we get a generalization of the genus 5 special branch found by Martins, plus three new ones. We also get two 14-vertex Hamiltonians. We solve all these Hamiltonians using CBA, and provide their spectrum, eigenfunctions and Bethe equations. Special attention is given to provide the specifications of our multi-parametric Hamiltonians that give back known Hamiltonians.

Extended Hamiltonian approach to continuous tempering

NASA Astrophysics Data System (ADS)

Gobbo, Gianpaolo; Leimkuhler, Benedict J.

2015-06-01

We introduce an enhanced sampling simulation technique based on continuous tempering, i.e., on continuously varying the temperature of the system under investigation. Our approach is mathematically straightforward, being based on an extended Hamiltonian formulation in which an auxiliary degree of freedom, determining the effective temperature, is coupled to the physical system. The physical system and its temperature evolve continuously in time according to the equations of motion derived from the extended Hamiltonian. Due to the Hamiltonian structure, it is easy to show that a particular subset of the configurations of the extended system is distributed according to the canonical ensemble for the physical system at the correct physical temperature.

Entanglement Hamiltonians for Chiral Fermions with Zero Modes.

PubMed

Klich, Israel; Vaman, Diana; Wong, Gabriel

2017-09-22

In this Letter, we study the effect of topological zero modes on entanglement Hamiltonians and the entropy of free chiral fermions in (1+1)D. We show how Riemann-Hilbert solutions combined with finite rank perturbation theory allow us to obtain exact expressions for entanglement Hamiltonians. In the absence of the zero mode, the resulting entanglement Hamiltonians consist of local and bilocal terms. In the periodic sector, the presence of a zero mode leads to an additional nonlocal contribution to the entanglement Hamiltonian. We derive an exact expression for this term and for the resulting change in the entanglement entropy.

Multi-Hamiltonian structure of equations of hydrodynamic type

NASA Astrophysics Data System (ADS)

Gümral, H.; Nutku, Y.

1990-11-01

The discussion of the Hamiltonian structure of two-component equations of hydrodynamic type is completed by presenting the Hamiltonian operators for Euler's equation governing the motion of plane sound waves of finite amplitude and another quasilinear second-order wave equation. There exists a doubly infinite family of conserved Hamiltonians for the equations of gas dynamics that degenerate into one, namely, the Benney sequence, for shallow-water waves. Infinite sequences of conserved quantities for these equations are also presented. In the case of multicomponent equations of hydrodynamic type, it is shown, that Kodama's generalization of the shallow-water equations admits bi-Hamiltonian structure.

Covariant hamiltonian spin dynamics in curved space-time

NASA Astrophysics Data System (ADS)

d'Ambrosi, G.; Satish Kumar, S.; van Holten, J. W.

2015-04-01

The dynamics of spinning particles in curved space-time is discussed, emphasizing the hamiltonian formulation. Different choices of hamiltonians allow for the description of different gravitating systems. We give full results for the simplest case with minimal hamiltonian, constructing constants of motion including spin. The analysis is illustrated by the example of motion in Schwarzschild space-time. We also discuss a non-minimal extension of the hamiltonian giving rise to a gravitational equivalent of the Stern-Gerlach force. We show that this extension respects a large class of known constants of motion for the minimal case.

Optimal adaptive control for quantum metrology with time-dependent Hamiltonians.

PubMed

Pang, Shengshi; Jordan, Andrew N

2017-03-09

Quantum metrology has been studied for a wide range of systems with time-independent Hamiltonians. For systems with time-dependent Hamiltonians, however, due to the complexity of dynamics, little has been known about quantum metrology. Here we investigate quantum metrology with time-dependent Hamiltonians to bridge this gap. We obtain the optimal quantum Fisher information for parameters in time-dependent Hamiltonians, and show proper Hamiltonian control is generally necessary to optimize the Fisher information. We derive the optimal Hamiltonian control, which is generally adaptive, and the measurement scheme to attain the optimal Fisher information. In a minimal example of a qubit in a rotating magnetic field, we find a surprising result that the fundamental limit of T 2 time scaling of quantum Fisher information can be broken with time-dependent Hamiltonians, which reaches T 4 in estimating the rotation frequency of the field. We conclude by considering level crossings in the derivatives of the Hamiltonians, and point out additional control is necessary for that case.

Optimal adaptive control for quantum metrology with time-dependent Hamiltonians

PubMed Central

Pang, Shengshi; Jordan, Andrew N.

2017-01-01

Quantum metrology has been studied for a wide range of systems with time-independent Hamiltonians. For systems with time-dependent Hamiltonians, however, due to the complexity of dynamics, little has been known about quantum metrology. Here we investigate quantum metrology with time-dependent Hamiltonians to bridge this gap. We obtain the optimal quantum Fisher information for parameters in time-dependent Hamiltonians, and show proper Hamiltonian control is generally necessary to optimize the Fisher information. We derive the optimal Hamiltonian control, which is generally adaptive, and the measurement scheme to attain the optimal Fisher information. In a minimal example of a qubit in a rotating magnetic field, we find a surprising result that the fundamental limit of T2 time scaling of quantum Fisher information can be broken with time-dependent Hamiltonians, which reaches T4 in estimating the rotation frequency of the field. We conclude by considering level crossings in the derivatives of the Hamiltonians, and point out additional control is necessary for that case. PMID:28276428

Hamiltonian identifiability assisted by a single-probe measurement

NASA Astrophysics Data System (ADS)

Sone, Akira; Cappellaro, Paola

2017-02-01

We study the Hamiltonian identifiability of a many-body spin-1 /2 system assisted by the measurement on a single quantum probe based on the eigensystem realization algorithm approach employed in Zhang and Sarovar, Phys. Rev. Lett. 113, 080401 (2014), 10.1103/PhysRevLett.113.080401. We demonstrate a potential application of Gröbner basis to the identifiability test of the Hamiltonian, and provide the necessary experimental resources, such as the lower bound in the number of the required sampling points, the upper bound in total required evolution time, and thus the total measurement time. Focusing on the examples of the identifiability in the spin-chain model with nearest-neighbor interaction, we classify the spin-chain Hamiltonian based on its identifiability, and provide the control protocols to engineer the nonidentifiable Hamiltonian to be an identifiable Hamiltonian.

Non-commuting two-local Hamiltonians for quantum error suppression

NASA Astrophysics Data System (ADS)

Jiang, Zhang; Rieffel, Eleanor G.

2017-04-01

Physical constraints make it challenging to implement and control many-body interactions. For this reason, designing quantum information processes with Hamiltonians consisting of only one- and two-local terms is a worthwhile challenge. Enabling error suppression with two-local Hamiltonians is particularly challenging. A no-go theorem of Marvian and Lidar (Phys Rev Lett 113(26):260504, 2014) demonstrates that, even allowing particles with high Hilbert space dimension, it is impossible to protect quantum information from single-site errors by encoding in the ground subspace of any Hamiltonian containing only commuting two-local terms. Here, we get around this no-go result by encoding in the ground subspace of a Hamiltonian consisting of non-commuting two-local terms arising from the gauge operators of a subsystem code. Specifically, we show how to protect stored quantum information against single-qubit errors using a Hamiltonian consisting of sums of the gauge generators from Bacon-Shor codes (Bacon in Phys Rev A 73(1):012340, 2006) and generalized-Bacon-Shor code (Bravyi in Phys Rev A 83(1):012320, 2011). Our results imply that non-commuting two-local Hamiltonians have more error-suppressing power than commuting two-local Hamiltonians. While far from providing full fault tolerance, this approach improves the robustness achievable in near-term implementable quantum storage and adiabatic quantum computations, reducing the number of higher-order terms required to encode commonly used adiabatic Hamiltonians such as the Ising Hamiltonians common in adiabatic quantum optimization and quantum annealing.

Taking on Turnover: An Action Guide for Child Care Center Teachers and Directors.

ERIC Educational Resources Information Center

Whitebook, Marcy; Bellm, Dan

Based on the "Taking On Turnover" training series conducted by the Center for the Child Care Workforce, this action guide for center-based child care teachers and directors is designed to assist in managing and reducing the increasingly serious problem of job turnover in the child care profession. Following several introductory sections,…

Non-singular black holes and the limiting curvature mechanism: a Hamiltonian perspective

NASA Astrophysics Data System (ADS)

Ben Achour, J.; Lamy, F.; Liu, H.; Noui, K.

2018-05-01

We revisit the non-singular black hole solution in (extended) mimetic gravity with a limiting curvature from a Hamiltonian point of view. We introduce a parameterization of the phase space which allows us to describe fully the Hamiltonian structure of the theory. We write down the equations of motion that we solve in the regime deep inside the black hole, and we recover that the black hole has no singularity, due to the limiting curvature mechanism. Then, we study the relation between such black holes and effective polymer black holes which have been introduced in the context of loop quantum gravity. As expected, contrary to what happens in the cosmological sector, mimetic gravity with a limiting curvature fails to reproduce the usual effective dynamics of spherically symmetric loop quantum gravity which are generically not covariant. Nonetheless, we exhibit a theory in the class of extended mimetic gravity whose dynamics reproduces the general shape of the effective corrections of spherically symmetric polymer models, but in an undeformed covariant manner. These covariant effective corrections are found to be always metric dependent, i.e. within the bar mu-scheme, underlying the importance of this ingredient for inhomogeneous polymer models. In that respect, extended mimetic gravity can be viewed as an effective covariant theory which naturally implements a covariant notion of point wise holonomy-like corrections. The difference between the mimetic and polymer Hamiltonian formulations provides us with a guide to understand the deformation of covariance in inhomogeneous polymer models.

The gravity duals of modular Hamiltonians

DOE PAGES

Jafferis, Daniel L.; Suh, S. Josephine

2016-09-12

In this study, we investigate modular Hamiltonians defined with respect to arbitrary spatial regions in quantum field theory states which have semi-classical gravity duals. We find prescriptions in the gravity dual for calculating the action of the modular Hamiltonian on its defining state, including its dual metric, and also on small excitations around the state. Curiously, use of the covariant holographic entanglement entropy formula leads us to the conclusion that the modular Hamiltonian, which in the quantum field theory acts only in the causal completion of the region, does not commute with bulk operators whose entire gauge-invariant description is space-likemore » to the causal completion of the region.« less

The gravity duals of modular Hamiltonians

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jafferis, Daniel L.; Suh, S. Josephine

In this study, we investigate modular Hamiltonians defined with respect to arbitrary spatial regions in quantum field theory states which have semi-classical gravity duals. We find prescriptions in the gravity dual for calculating the action of the modular Hamiltonian on its defining state, including its dual metric, and also on small excitations around the state. Curiously, use of the covariant holographic entanglement entropy formula leads us to the conclusion that the modular Hamiltonian, which in the quantum field theory acts only in the causal completion of the region, does not commute with bulk operators whose entire gauge-invariant description is space-likemore » to the causal completion of the region.« less

Symmetric quadratic Hamiltonians with pseudo-Hermitian matrix representation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fernández, Francisco M., E-mail: fernande@quimica.unlp.edu.ar

2016-06-15

We prove that any symmetric Hamiltonian that is a quadratic function of the coordinates and momenta has a pseudo-Hermitian adjoint or regular matrix representation. The eigenvalues of the latter matrix are the natural frequencies of the Hamiltonian operator. When all the eigenvalues of the matrix are real, then the spectrum of the symmetric Hamiltonian is real and the operator is Hermitian. As illustrative examples we choose the quadratic Hamiltonians that model a pair of coupled resonators with balanced gain and loss, the electromagnetic self-force on an oscillating charged particle and an active LRC circuit. -- Highlights: •Symmetric quadratic operators aremore » useful models for many physical applications. •Any such operator exhibits a pseudo-Hermitian matrix representation. •Its eigenvalues are the natural frequencies of the Hamiltonian operator. •The eigenvalues may be real or complex and describe a phase transition.« less

Hamiltonian analysis of higher derivative scalar-tensor theories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Langlois, David; Noui, Karim, E-mail: langlois@apc.univ-paris7.fr, E-mail: karim.noui@lmpt.univ-tours.fr

2016-07-01

We perform a Hamiltonian analysis of a large class of scalar-tensor Lagrangians which depend quadratically on the second derivatives of a scalar field. By resorting to a convenient choice of dynamical variables, we show that the Hamiltonian can be written in a very simple form, where the Hamiltonian and the momentum constraints are easily identified. In the case of degenerate Lagrangians, which include the Horndeski and beyond Horndeski quartic Lagrangians, our analysis confirms that the dimension of the physical phase space is reduced by the primary and secondary constraints due to the degeneracy, thus leading to the elimination of themore » dangerous Ostrogradsky ghost. We also present the Hamiltonian formulation for nondegenerate theories and find that they contain four degrees of freedom, including a ghost, as expected. We finally discuss the status of the unitary gauge from the Hamiltonian perspective.« less

Hamiltonian modelling of relative motion.

PubMed

Kasdin, N Jeremy; Gurfil, Pini

2004-05-01

This paper presents a Hamiltonian approach to modelling relative spacecraft motion based on derivation of canonical coordinates for the relative state-space dynamics. The Hamiltonian formulation facilitates the modelling of high-order terms and orbital perturbations while allowing us to obtain closed-form solutions to the relative motion problem. First, the Hamiltonian is partitioned into a linear term and a high-order term. The Hamilton-Jacobi equations are solved for the linear part by separation, and new constants for the relative motions are obtained, they are called epicyclic elements. The influence of higher order terms and perturbations, such as the oblateness of the Earth, are incorporated into the analysis by a variation of parameters procedure. Closed-form solutions for J(2-) and J(4-)invariant orbits and for periodic high-order unperturbed relative motion, in terms of the relative motion elements only, are obtained.

Geometric construction of quantum hall clustering Hamiltonians

DOE PAGES

Lee, Ching Hua; Papić, Zlatko; Thomale, Ronny

2015-10-08

In this study, many fractional quantum Hall wave functions are known to be unique highest-density zero modes of certain “pseudopotential” Hamiltonians. While a systematic method to construct such parent Hamiltonians has been available for the infinite plane and sphere geometries, the generalization to manifolds where relative angular momentum is not an exact quantum number, i.e., the cylinder or torus, remains an open problem. This is particularly true for non-Abelian states, such as the Read-Rezayi series (in particular, the Moore-Read and Read-Rezayi Z 3 states) and more exotic nonunitary (Haldane-Rezayi and Gaffnian) or irrational (Haffnian) states, whose parent Hamiltonians involve complicatedmore » many-body interactions. Here, we develop a universal geometric approach for constructing pseudopotential Hamiltonians that is applicable to all geometries. Our method straightforwardly generalizes to the multicomponent SU(n) cases with a combination of spin or pseudospin (layer, subband, or valley) degrees of freedom. We demonstrate the utility of our approach through several examples, some of which involve non-Abelian multicomponent states whose parent Hamiltonians were previously unknown, and we verify the results by numerically computing their entanglement properties.« less

Action with Acceleration II: Euclidean Hamiltonian and Jordan Blocks

NASA Astrophysics Data System (ADS)

Baaquie, Belal E.

2013-10-01

The Euclidean action with acceleration has been analyzed in Ref. 1, and referred to henceforth as Paper I, for its Hamiltonian and path integral. In this paper, the state space of the Hamiltonian is analyzed for the case when it is pseudo-Hermitian (equivalent to a Hermitian Hamiltonian), as well as the case when it is inequivalent. The propagator is computed using both creation and destruction operators as well as the path integral. A state space calculation of the propagator shows the crucial role played by the dual state vectors that yields a result impossible to obtain from a Hermitian Hamiltonian. When it is not pseudo-Hermitian, the Hamiltonian is shown to be a direct sum of Jordan blocks.

Vibroacoustic payload environment prediction system (VAPEPS): Data base management center remote access guide

NASA Technical Reports Server (NTRS)

Thomas, V. C.

1986-01-01

A Vibroacoustic Data Base Management Center has been established at the Jet Propulsion Laboratory (JPL). The center utilizes the Vibroacoustic Payload Environment Prediction System (VAPEPS) software package to manage a data base of shuttle and expendable launch vehicle flight and ground test data. Remote terminal access over telephone lines to a dedicated VAPEPS computer system has been established to provide the payload community a convenient means of querying the global VAPEPS data base. This guide describes the functions of the JPL Data Base Management Center and contains instructions for utilizing the resources of the center.

A New Scheme of Integrability for (bi)Hamiltonian PDE

NASA Astrophysics Data System (ADS)

De Sole, Alberto; Kac, Victor G.; Valeri, Daniele

2016-10-01

We develop a new method for constructing integrable Hamiltonian hierarchies of Lax type equations, which combines the fractional powers technique of Gelfand and Dickey, and the classical Hamiltonian reduction technique of Drinfeld and Sokolov. The method is based on the notion of an Adler type matrix pseudodifferential operator and the notion of a generalized quasideterminant. We also introduce the notion of a dispersionless Adler type series, which is applied to the study of dispersionless Hamiltonian equations. Non-commutative Hamiltonian equations are discussed in this framework as well.

Gravitational surface Hamiltonian and entropy quantization

NASA Astrophysics Data System (ADS)

Bakshi, Ashish; Majhi, Bibhas Ranjan; Samanta, Saurav

2017-02-01

The surface Hamiltonian corresponding to the surface part of a gravitational action has xp structure where p is conjugate momentum of x. Moreover, it leads to TS on the horizon of a black hole. Here T and S are temperature and entropy of the horizon. Imposing the hermiticity condition we quantize this Hamiltonian. This leads to an equidistant spectrum of its eigenvalues. Using this we show that the entropy of the horizon is quantized. This analysis holds for any order of Lanczos-Lovelock gravity. For general relativity, the area spectrum is consistent with Bekenstein's observation. This provides a more robust confirmation of this earlier result as the calculation is based on the direct quantization of the Hamiltonian in the sense of usual quantum mechanics.

Linear transformation and oscillation criteria for Hamiltonian systems

NASA Astrophysics Data System (ADS)

Zheng, Zhaowen

2007-08-01

Using a linear transformation similar to the Kummer transformation, some new oscillation criteria for linear Hamiltonian systems are established. These results generalize and improve the oscillation criteria due to I.S. Kumari and S. Umanaheswaram [I. Sowjaya Kumari, S. Umanaheswaram, Oscillation criteria for linear matrix Hamiltonian systems, J. Differential Equations 165 (2000) 174-198], Q. Yang et al. [Q. Yang, R. Mathsen, S. Zhu, Oscillation theorems for self-adjoint matrix Hamiltonian systems, J. Differential Equations 190 (2003) 306-329], and S. Chen and Z. Zheng [Shaozhu Chen, Zhaowen Zheng, Oscillation criteria of Yan type for linear Hamiltonian systems, Comput. Math. Appl. 46 (2003) 855-862]. These criteria also unify many of known criteria in literature and simplify the proofs.

First principles of Hamiltonian medicine.

PubMed

Crespi, Bernard; Foster, Kevin; Úbeda, Francisco

2014-05-19

We introduce the field of Hamiltonian medicine, which centres on the roles of genetic relatedness in human health and disease. Hamiltonian medicine represents the application of basic social-evolution theory, for interactions involving kinship, to core issues in medicine such as pathogens, cancer, optimal growth and mental illness. It encompasses three domains, which involve conflict and cooperation between: (i) microbes or cancer cells, within humans, (ii) genes expressed in humans, (iii) human individuals. A set of six core principles, based on these domains and their interfaces, serves to conceptually organize the field, and contextualize illustrative examples. The primary usefulness of Hamiltonian medicine is that, like Darwinian medicine more generally, it provides novel insights into what data will be productive to collect, to address important clinical and public health problems. Our synthesis of this nascent field is intended predominantly for evolutionary and behavioural biologists who aspire to address questions directly relevant to human health and disease.

User-centered Design of the eyeGuide: A Tailored Glaucoma Behavior Change Program.

PubMed

Killeen, Olivia J; MacKenzie, Chamisa; Heisler, Michele; Resnicow, Ken; Lee, Paul P; Newman-Casey, Paula Anne

2016-10-01

We employed user-centered design to refine a prototype of the eyeGuide, a novel, tailored behavior change program intended to improve medication adherence among glaucoma patients. Glaucoma patients age 40 years and above prescribed ≥1 glaucoma medication were included. The eyeGuide consists of tailored educational content and tailored testimonials in which patients share how they were able to overcome barriers to improve their medication adherence. A hybrid of semistructured diagnostic and pretesting interviews were used to refine the content of the eyeGuide. Purposeful sampling was used to recruit a study population representative of the glaucoma patient population. Interviews were conducted until thematic saturation was reached. Interviews were audiorecorded and transcribed verbatim. Three researchers analyzed the transcripts, generated a codebook, and identified key themes using NVivo 10.0 to further refine the eyeGuide. Twenty-one glaucoma patients were interviewed; mean age 72±12.4 years, 5 (24%) African Americans, 9 (43%) with poor self-reported adherence, 10 (47.6%) age 75 years and above, 10 (47.6%) with poor vision, and 9 (42.9%) women. Qualitative analysis identified 5 important themes for improving glaucoma self-management: social support, patient-provider relationship, medication routine, patients' beliefs about disease and treatment, and eye drop instillation. All participants expressed satisfaction with in-person delivery of the eyeGuide and preferred this to a Web-based module. Participant feedback resulted in revised content. User-centered design generated improvements in the eyeGuide that would not have been possible without patient input. Participants expressed satisfaction with the tailored content.

Uncertainty relation for non-Hamiltonian quantum systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tarasov, Vasily E.

2013-01-15

General forms of uncertainty relations for quantum observables of non-Hamiltonian quantum systems are considered. Special cases of uncertainty relations are discussed. The uncertainty relations for non-Hamiltonian quantum systems are considered in the Schroedinger-Robertson form since it allows us to take into account Lie-Jordan algebra of quantum observables. In uncertainty relations, the time dependence of quantum observables and the properties of this dependence are discussed. We take into account that a time evolution of observables of a non-Hamiltonian quantum system is not an endomorphism with respect to Lie, Jordan, and associative multiplications.

The Cispus Experience: A Curriculum Guide for the Cispus Learning Center.

ERIC Educational Resources Information Center

Association of Washington School Principals, Olympia.

This curriculum guide presents lesson plans for outdoor and environmental education at the Cispus Learning Center, a camp in Randle, Washington. Objectives for the Cispus experience cover student learning of content, socialization as a team member, development of aesthetic awareness of nature and art, and increased physical wellness. Lesson plans…

Model Hamiltonian Calculations of the Nonlinear Polarizabilities of Conjugated Molecules.

NASA Astrophysics Data System (ADS)

Risser, Steven Michael

This dissertation advances the theoretical knowledge of the nonlinear polarizabilities of conjugated molecules. The unifying feature of these molecules is an extended delocalized pi electron structure. The pi electrons dominate the electronic properties of the molecules, allowing prediction of molecular properties based on the treatment of just the pi electrons. Two separate pi electron Hamiltonians are used in the research. The principal Hamiltonian used is the non-interacting single-particle Huckel Hamiltonian, which replaces the Coulomb interaction among the pi electrons with a mean field interaction. The simplification allows for exact solution of the Hamiltonian for large molecules. The second Hamiltonian used for this research is the interacting multi-particle Pariser-Parr-Pople (PPP) Hamiltonian, which retains explicit Coulomb interactions. This limits exact solutions to molecules containing at most eight electrons. The molecular properties being investigated are the linear polarizability, and the second and third order hyperpolarizabilities. The hyperpolarizabilities determine the nonlinear optical response of materials. These molecular parameters are determined by two independent approaches. The results from the Huckel Hamiltonian are obtained through first, second and third order perturbation theory. The results from the PPP Hamiltonian are obtained by including the applied field directly in the Hamiltonian and determining the ground state energy at a series of field strengths. By fitting the energy to a polynomial in field strength, the polarizability and hyperpolarizabilities are determined. The Huckel Hamiltonian is used to calculate the third order hyperpolarizability of polyenes. These calculations were the first to show the average hyperpolarizability of the polyenes to be positive, and also to show the saturation of the hyperpolarizability. Comparison of these Huckel results to those from the PPP Hamiltonian shows the lack of explicit Coulomb

Guiding-center equations for electrons in ultraintense laser fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Moore, J.E.; Fisch, N.J.

1994-01-01

The guiding-center equations are derived for electrons in arbitrarily intense laser fields also subject to external fields and ponderomotive forces. Exhibiting the relativistic mass increase of the oscillating electrons, a simple frame-invariant equation is shown to govern the behavior of the electrons for sufficiently weak background fields and ponderomotive forces. The parameter regime for which such a formulation is valid is made precise, and some predictions of the equation are checked by numerical simulation.

Alternative bi-Hamiltonian structures for WDVV equations of associativity

NASA Astrophysics Data System (ADS)

Kalayci, J.; Nutku, Y.

1998-01-01

The WDVV equations of associativity in two-dimensional topological field theory are completely integrable third-order Monge-Ampère equations which admit bi-Hamiltonian structure. The time variable plays a distinguished role in the discussion of Hamiltonian structure, whereas in the theory of WDVV equations none of the independent variables merits such a distinction. WDVV equations admit very different alternative Hamiltonian structures under different possible choices of the time variable, but all these various Hamiltonian formulations can be brought together in the framework of the covariant theory of symplectic structure. They can be identified as different components of the covariant Witten-Zuckerman symplectic 2-form current density where a variational formulation of the WDVV equation that leads to the Hamiltonian operator through the Dirac bracket is available.

Local Hamiltonians for maximally multipartite-entangled states

NASA Astrophysics Data System (ADS)

Facchi, P.; Florio, G.; Pascazio, S.; Pepe, F.

2010-10-01

We study the conditions for obtaining maximally multipartite-entangled states (MMESs) as nondegenerate eigenstates of Hamiltonians that involve only short-range interactions. We investigate small-size systems (with a number of qubits ranging from 3 to 5) and show some example Hamiltonians with MMESs as eigenstates.

Greenberger-Horne-Zeilinger States and Few-Body Hamiltonians

NASA Astrophysics Data System (ADS)

Facchi, Paolo; Florio, Giuseppe; Pascazio, Saverio; Pepe, Francesco V.

2011-12-01

The generation of Greenberger-Horne-Zeilinger (GHZ) states is a crucial problem in quantum information. We derive general conditions for obtaining GHZ states as eigenstates of a Hamiltonian. We find that a necessary condition for an n-qubit GHZ state to be a nondegenerate eigenstate of a Hamiltonian is the presence of m-qubit couplings with m≥[(n+1)/2]. Moreover, we introduce a Hamiltonian with a GHZ eigenstate and derive sufficient conditions for the removal of the degeneracy.

Greenberger-Horne-Zeilinger states and few-body Hamiltonians.

PubMed

Facchi, Paolo; Florio, Giuseppe; Pascazio, Saverio; Pepe, Francesco V

2011-12-23

The generation of Greenberger-Horne-Zeilinger (GHZ) states is a crucial problem in quantum information. We derive general conditions for obtaining GHZ states as eigenstates of a Hamiltonian. We find that a necessary condition for an n-qubit GHZ state to be a nondegenerate eigenstate of a Hamiltonian is the presence of m-qubit couplings with m≥[(n+1)/2]. Moreover, we introduce a Hamiltonian with a GHZ eigenstate and derive sufficient conditions for the removal of the degeneracy.

Effective Hamiltonian for travelling discrete breathers

NASA Astrophysics Data System (ADS)

MacKay, Robert S.; Sepulchre, Jacques-Alexandre

2002-05-01

Hamiltonian chains of oscillators in general probably do not sustain exact travelling discrete breathers. However solutions which look like moving discrete breathers for some time are not difficult to observe in numerics. In this paper we propose an abstract framework for the description of approximate travelling discrete breathers in Hamiltonian chains of oscillators. The method is based on the construction of an effective Hamiltonian enabling one to describe the dynamics of the translation degree of freedom of moving breathers. Error estimate on the approximate dynamics is also studied. The concept of the Peierls-Nabarro barrier can be made clear in this framework. We illustrate the method with two simple examples, namely the Salerno model which interpolates between the Ablowitz-Ladik lattice and the discrete nonlinear Schrödinger system, and the Fermi-Pasta-Ulam chain.

Approximate symmetries of Hamiltonians

NASA Astrophysics Data System (ADS)

Chubb, Christopher T.; Flammia, Steven T.

2017-08-01

We explore the relationship between approximate symmetries of a gapped Hamiltonian and the structure of its ground space. We start by considering approximate symmetry operators, defined as unitary operators whose commutators with the Hamiltonian have norms that are sufficiently small. We show that when approximate symmetry operators can be restricted to the ground space while approximately preserving certain mutual commutation relations. We generalize the Stone-von Neumann theorem to matrices that approximately satisfy the canonical (Heisenberg-Weyl-type) commutation relations and use this to show that approximate symmetry operators can certify the degeneracy of the ground space even though they only approximately form a group. Importantly, the notions of "approximate" and "small" are all independent of the dimension of the ambient Hilbert space and depend only on the degeneracy in the ground space. Our analysis additionally holds for any gapped band of sufficiently small width in the excited spectrum of the Hamiltonian, and we discuss applications of these ideas to topological quantum phases of matter and topological quantum error correcting codes. Finally, in our analysis, we also provide an exponential improvement upon bounds concerning the existence of shared approximate eigenvectors of approximately commuting operators under an added normality constraint, which may be of independent interest.

Finite Nilpotent BRST Transformations in Hamiltonian Formulation

NASA Astrophysics Data System (ADS)

Rai, Sumit Kumar; Mandal, Bhabani Prasad

2013-10-01

We consider the finite field dependent BRST (FFBRST) transformations in the context of Hamiltonian formulation using Batalin-Fradkin-Vilkovisky method. The non-trivial Jacobian of such transformations is calculated in extended phase space. The contribution from Jacobian can be written as exponential of some local functional of fields which can be added to the effective Hamiltonian of the system. Thus, FFBRST in Hamiltonian formulation with extended phase space also connects different effective theories. We establish this result with the help of two explicit examples. We also show that the FFBRST transformations is similar to the canonical transformations in the sector of Lagrange multiplier and its corresponding momenta.

User-Centered Design of the eyeGuide, a Tailored Glaucoma Behavior Change Program

PubMed Central

Killeen, Olivia; MacKenzie, Chamisa; Heisler, Michele; Resnicow, Ken; Lee, Paul P.; Newman-Casey, Paula Anne

2016-01-01

PURPOSE We employed user-centered design to refine a prototype of the eyeGuide, a novel, tailored behavior change program intended to improve medication adherence among glaucoma patients. PATIENTS Glaucoma patients ≥ age 40 prescribed ≥1 glaucoma medication were included. METHODS The eyeGuide consists of tailored educational content and tailored testimonials in which patients share how they were able to overcome barriers to improve their medication adherence. A hybrid of semi-structured diagnostic and pre-testing interviews were used to refine the content of the eyeGuide. Purposeful sampling was used to recruit a study population representative of the glaucoma patient population. Interviews were conducted until thematic saturation was reached. Interviews were audio recorded and transcribed verbatim. Three researchers analyzed the transcripts, generated a codebook and identified key themes using NVivo 10.0 to further refine the eyeGuide. RESULTS Twenty-one glaucoma patients were interviewed; mean age 72 ± 12.4 years, five (24%) African-Americans, nine (43%) with poor self-reported adherence, ten (47.6%) ≥ age 75, ten (47.6%) with poor vision and nine (42.9%) women. Qualitative analysis identified five important themes for improving glaucoma self-management: social support, patient-provider relationship, medication routine, patients’ beliefs about disease and treatment, and eye drop instillation. All participants expressed satisfaction with in-person delivery of the eyeGuide and preferred this to a web-based module. Participant feedback resulted in revised content. CONCLUSIONS User-centered design generated improvements in the eyeGuide that would not have been possible without patient input. Participants expressed satisfaction with the tailored content. PMID:27096721

Investigation of the effect of scattering centers on low dimensional nanowire channel

NASA Astrophysics Data System (ADS)

Cariappa, K. S.; Shukla, Raja; Sarkar, Niladri

2018-05-01

In this work, we studied the effect of scattering centers on the electron density profiles of a one dimensional Nanowire channel. Density Matrix Formalism is used for calculating the local electron densities at room temperature. Various scattering centers have been simulated in the channel. The nearest neighbor tight binding method is applied to construct the Hamiltonian of nanoscale devices. We invoke scattering centers by adding local scattering potentials to the Hamiltonian. This analysis could give an insight into the understanding and utilization of defects for device engineering.

Systematizing the Delivery of Local Employment and Training Services. The Job Center Technical Assistance Guide.

ERIC Educational Resources Information Center

Wisconsin State Dept. of Industry, Labor and Human Relations, Madison.

This technical assistance guide was developed to consolidate a statewide understanding of the effort to systematize the delivery of employment and training programs through the local formation of job centers in Wisconsin, and to provide a compilation, drawn from 20 local models, that explains how the programs are delivered. The guide is organized…

Exploring corrections to the Optomechanical Hamiltonian.

PubMed

Sala, Kamila; Tufarelli, Tommaso

2018-06-14

We compare two approaches for deriving corrections to the "linear model" of cavity optomechanics, in order to describe effects that are beyond first order in the radiation pressure coupling. In the regime where the mechanical frequency is much lower than the cavity one, we compare: (I) a widely used phenomenological Hamiltonian conserving the photon number; (II) a two-mode truncation of C. K. Law's microscopic model, which we take as the "true" system Hamiltonian. While these approaches agree at first order, the latter model does not conserve the photon number, resulting in challenging computations. We find that approach (I) allows for several analytical predictions, and significantly outperforms the linear model in our numerical examples. Yet, we also find that the phenomenological Hamiltonian cannot fully capture all high-order corrections arising from the C. K. Law model.

Finite Group Invariance and Solution of Jaynes-Cummings Hamiltonian

DOE Office of Scientific and Technical Information (OSTI.GOV)

Haydargil, Derya; Koc, Ramazan

2004-10-04

The finite group invariance of the E x {beta} and Jaynes-Cummings models are studied. A method is presented to obtain finite group invariance of the E x {beta} system.A suitable transformation of a Jaynes-Cummings Hamiltonian leads to equivalence of E x {beta} system. Then a general method is applied to obtain the solution of Jaynes-Cummings Hamiltonian with Kerr nonlinearity. Number operator for this structure and the generators of su(2) algebra are used to find the eigenvalues of the Jaynes-Cummings Hamiltonian for different states. By using the invariance of number operator the solution of modified Jaynes-Cummings Hamiltonian is also discussed.

Comparative effectiveness of patient-centered strategies to improve FDA medication guides.

PubMed

Wolf, Michael S; Bailey, Stacy C; Serper, Marina; Smith, Meredith; Davis, Terry C; Russell, Allison L; Manzoor, Beenish S; Belter, Lisa; Parker, Ruth M; Lambert, Bruce

2014-09-01

Med Guides are the only Food and Drug Administration-regulated source of written patient information distributed with prescriptions drugs. Despite their potential value, studies have found them to have limited utility. To evaluate the effectiveness of patient-centered strategies for the design of Med Guides to improve comprehension. A cross-sectional, randomized trial. Two primary care clinics in Chicago, Illinois; one based in a public university hospital and the other within a private academic medical center. A total of 1003 adults aged 18-85 years. The format and layout of content from 3 typical Med Guides (by reading difficulty, length, exposure) were modified several ways to promote information accessibility. Working with patients, the 3 most preferred versions were evaluated. The first used 2 columns to organize content (Column), a second mimicked over-the-counter "Drug Facts" labeling (Drug Facts), and the third followed health literacy best practices using a simple table format (Health Literacy prototype). Tailored comprehension assessment of content from 3 representative Med Guides. Comprehension was significantly greater for all 3 prototypes compared with the current standard (all P<0.001). The Health Literacy prototype consistently demonstrated the highest comprehension scores, and in multivariable analyses, outperformed both the Drug Facts [β=-4.43, 95% confidence interval (CI), -6.21 to -2.66] and Column (β=-4.04, 95% CI, -5.82 to -2.26) prototypes. Both older age (older than 60 y: β=-10.54, 95% CI, -15.12 to -5.96), low and marginal literacy skills were independently associated with poorer comprehension (low: β=-31.92, 95% CI, -35.72 to -28.12; marginal: β=-12.91, 95% CI, -16.01 to -9.82). The application of evidence-based practices to the redesign of Med Guides significantly improved patient comprehension. Although some age and literacy disparities were reduced with the Health Literacy format in particular, both older age and low literacy

Does finite-temperature decoding deliver better optima for noisy Hamiltonians?

NASA Astrophysics Data System (ADS)

Ochoa, Andrew J.; Nishimura, Kohji; Nishimori, Hidetoshi; Katzgraber, Helmut G.

The minimization of an Ising spin-glass Hamiltonian is an NP-hard problem. Because many problems across disciplines can be mapped onto this class of Hamiltonian, novel efficient computing techniques are highly sought after. The recent development of quantum annealing machines promises to minimize these difficult problems more efficiently. However, the inherent noise found in these analog devices makes the minimization procedure difficult. While the machine might be working correctly, it might be minimizing a different Hamiltonian due to the inherent noise. This means that, in general, the ground-state configuration that correctly minimizes a noisy Hamiltonian might not minimize the noise-less Hamiltonian. Inspired by rigorous results that the energy of the noise-less ground-state configuration is equal to the expectation value of the energy of the noisy Hamiltonian at the (nonzero) Nishimori temperature [J. Phys. Soc. Jpn., 62, 40132930 (1993)], we numerically study the decoding probability of the original noise-less ground state with noisy Hamiltonians in two space dimensions, as well as the D-Wave Inc. Chimera topology. Our results suggest that thermal fluctuations might be beneficial during the optimization process in analog quantum annealing machines.

Bi-Hamiltonian Structure in 2-d Field Theory

NASA Astrophysics Data System (ADS)

Ferapontov, E. V.; Galvão, C. A. P.; Mokhov, O. I.; Nutku, Y.

We exhibit the bi-Hamiltonian structure of the equations of associativity (Witten-Dijkgraaf-Verlinde-Verlinde-Dubrovin equations) in 2-d topological field theory, which reduce to a single equation of Monge-Ampère type $ fttt}=f{xxt;;;;;2 - fxxx}f{xtt ,$ in the case of three primary fields. The first Hamiltonian structure of this equation is based on its representation as a 3-component system of hydrodynamic type and the second Hamiltonian structure follows from its formulation in terms of a variational principle with a degenerate Lagrangian.

Finite-dimensional Liouville integrable Hamiltonian systems generated from Lax pairs of a bi-Hamiltonian soliton hierarchy by symmetry constraints

NASA Astrophysics Data System (ADS)

Manukure, Solomon

2018-04-01

We construct finite-dimensional Hamiltonian systems by means of symmetry constraints from the Lax pairs and adjoint Lax pairs of a bi-Hamiltonian hierarchy of soliton equations associated with the 3-dimensional special linear Lie algebra, and discuss the Liouville integrability of these systems based on the existence of sufficiently many integrals of motion.

Local modular Hamiltonians from the quantum null energy condition

NASA Astrophysics Data System (ADS)

Koeller, Jason; Leichenauer, Stefan; Levine, Adam; Shahbazi-Moghaddam, Arvin

2018-03-01

The vacuum modular Hamiltonian K of the Rindler wedge in any relativistic quantum field theory is given by the boost generator. Here we investigate the modular Hamiltonian for more general half-spaces which are bounded by an arbitrary smooth cut of a null plane. We derive a formula for the second derivative of the modular Hamiltonian with respect to the coordinates of the cut which schematically reads K''=Tv v . This formula can be integrated twice to obtain a simple expression for the modular Hamiltonian. The result naturally generalizes the standard expression for the Rindler modular Hamiltonian to this larger class of regions. Our primary assumptions are the quantum null energy condition—an inequality between the second derivative of the von Neumann entropy of a region and the stress tensor—and its saturation in the vacuum for these regions. We discuss the validity of these assumptions in free theories and holographic theories to all orders in 1 /N .

Hamiltonian surface charges using external sources

DOE Office of Scientific and Technical Information (OSTI.GOV)

Troessaert, Cédric, E-mail: troessaert@cecs.cl

2016-05-15

In this work, we interpret part of the boundary conditions as external sources in order to partially solve the integrability problem present in the computation of surface charges associated to gauge symmetries in the hamiltonian formalism. We start by describing the hamiltonian structure of external symmetries preserving the action up to a transformation of the external sources of the theory. We then extend these results to the computation of surface charges for field theories with non-trivial boundary conditions.

Contact Hamiltonian systems and complete integrability

NASA Astrophysics Data System (ADS)

Visinescu, Mihai

2017-12-01

We summarize recent results on the integrability of Hamiltonian systems on contact manifolds. We explain how to extend the classical formulation of action-angle variables to contact integrable systems. Using the Jacobi brackets defined on contact manifolds, we discuss the commutativity of first integrals for contact Hamiltonian systems and present the construction of generalized contact action-angle variables. We illustrate the integrability in the contact geometry on the five-dimensional Sasaki-Einstein spaces T1,1 and Yp,q.

Hamiltonian structure of real Monge - Ampère equations

NASA Astrophysics Data System (ADS)

Nutku, Y.

1996-06-01

The variational principle for the real homogeneous Monge - Ampère equation in two dimensions is shown to contain three arbitrary functions of four variables. There exist two different specializations of this variational principle where the Lagrangian is degenerate and furthermore contains an arbitrary function of two variables. The Hamiltonian formulation of these degenerate Lagrangian systems requires the use of Dirac's theory of constraints. As in the case of most completely integrable systems the constraints are second class and Dirac brackets directly yield the Hamiltonian operators. Thus the real homogeneous Monge - Ampère equation in two dimensions admits two classes of infinitely many Hamiltonian operators, namely a family of local, as well as another family non-local Hamiltonian operators and symplectic 2-forms which depend on arbitrary functions of two variables. The simplest non-local Hamiltonian operator corresponds to the Kac - Moody algebra of vector fields and functions on the unit circle. Hamiltonian operators that belong to either class are compatible with each other but between classes there is only one compatible pair. In the case of real Monge - Ampère equations with constant right-hand side this compatible pair is the only pair of Hamiltonian operators that survives. Then the complete integrability of all these real Monge - Ampère equations follows by Magri's theorem. Some of the remarkable properties we have obtained for the Hamiltonian structure of the real homogeneous Monge - Ampère equation in two dimensions turn out to be generic to the real homogeneous Monge - Ampère equation and the geodesic flow for the complex homogeneous Monge - Ampère equation in arbitrary number of dimensions. Hence among all integrable nonlinear evolution equations in one space and one time dimension, the real homogeneous Monge - Ampère equation is distinguished as one that retains its character as an integrable system in multiple dimensions.

Hamiltonian formulation of the KdV equation

NASA Astrophysics Data System (ADS)

Nutku, Y.

1984-06-01

We consider the canonical formulation of Whitham's variational principle for the KdV equation. This Lagrangian is degenerate and we have found it necessary to use Dirac's theory of constrained systems in constructing the Hamiltonian. Earlier discussions of the Hamiltonian structure of the KdV equation were based on various different decompositions of the field which is avoided by this new approach.

Intertwined Hamiltonians in two-dimensional curved spaces

NASA Astrophysics Data System (ADS)

Aghababaei Samani, Keivan; Zarei, Mina

2005-04-01

The problem of intertwined Hamiltonians in two-dimensional curved spaces is investigated. Explicit results are obtained for Euclidean plane, Minkowski plane, Poincaré half plane (AdS2), de Sitter plane (dS2), sphere, and torus. It is shown that the intertwining operator is related to the Killing vector fields and the isometry group of corresponding space. It is shown that the intertwined potentials are closely connected to the integral curves of the Killing vector fields. Two problems are considered as applications of the formalism presented in the paper. The first one is the problem of Hamiltonians with equispaced energy levels and the second one is the problem of Hamiltonians whose spectrum is like the spectrum of a free particle.

Contact symmetries and Hamiltonian thermodynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bravetti, A., E-mail: bravetti@correo.nucleares.unam.mx; Lopez-Monsalvo, C.S., E-mail: cesar.slm@correo.nucleares.unam.mx; Nettel, F., E-mail: Francisco.Nettel@roma1.infn.it

It has been shown that contact geometry is the proper framework underlying classical thermodynamics and that thermodynamic fluctuations are captured by an additional metric structure related to Fisher’s Information Matrix. In this work we analyse several unaddressed aspects about the application of contact and metric geometry to thermodynamics. We consider here the Thermodynamic Phase Space and start by investigating the role of gauge transformations and Legendre symmetries for metric contact manifolds and their significance in thermodynamics. Then we present a novel mathematical characterization of first order phase transitions as equilibrium processes on the Thermodynamic Phase Space for which the Legendremore » symmetry is broken. Moreover, we use contact Hamiltonian dynamics to represent thermodynamic processes in a way that resembles the classical Hamiltonian formulation of conservative mechanics and we show that the relevant Hamiltonian coincides with the irreversible entropy production along thermodynamic processes. Therefore, we use such property to give a geometric definition of thermodynamically admissible fluctuations according to the Second Law of thermodynamics. Finally, we show that the length of a curve describing a thermodynamic process measures its entropy production.« less

Family Literacy Project. Learning Centers for Parents and Children. A Resource Guide.

ERIC Educational Resources Information Center

Crocker, M. Judith, Ed.; And Others

This guide is intended to help adult education programs establish family literacy programs and create Family Learning Centers in Cleveland Public Schools. The information should assist program coordinators in developing educational components that offer activities to raise the self-esteem of the parents and provide them with the knowledge and…

Explicit methods in extended phase space for inseparable Hamiltonian problems

NASA Astrophysics Data System (ADS)

Pihajoki, Pauli

2015-03-01

We present a method for explicit leapfrog integration of inseparable Hamiltonian systems by means of an extended phase space. A suitably defined new Hamiltonian on the extended phase space leads to equations of motion that can be numerically integrated by standard symplectic leapfrog (splitting) methods. When the leapfrog is combined with coordinate mixing transformations, the resulting algorithm shows good long term stability and error behaviour. We extend the method to non-Hamiltonian problems as well, and investigate optimal methods of projecting the extended phase space back to original dimension. Finally, we apply the methods to a Hamiltonian problem of geodesics in a curved space, and a non-Hamiltonian problem of a forced non-linear oscillator. We compare the performance of the methods to a general purpose differential equation solver LSODE, and the implicit midpoint method, a symplectic one-step method. We find the extended phase space methods to compare favorably to both for the Hamiltonian problem, and to the implicit midpoint method in the case of the non-linear oscillator.

NLO renormalization in the Hamiltonian truncation

NASA Astrophysics Data System (ADS)

Elias-Miró, Joan; Rychkov, Slava; Vitale, Lorenzo G.

2017-09-01

Hamiltonian truncation (also known as "truncated spectrum approach") is a numerical technique for solving strongly coupled quantum field theories, in which the full Hilbert space is truncated to a finite-dimensional low-energy subspace. The accuracy of the method is limited only by the available computational resources. The renormalization program improves the accuracy by carefully integrating out the high-energy states, instead of truncating them away. In this paper, we develop the most accurate ever variant of Hamiltonian Truncation, which implements renormalization at the cubic order in the interaction strength. The novel idea is to interpret the renormalization procedure as a result of integrating out exactly a certain class of high-energy "tail states." We demonstrate the power of the method with high-accuracy computations in the strongly coupled two-dimensional quartic scalar theory and benchmark it against other existing approaches. Our work will also be useful for the future goal of extending Hamiltonian truncation to higher spacetime dimensions.

An algorithm for finding a similar subgraph of all Hamiltonian cycles

NASA Astrophysics Data System (ADS)

Wafdan, R.; Ihsan, M.; Suhaimi, D.

2018-01-01

This paper discusses an algorithm to find a similar subgraph called findSimSubG algorithm. A similar subgraph is a subgraph with a maximum number of edges, contains no isolated vertex and is contained in every Hamiltonian cycle of a Hamiltonian Graph. The algorithm runs only on Hamiltonian graphs with at least two Hamiltonian cycles. The algorithm works by examining whether the initial subgraph of the first Hamiltonian cycle is a subgraph of comparison graphs. If the initial subgraph is not in comparison graphs, the algorithm will remove edges and vertices of the initial subgraph that are not in comparison graphs. There are two main processes in the algorithm, changing Hamiltonian cycle into a cycle graph and removing edges and vertices of the initial subgraph that are not in comparison graphs. The findSimSubG algorithm can find the similar subgraph without using backtracking method. The similar subgraph cannot be found on certain graphs, such as an n-antiprism graph, complete bipartite graph, complete graph, 2n-crossed prism graph, n-crown graph, n-möbius ladder, prism graph, and wheel graph. The complexity of this algorithm is O(m|V|), where m is the number of Hamiltonian cycles and |V| is the number of vertices of a Hamiltonian graph.

Hamiltonian description of closed configurations of the vacuum magnetic field

NASA Astrophysics Data System (ADS)

Skovoroda, A. A.

2015-05-01

Methods of obtaining and using the Hamiltonians of closed vacuum magnetic configurations of fusion research systems are reviewed. Various approaches to calculate the flux functions determining the Hamiltonian are discussed. It is shown that the Hamiltonian description allows one not only to reproduce all traditional results, but also to study the behavior of magnetic field lines by using the theory of dynamic systems. The potentialities of the Hamiltonian formalism and its close relation to traditional methods are demonstrated using a large number of classical examples adopted from the fundamental works by A.I. Morozov, L.S. Solov'ev, and V.D. Shafranov.

Non-stoquastic Hamiltonians in quantum annealing via geometric phases

NASA Astrophysics Data System (ADS)

Vinci, Walter; Lidar, Daniel A.

2017-09-01

We argue that a complete description of quantum annealing implemented with continuous variables must take into account the non-adiabatic Aharonov-Anandan geometric phase that arises when the system Hamiltonian changes during the anneal. We show that this geometric effect leads to the appearance of non-stoquasticity in the effective quantum Ising Hamiltonians that are typically used to describe quantum annealing with flux qubits. We explicitly demonstrate the effect of this geometric non-stoquasticity when quantum annealing is performed with a system of one and two coupled flux qubits. The realization of non-stoquastic Hamiltonians has important implications from a computational complexity perspective, since it is believed that in many cases quantum annealing with stoquastic Hamiltonians can be efficiently simulated via classical algorithms such as Quantum Monte Carlo. It is well known that the direct implementation of non-stoquastic Hamiltonians with flux qubits is particularly challenging. Our results suggest an alternative path for the implementation of non-stoquasticity via geometric phases that can be exploited for computational purposes.

Early Warning System Implementation Guide: For Use with the National High School Center's Early Warning System Tool v2.0

ERIC Educational Resources Information Center

Therriault, Susan Bowles; Heppen, Jessica; O'Cummings, Mindee; Fryer, Lindsay; Johnson, Amy

2010-01-01

This Early Warning System (EWS) Implementation Guide is a supporting document for schools and districts that are implementing the National High School Center's Early Warning System (EWS) Tool v2.0. Developed by the National High School Center at the American Institutes for Research (AIR), the guide and tool support the establishment and…

An electromechanical Ising Hamiltonian

PubMed Central

Mahboob, Imran; Okamoto, Hajime; Yamaguchi, Hiroshi

2016-01-01

Solving intractable mathematical problems in simulators composed of atoms, ions, photons, or electrons has recently emerged as a subject of intense interest. We extend this concept to phonons that are localized in spectrally pure resonances in an electromechanical system that enables their interactions to be exquisitely fashioned via electrical means. We harness this platform to emulate the Ising Hamiltonian whose spin 1/2 particles are replicated by the phase bistable vibrations from the parametric resonances of multiple modes. The coupling between the mechanical spins is created by generating two-mode squeezed states, which impart correlations between modes that can imitate a random, ferromagnetic state or an antiferromagnetic state on demand. These results suggest that an electromechanical simulator could be built for the Ising Hamiltonian in a nontrivial configuration, namely, for a large number of spins with multiple degrees of coupling. PMID:28861469

An electromechanical Ising Hamiltonian.

PubMed

Mahboob, Imran; Okamoto, Hajime; Yamaguchi, Hiroshi

2016-06-01

Solving intractable mathematical problems in simulators composed of atoms, ions, photons, or electrons has recently emerged as a subject of intense interest. We extend this concept to phonons that are localized in spectrally pure resonances in an electromechanical system that enables their interactions to be exquisitely fashioned via electrical means. We harness this platform to emulate the Ising Hamiltonian whose spin 1/2 particles are replicated by the phase bistable vibrations from the parametric resonances of multiple modes. The coupling between the mechanical spins is created by generating two-mode squeezed states, which impart correlations between modes that can imitate a random, ferromagnetic state or an antiferromagnetic state on demand. These results suggest that an electromechanical simulator could be built for the Ising Hamiltonian in a nontrivial configuration, namely, for a large number of spins with multiple degrees of coupling.

The Artificial Hamiltonian, First Integrals, and Closed-Form Solutions of Dynamical Systems for Epidemics

NASA Astrophysics Data System (ADS)

Naz, Rehana; Naeem, Imran

2018-03-01

The non-standard Hamiltonian system, also referred to as a partial Hamiltonian system in the literature, of the form {\\dot q^i} = {partial H}/{partial {p_i}},\\dot p^i = - {partial H}/{partial {q_i}} + {Γ ^i}(t,{q^i},{p_i}) appears widely in economics, physics, mechanics, and other fields. The non-standard (partial) Hamiltonian systems arise from physical Hamiltonian structures as well as from artificial Hamiltonian structures. We introduce the term `artificial Hamiltonian' for the Hamiltonian of a model having no physical structure. We provide here explicitly the notion of an artificial Hamiltonian for dynamical systems of ordinary differential equations (ODEs). Also, we show that every system of second-order ODEs can be expressed as a non-standard (partial) Hamiltonian system of first-order ODEs by introducing an artificial Hamiltonian. This notion of an artificial Hamiltonian gives a new way to solve dynamical systems of first-order ODEs and systems of second-order ODEs that can be expressed as a non-standard (partial) Hamiltonian system by using the known techniques applicable to the non-standard Hamiltonian systems. We employ the proposed notion to solve dynamical systems of first-order ODEs arising in epidemics.

Boson Hamiltonians and stochasticity for the vorticity equation

NASA Technical Reports Server (NTRS)

Shen, Hubert H.

1990-01-01

The evolution of the vorticity in time for two-dimensional inviscid flow and in Lagrangian time for three-dimensional viscous flow is written in Hamiltonian form by introducing Bose operators. The addition of the viscous and convective terms, respectively, leads to an interpretation of the Hamiltonian contribution to the evolution as Langevin noise.

Nonunitary quantum computation in the ground space of local Hamiltonians

NASA Astrophysics Data System (ADS)

Usher, Naïri; Hoban, Matty J.; Browne, Dan E.

2017-09-01

A central result in the study of quantum Hamiltonian complexity is that the k -local Hamiltonian problem is quantum-Merlin-Arthur-complete. In that problem, we must decide if the lowest eigenvalue of a Hamiltonian is bounded below some value, or above another, promised one of these is true. Given the ground state of the Hamiltonian, a quantum computer can determine this question, even if the ground state itself may not be efficiently quantum preparable. Kitaev's proof of QMA-completeness encodes a unitary quantum circuit in QMA into the ground space of a Hamiltonian. However, we now have quantum computing models based on measurement instead of unitary evolution; furthermore, we can use postselected measurement as an additional computational tool. In this work, we generalize Kitaev's construction to allow for nonunitary evolution including postselection. Furthermore, we consider a type of postselection under which the construction is consistent, which we call tame postselection. We consider the computational complexity consequences of this construction and then consider how the probability of an event upon which we are postselecting affects the gap between the ground-state energy and the energy of the first excited state of its corresponding Hamiltonian. We provide numerical evidence that the two are not immediately related by giving a family of circuits where the probability of an event upon which we postselect is exponentially small, but the gap in the energy levels of the Hamiltonian decreases as a polynomial.

Next generation of the self-consistent and environment-dependent Hamiltonian: Applications to various boron allotropes from zero- to three-dimensional structures

NASA Astrophysics Data System (ADS)

Tandy, P.; Yu, Ming; Leahy, C.; Jayanthi, C. S.; Wu, S. Y.

2015-03-01

An upgrade of the previous self-consistent and environment-dependent linear combination of atomic orbitals Hamiltonian (referred as SCED-LCAO) has been developed. This improved version of the semi-empirical SCED-LCAO Hamiltonian, in addition to the inclusion of self-consistent determination of charge redistribution, multi-center interactions, and modeling of electron-electron correlation, has taken into account the effect excited on the orbitals due to the atomic aggregation. This important upgrade has been subjected to a stringent test, the construction of the SCED-LCAO Hamiltonian for boron. It was shown that the Hamiltonian for boron has successfully characterized the electron deficiency of boron and captured the complex chemical bonding in various boron allotropes, including the planar and quasi-planar, the convex, the ring, the icosahedral, and the fullerene-like clusters, the two-dimensional monolayer sheets, and the bulk alpha boron, demonstrating its transferability, robustness, reliability, and predictive power. The molecular dynamics simulation scheme based on the Hamiltonian has been applied to explore the existence and the energetics of ˜230 compact boron clusters BN with N in the range from ˜100 to 768, including the random, the rhombohedral, and the spherical icosahedral structures. It was found that, energetically, clusters containing whole icosahedral B12 units are more stable for boron clusters of larger size (N > 200). The ease with which the simulations both at 0 K and finite temperatures were completed is a demonstration of the efficiency of the SCED-LCAO Hamiltonian.

Multi-Hamiltonian structure of the Born-Infeld equation

NASA Astrophysics Data System (ADS)

Arik, Metin; Neyzi, Fahrünisa; Nutku, Yavuz; Olver, Peter J.; Verosky, John M.

1989-06-01

The multi-Hamiltonian structure, conservation laws, and higher order symmetries for the Born-Infeld equation are exhibited. A new transformation of the Born-Infeld equation to the equations of a Chaplygin gas is presented and explored. The Born-Infeld equation is distinguished among two-dimensional hyperbolic systems by its wealth of such multi-Hamiltonian structures.

Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity

NASA Astrophysics Data System (ADS)

Bridges, Thomas J.; Reich, Sebastian

2001-06-01

The symplectic numerical integration of finite-dimensional Hamiltonian systems is a well established subject and has led to a deeper understanding of existing methods as well as to the development of new very efficient and accurate schemes, e.g., for rigid body, constrained, and molecular dynamics. The numerical integration of infinite-dimensional Hamiltonian systems or Hamiltonian PDEs is much less explored. In this Letter, we suggest a new theoretical framework for generalizing symplectic numerical integrators for ODEs to Hamiltonian PDEs in R2: time plus one space dimension. The central idea is that symplecticity for Hamiltonian PDEs is directional: the symplectic structure of the PDE is decomposed into distinct components representing space and time independently. In this setting PDE integrators can be constructed by concatenating uni-directional ODE symplectic integrators. This suggests a natural definition of multi-symplectic integrator as a discretization that conserves a discrete version of the conservation of symplecticity for Hamiltonian PDEs. We show that this approach leads to a general framework for geometric numerical schemes for Hamiltonian PDEs, which have remarkable energy and momentum conservation properties. Generalizations, including development of higher-order methods, application to the Euler equations in fluid mechanics, application to perturbed systems, and extension to more than one space dimension are also discussed.

On a new class of completely integrable nonlinear wave equations. II. Multi-Hamiltonian structure

NASA Astrophysics Data System (ADS)

Nutku, Y.

1987-11-01

The multi-Hamiltonian structure of a class of nonlinear wave equations governing the propagation of finite amplitude waves is discussed. Infinitely many conservation laws had earlier been obtained for these equations. Starting from a (primary) Hamiltonian formulation of these equations the necessary and sufficient conditions for the existence of bi-Hamiltonian structure are obtained and it is shown that the second Hamiltonian operator can be constructed solely through a knowledge of the first Hamiltonian function. The recursion operator which first appears at the level of bi-Hamiltonian structure gives rise to an infinite sequence of conserved Hamiltonians. It is found that in general there exist two different infinite sequences of conserved quantities for these equations. The recursion relation defining higher Hamiltonian structures enables one to obtain the necessary and sufficient conditions for the existence of the (k+1)st Hamiltonian operator which depends on the kth Hamiltonian function. The infinite sequence of conserved Hamiltonians are common to all the higher Hamiltonian structures. The equations of gas dynamics are discussed as an illustration of this formalism and it is shown that in general they admit tri-Hamiltonian structure with two distinct infinite sets of conserved quantities. The isothermal case of γ=1 is an exceptional one that requires separate treatment. This corresponds to a specialization of the equations governing the expansion of plasma into vacuum which will be shown to be equivalent to Poisson's equation in nonlinear acoustics.

Hamiltonian thermodynamics of three-dimensional dilatonic black holes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dias, Goncalo A. S.; Lemos, Jose P. S.

2008-08-15

The action for a class of three-dimensional dilaton-gravity theories with a negative cosmological constant can be recast in a Brans-Dicke type action, with its free {omega} parameter. These theories have static spherically symmetric black holes. Those with well formulated asymptotics are studied through a Hamiltonian formalism, and their thermodynamical properties are found out. The theories studied are general relativity ({omega}{yields}{infinity}), a dimensionally reduced cylindrical four-dimensional general relativity theory ({omega}=0), and a theory representing a class of theories ({omega}=-3). The Hamiltonian formalism is set up in three dimensions through foliations on the right region of the Carter-Penrose diagram, with the bifurcationmore » 1-sphere as the left boundary, and anti-de Sitter infinity as the right boundary. The metric functions on the foliated hypersurfaces are the canonical coordinates. The Hamiltonian action is written, the Hamiltonian being a sum of constraints. One finds a new action which yields an unconstrained theory with one pair of canonical coordinates (M,P{sub M}), M being the mass parameter and P{sub M} its conjugate momenta The resulting Hamiltonian is a sum of boundary terms only. A quantization of the theory is performed. The Schroedinger evolution operator is constructed, the trace is taken, and the partition function of the canonical ensemble is obtained. The black hole entropies differ, in general, from the usual quarter of the horizon area due to the dilaton.« less

Exploring Hamiltonian dielectric solvent molecular dynamics

NASA Astrophysics Data System (ADS)

Bauer, Sebastian; Tavan, Paul; Mathias, Gerald

2014-09-01

Hamiltonian dielectric solvent (HADES) is a recent method [7,25], which enables Hamiltonian molecular dynamics (MD) simulations of peptides and proteins in dielectric continua. Sample simulations of an α-helical decapeptide with and without explicit solvent demonstrate the high efficiency of HADES-MD. Addressing the folding of this peptide by replica exchange MD we study the properties of HADES by comparing melting curves, secondary structure motifs and salt bridges with explicit solvent results. Despite the unoptimized ad hoc parametrization of HADES, calculated reaction field energies correlate well with numerical grid solutions of the dielectric Poisson equation.

Hamiltonian dynamics for complex food webs

NASA Astrophysics Data System (ADS)

Kozlov, Vladimir; Vakulenko, Sergey; Wennergren, Uno

2016-03-01

We investigate stability and dynamics of large ecological networks by introducing classical methods of dynamical system theory from physics, including Hamiltonian and averaging methods. Our analysis exploits the topological structure of the network, namely the existence of strongly connected nodes (hubs) in the networks. We reveal new relations between topology, interaction structure, and network dynamics. We describe mechanisms of catastrophic phenomena leading to sharp changes of dynamics and hence completely altering the ecosystem. We also show how these phenomena depend on the structure of interaction between species. We can conclude that a Hamiltonian structure of biological interactions leads to stability and large biodiversity.

Next generation of the self-consistent and environment-dependent Hamiltonian: Applications to various boron allotropes from zero- to three-dimensional structures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tandy, P.; Yu, Ming; Leahy, C.

2015-03-28

An upgrade of the previous self-consistent and environment-dependent linear combination of atomic orbitals Hamiltonian (referred as SCED-LCAO) has been developed. This improved version of the semi-empirical SCED-LCAO Hamiltonian, in addition to the inclusion of self-consistent determination of charge redistribution, multi-center interactions, and modeling of electron-electron correlation, has taken into account the effect excited on the orbitals due to the atomic aggregation. This important upgrade has been subjected to a stringent test, the construction of the SCED-LCAO Hamiltonian for boron. It was shown that the Hamiltonian for boron has successfully characterized the electron deficiency of boron and captured the complex chemicalmore » bonding in various boron allotropes, including the planar and quasi-planar, the convex, the ring, the icosahedral, and the fullerene-like clusters, the two-dimensional monolayer sheets, and the bulk alpha boron, demonstrating its transferability, robustness, reliability, and predictive power. The molecular dynamics simulation scheme based on the Hamiltonian has been applied to explore the existence and the energetics of ∼230 compact boron clusters B{sub N} with N in the range from ∼100 to 768, including the random, the rhombohedral, and the spherical icosahedral structures. It was found that, energetically, clusters containing whole icosahedral B{sub 12} units are more stable for boron clusters of larger size (N > 200). The ease with which the simulations both at 0 K and finite temperatures were completed is a demonstration of the efficiency of the SCED-LCAO Hamiltonian.« less

Hamiltonian Analysis of Subcritical Stochastic Epidemic Dynamics

PubMed Central

2017-01-01

We extend a technique of approximation of the long-term behavior of a supercritical stochastic epidemic model, using the WKB approximation and a Hamiltonian phase space, to the subcritical case. The limiting behavior of the model and approximation are qualitatively different in the subcritical case, requiring a novel analysis of the limiting behavior of the Hamiltonian system away from its deterministic subsystem. This yields a novel, general technique of approximation of the quasistationary distribution of stochastic epidemic and birth-death models and may lead to techniques for analysis of these models beyond the quasistationary distribution. For a classic SIS model, the approximation found for the quasistationary distribution is very similar to published approximations but not identical. For a birth-death process without depletion of susceptibles, the approximation is exact. Dynamics on the phase plane similar to those predicted by the Hamiltonian analysis are demonstrated in cross-sectional data from trachoma treatment trials in Ethiopia, in which declining prevalences are consistent with subcritical epidemic dynamics. PMID:28932256

Potentials of Mean Force With Ab Initio Mixed Hamiltonian Models of Solvation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dupuis, Michel; Schenter, Gregory K.; Garrett, Bruce C.

2003-08-01

We give an account of a computationally tractable and efficient procedure for the calculation of potentials of mean force using mixed Hamiltonian models of electronic structure where quantum subsystems are described with computationally intensive ab initio wavefunctions. The mixed Hamiltonian is mapped into an all-classical Hamiltonian that is amenable to a thermodynamic perturbation treatment for the calculation of free energies. A small number of statistically uncorrelated (solute-solvent) configurations are selected from the Monte Carlo random walk generated with the all-classical Hamiltonian approximation. Those are used in the averaging of the free energy using the mixed quantum/classical Hamiltonian. The methodology ismore » illustrated for the micro-solvated SN2 substitution reaction of methyl chloride by hydroxide. We also compare the potential of mean force calculated with the above protocol with an approximate formalism, one in which the potential of mean force calculated with the all-classical Hamiltonian is simply added to the energy of the isolated (non-solvated) solute along the reaction path. Interestingly the latter approach is found to be in semi-quantitative agreement with the full mixed Hamiltonian approximation.« less

Is the addition of an assisted driving Hamiltonian always useful for adiabatic evolution?

NASA Astrophysics Data System (ADS)

Sun, Jie; Lu, Songfeng; Li, Li

2017-04-01

It has been known that when an assisted driving item is added to the main system Hamiltonian, the efficiency of the resultant adiabatic evolution can be significantly improved. In some special cases, it can be seen that only through adding an assisted driving Hamiltonian can the resulting adiabatic evolution be made not to fail. Thus the additional driving Hamiltonian plays an important role in adiabatic computing. In this paper, we show that if the driving Hamiltonian is chosen inappropriately, the adiabatic computation may still fail. More importantly, we find that the adiabatic computation can only succeed if the assisted driving Hamiltonian has a relatively fixed form. This may help us understand why in the related literature all of the driving Hamiltonians used share the same form.

Hamiltonian replica exchange combined with elastic network analysis to enhance global domain motions in atomistic molecular dynamics simulations.

PubMed

Ostermeir, Katja; Zacharias, Martin

2014-12-01

Coarse-grained elastic network models (ENM) of proteins offer a low-resolution representation of protein dynamics and directions of global mobility. A Hamiltonian-replica exchange molecular dynamics (H-REMD) approach has been developed that combines information extracted from an ENM analysis with atomistic explicit solvent MD simulations. Based on a set of centers representing rigid segments (centroids) of a protein, a distance-dependent biasing potential is constructed by means of an ENM analysis to promote and guide centroid/domain rearrangements. The biasing potentials are added with different magnitude to the force field description of the MD simulation along the replicas with one reference replica under the control of the original force field. The magnitude and the form of the biasing potentials are adapted during the simulation based on the average sampled conformation to reach a near constant biasing in each replica after equilibration. This allows for canonical sampling of conformational states in each replica. The application of the methodology to a two-domain segment of the glycoprotein 130 and to the protein cyanovirin-N indicates significantly enhanced global domain motions and improved conformational sampling compared with conventional MD simulations. © 2014 Wiley Periodicals, Inc.

Phase space flows for non-Hamiltonian systems with constraints

NASA Astrophysics Data System (ADS)

Sergi, Alessandro

2005-09-01

In this paper, non-Hamiltonian systems with holonomic constraints are treated by a generalization of Dirac’s formalism. Non-Hamiltonian phase space flows can be described by generalized antisymmetric brackets or by general Liouville operators which cannot be derived from brackets. Both situations are treated. In the first case, a Nosé-Dirac bracket is introduced as an example. In the second one, Dirac’s recipe for projecting out constrained variables from time translation operators is generalized and then applied to non-Hamiltonian linear response. Dirac’s formalism avoids spurious terms in the response function of constrained systems. However, corrections coming from phase space measure must be considered for general perturbations.

An infinite-order two-component relativistic Hamiltonian by a simple one-step transformation.

PubMed

Ilias, Miroslav; Saue, Trond

2007-02-14

The authors report the implementation of a simple one-step method for obtaining an infinite-order two-component (IOTC) relativistic Hamiltonian using matrix algebra. They apply the IOTC Hamiltonian to calculations of excitation and ionization energies as well as electric and magnetic properties of the radon atom. The results are compared to corresponding calculations using identical basis sets and based on the four-component Dirac-Coulomb Hamiltonian as well as Douglas-Kroll-Hess and zeroth-order regular approximation Hamiltonians, all implemented in the DIRAC program package, thus allowing a comprehensive comparison of relativistic Hamiltonians within the finite basis approximation.

Hamiltonian structures for systems of hyperbolic conservation laws

NASA Astrophysics Data System (ADS)

Olver, Peter J.; Nutku, Yavuz

1988-07-01

The bi-Hamiltonian structure for a large class of one-dimensional hyberbolic systems of conservation laws in two field variables, including the equations of gas dynamics, shallow water waves, one-dimensional elastic media, and the Born-Infeld equation from nonlinear electrodynamics, is exhibited. For polytropic gas dynamics, these results lead to a quadri-Hamiltonian structure. New higher-order entropy-flux pairs (conservation laws) and higher-order symmetries are exhibited.

R matrices of three-state Hamiltonians solvable by coordinate Bethe ansatz

NASA Astrophysics Data System (ADS)

Fonseca, T.; Frappat, L.; Ragoucy, E.

2015-01-01

We review some of the strategies that can be implemented to infer an R-matrix from the knowledge of its Hamiltonian. We apply them to the classification achieved in Crampé, Frappat, and Ragoucy, J. Phys. A 46, 405001 (2013), on three state U(1)-invariant Hamiltonians solvable by coordinate Bethe ansatz, focusing on models for which the S-matrix is not trivial. For the 19-vertex solutions, we recover the R-matrices of the well-known Zamolodchikov-Fateev and Izergin-Korepin models. We point out that the generalized Bariev Hamiltonian is related to both main and special branches studied by Martins in Nucl. Phys. B 874, 243 (2013), that we prove to generate the same Hamiltonian. The 19-vertex SpR model still resists to the analysis, although we are able to state some no-go theorems on its R-matrix. For 17-vertex Hamiltonians, we produce a new R-matrix.

Dynamical tunneling versus fast diffusion for a non-convex Hamiltonian

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pittman, S. M.; Tannenbaum, E.; Heller, E. J.

This paper attempts to resolve the issue of the nature of the 0.01-0.1 cm{sup −1} peak splittings observed in high-resolution IR spectra of polyatomic molecules. One hypothesis is that these splittings are caused by dynamical tunneling, a quantum-mechanical phenomenon whereby energy flows between two disconnected regions of phase-space across dynamical barriers. However, a competing classical mechanism for energy flow is Arnol’d diffusion, which connects different regions of phase-space by a resonance network known as the Arnol’d web. The speed of diffusion is bounded by the Nekhoroshev theorem, which guarantees stability on exponentially long time scales if the Hamiltonian is steep.more » Here we consider a non-convex Hamiltonian that contains the characteristics of a molecular Hamiltonian, but does not satisfy the Nekhoroshev theorem. The diffusion along the Arnol’d web is expected to be fast for a non-convex Hamiltonian. While fast diffusion is an unlikely competitor for longtime energy flow in molecules, we show how dynamical tunneling dominates compared to fast diffusion in the nearly integrable regime for a non-convex Hamiltonian, as well as present a new kind of dynamical tunneling.« less

The use of head/eye-centered, hand-centered and allocentric representations for visually guided hand movements and perceptual judgments.

PubMed

Thaler, Lore; Todd, James T

2009-04-01

Two experiments are reported that were designed to measure the accuracy and reliability of both visually guided hand movements (Exp. 1) and perceptual matching judgments (Exp. 2). The specific procedure for informing subjects of the required response on each trial was manipulated so that some tasks could only be performed using an allocentric representation of the visual target; others could be performed using either an allocentric or hand-centered representation; still others could be performed based on an allocentric, hand-centered or head/eye-centered representation. Both head/eye and hand centered representations are egocentric because they specify visual coordinates with respect to the subject. The results reveal that accuracy and reliability of both motor and perceptual responses are highest when subjects direct their response towards a visible target location, which allows them to rely on a representation of the target in head/eye-centered coordinates. Systematic changes in averages and standard deviations of responses are observed when subjects cannot direct their response towards a visible target location, but have to represent target distance and direction in either hand-centered or allocentric visual coordinates instead. Subjects' motor and perceptual performance agree quantitatively well. These results strongly suggest that subjects process head/eye-centered representations differently from hand-centered or allocentric representations, but that they process visual information for motor actions and perceptual judgments together.

Hamiltonian dynamics of extended objects

NASA Astrophysics Data System (ADS)

Capovilla, R.; Guven, J.; Rojas, E.

2004-12-01

We consider relativistic extended objects described by a reparametrization-invariant local action that depends on the extrinsic curvature of the worldvolume swept out by the object as it evolves. We provide a Hamiltonian formulation of the dynamics of such higher derivative models which is motivated by the ADM formulation of general relativity. The canonical momenta are identified by looking at boundary behaviour under small deformations of the action; the relationship between the momentum conjugate to the embedding functions and the conserved momentum density is established. The canonical Hamiltonian is constructed explicitly; the constraints on the phase space, both primary and secondary, are identified and the role they play in the theory is described. The multipliers implementing the primary constraints are identified in terms of the ADM lapse and shift variables and Hamilton's equations are shown to be consistent with the Euler Lagrange equations.

Cluster expansion for ground states of local Hamiltonians

NASA Astrophysics Data System (ADS)

Bastianello, Alvise; Sotiriadis, Spyros

2016-08-01

A central problem in many-body quantum physics is the determination of the ground state of a thermodynamically large physical system. We construct a cluster expansion for ground states of local Hamiltonians, which naturally incorporates physical requirements inherited by locality as conditions on its cluster amplitudes. Applying a diagrammatic technique we derive the relation of these amplitudes to thermodynamic quantities and local observables. Moreover we derive a set of functional equations that determine the cluster amplitudes for a general Hamiltonian, verify the consistency with perturbation theory and discuss non-perturbative approaches. Lastly we verify the persistence of locality features of the cluster expansion under unitary evolution with a local Hamiltonian and provide applications to out-of-equilibrium problems: a simplified proof of equilibration to the GGE and a cumulant expansion for the statistics of work, for an interacting-to-free quantum quench.

A theorem about Hamiltonian systems.

PubMed

Case, K M

1984-09-01

A simple theorem in Hamiltonian mechanics is pointed out. One consequence is a generalization of the classical result that symmetries are generated by Poisson brackets of conserved functionals. General applications are discussed. Special emphasis is given to the Kadomtsev-Petviashvili equation.

Relativistic Hamiltonian dynamics for N point particles

NASA Astrophysics Data System (ADS)

King, M. J.

1980-08-01

The theory is quantized canonically to give a relativistic quantum mechanics for N particles. The existence of such a theory has been in doubt since the proof of the No-interaction theorem. However, such a theory does exist and was generalized. This dynamics is expressed in terms of N + 1 pairs of canonical fourvectors (center-of-momentum variables or CMV). A gauge independent reduction due to N + 3 first class kinematic constraints leads to a 6N + 2 dimensional minimum kinematic phase space, K. The kinematics and dynamics of particles with intrinsic spin were also considered. To this end known constraint techniques were generalized to make use of graded Lie algebras. The (Poincare) invariant Hamiltonian is specified in terms of the gauge invarient variables of K. The covariant worldline variables of each particle were found to be gauge dependent. As such they will usually not satisfy a canonical algebra. An exception exists for free particles. The No-interaction theorem therefore is not violated.

A theorem about Hamiltonian systems

PubMed Central

Case, K. M.

1984-01-01

A simple theorem in Hamiltonian mechanics is pointed out. One consequence is a generalization of the classical result that symmetries are generated by Poisson brackets of conserved functionals. General applications are discussed. Special emphasis is given to the Kadomtsev-Petviashvili equation. PMID:16593515

Convergence to equilibrium under a random Hamiltonian.

PubMed

Brandão, Fernando G S L; Ćwikliński, Piotr; Horodecki, Michał; Horodecki, Paweł; Korbicz, Jarosław K; Mozrzymas, Marek

2012-09-01

We analyze equilibration times of subsystems of a larger system under a random total Hamiltonian, in which the basis of the Hamiltonian is drawn from the Haar measure. We obtain that the time of equilibration is of the order of the inverse of the arithmetic average of the Bohr frequencies. To compute the average over a random basis, we compute the inverse of a matrix of overlaps of operators which permute four systems. We first obtain results on such a matrix for a representation of an arbitrary finite group and then apply it to the particular representation of the permutation group under consideration.

Convergence to equilibrium under a random Hamiltonian

NASA Astrophysics Data System (ADS)

Brandão, Fernando G. S. L.; Ćwikliński, Piotr; Horodecki, Michał; Horodecki, Paweł; Korbicz, Jarosław K.; Mozrzymas, Marek

2012-09-01

We analyze equilibration times of subsystems of a larger system under a random total Hamiltonian, in which the basis of the Hamiltonian is drawn from the Haar measure. We obtain that the time of equilibration is of the order of the inverse of the arithmetic average of the Bohr frequencies. To compute the average over a random basis, we compute the inverse of a matrix of overlaps of operators which permute four systems. We first obtain results on such a matrix for a representation of an arbitrary finite group and then apply it to the particular representation of the permutation group under consideration.

Constructing polyatomic potential energy surfaces by interpolating diabatic Hamiltonian matrices with demonstration on green fluorescent protein chromophore

DOE Office of Scientific and Technical Information (OSTI.GOV)

Park, Jae Woo; Rhee, Young Min, E-mail: ymrhee@postech.ac.kr; Department of Chemistry, Pohang University of Science and Technology

2014-04-28

Simulating molecular dynamics directly on quantum chemically obtained potential energy surfaces is generally time consuming. The cost becomes overwhelming especially when excited state dynamics is aimed with multiple electronic states. The interpolated potential has been suggested as a remedy for the cost issue in various simulation settings ranging from fast gas phase reactions of small molecules to relatively slow condensed phase dynamics with complex surrounding. Here, we present a scheme for interpolating multiple electronic surfaces of a relatively large molecule, with an intention of applying it to studying nonadiabatic behaviors. The scheme starts with adiabatic potential information and its diabaticmore » transformation, both of which can be readily obtained, in principle, with quantum chemical calculations. The adiabatic energies and their derivatives on each interpolation center are combined with the derivative coupling vectors to generate the corresponding diabatic Hamiltonian and its derivatives, and they are subsequently adopted in producing a globally defined diabatic Hamiltonian function. As a demonstration, we employ the scheme to build an interpolated Hamiltonian of a relatively large chromophore, para-hydroxybenzylidene imidazolinone, in reference to its all-atom analytical surface model. We show that the interpolation is indeed reliable enough to reproduce important features of the reference surface model, such as its adiabatic energies and derivative couplings. In addition, nonadiabatic surface hopping simulations with interpolation yield population transfer dynamics that is well in accord with the result generated with the reference analytic surface. With these, we conclude by suggesting that the interpolation of diabatic Hamiltonians will be applicable for studying nonadiabatic behaviors of sizeable molecules.« less

BRST theory without Hamiltonian and Lagrangian

NASA Astrophysics Data System (ADS)

Lyakhovich, S. L.; Sharapov, A. A.

2005-03-01

We consider a generic gauge system, whose physical degrees of freedom are obtained by restriction on a constraint surface followed by factorization with respect to the action of gauge transformations; in so doing, no Hamiltonian structure or action principle is supposed to exist. For such a generic gauge system we construct a consistent BRST formulation, which includes the conventional BV Lagrangian and BFV Hamiltonian schemes as particular cases. If the original manifold carries a weak Poisson structure (a bivector field giving rise to a Poisson bracket on the space of physical observables) the generic gauge system is shown to admit deformation quantization by means of the Kontsevich formality theorem. A sigma-model interpretation of this quantization algorithm is briefly discussed.

Diffusion Monte Carlo approach versus adiabatic computation for local Hamiltonians

NASA Astrophysics Data System (ADS)

Bringewatt, Jacob; Dorland, William; Jordan, Stephen P.; Mink, Alan

2018-02-01

Most research regarding quantum adiabatic optimization has focused on stoquastic Hamiltonians, whose ground states can be expressed with only real non-negative amplitudes and thus for whom destructive interference is not manifest. This raises the question of whether classical Monte Carlo algorithms can efficiently simulate quantum adiabatic optimization with stoquastic Hamiltonians. Recent results have given counterexamples in which path-integral and diffusion Monte Carlo fail to do so. However, most adiabatic optimization algorithms, such as for solving MAX-k -SAT problems, use k -local Hamiltonians, whereas our previous counterexample for diffusion Monte Carlo involved n -body interactions. Here we present a 6-local counterexample which demonstrates that even for these local Hamiltonians there are cases where diffusion Monte Carlo cannot efficiently simulate quantum adiabatic optimization. Furthermore, we perform empirical testing of diffusion Monte Carlo on a standard well-studied class of permutation-symmetric tunneling problems and similarly find large advantages for quantum optimization over diffusion Monte Carlo.

Path-integral isomorphic Hamiltonian for including nuclear quantum effects in non-adiabatic dynamics

NASA Astrophysics Data System (ADS)

Tao, Xuecheng; Shushkov, Philip; Miller, Thomas F.

2018-03-01

We describe a path-integral approach for including nuclear quantum effects in non-adiabatic chemical dynamics simulations. For a general physical system with multiple electronic energy levels, a corresponding isomorphic Hamiltonian is introduced such that Boltzmann sampling of the isomorphic Hamiltonian with classical nuclear degrees of freedom yields the exact quantum Boltzmann distribution for the original physical system. In the limit of a single electronic energy level, the isomorphic Hamiltonian reduces to the familiar cases of either ring polymer molecular dynamics (RPMD) or centroid molecular dynamics Hamiltonians, depending on the implementation. An advantage of the isomorphic Hamiltonian is that it can easily be combined with existing mixed quantum-classical dynamics methods, such as surface hopping or Ehrenfest dynamics, to enable the simulation of electronically non-adiabatic processes with nuclear quantum effects. We present numerical applications of the isomorphic Hamiltonian to model two- and three-level systems, with encouraging results that include improvement upon a previously reported combination of RPMD with surface hopping in the deep-tunneling regime.

Resolving the issue of branched Hamiltonian in modified Lanczos-Lovelock gravity

NASA Astrophysics Data System (ADS)

Ruz, Soumendranath; Mandal, Ranajit; Debnath, Subhra; Sanyal, Abhik Kumar

2016-07-01

The Hamiltonian constraint H_c = N{H} = 0, defines a diffeomorphic structure on spatial manifolds by the lapse function N in general theory of relativity. However, it is not manifest in Lanczos-Lovelock gravity, since the expression for velocity in terms of the momentum is multivalued. Thus the Hamiltonian is a branch function of momentum. Here we propose an extended theory of Lanczos-Lovelock gravity to construct a unique Hamiltonian in its minisuperspace version, which results in manifest diffeomorphic invariance and canonical quantization.

Time and a physical Hamiltonian for quantum gravity.

PubMed

Husain, Viqar; Pawłowski, Tomasz

2012-04-06

We present a nonperturbative quantization of general relativity coupled to dust and other matter fields. The dust provides a natural time variable, leading to a physical Hamiltonian with spatial diffeomorphism symmetry. The surprising feature is that the Hamiltonian is not a square root. This property, together with the kinematical structure of loop quantum gravity, provides a complete theory of quantum gravity, and puts applications to cosmology, quantum gravitational collapse, and Hawking radiation within technical reach. © 2012 American Physical Society

The Lagrangian-Hamiltonian formalism for higher order field theories

NASA Astrophysics Data System (ADS)

Vitagliano, Luca

2010-06-01

We generalize the Lagrangian-Hamiltonian formalism of Skinner and Rusk to higher order field theories on fiber bundles. As a byproduct we solve the long standing problem of defining, in a coordinate free manner, a Hamiltonian formalism for higher order Lagrangian field theories. Namely, our formalism does only depend on the action functional and, therefore, unlike previously proposed ones, is free from any relevant ambiguity.

Effective Hamiltonian for protected edge states in graphene

DOE Office of Scientific and Technical Information (OSTI.GOV)

Winkler, R.; Deshpande, H.

Edge states in topological insulators (TIs) disperse symmetrically about one of the time-reversal invariant momenta Λ in the Brillouin zone (BZ) with protected degeneracies at Λ. Commonly TIs are distinguished from trivial insulators by the values of one or multiple topological invariants that require an analysis of the bulk band structure across the BZ. We propose an effective two-band Hamiltonian for the electronic states in graphene based on a Taylor expansion of the tight-binding Hamiltonian about the time-reversal invariant M point at the edge of the BZ. This Hamiltonian provides a faithful description of the protected edge states for bothmore » zigzag and armchair ribbons, though the concept of a BZ is not part of such an effective model. In conclusion, we show that the edge states are determined by a band inversion in both reciprocal and real space, which allows one to select Λ for the edge states without affecting the bulk spectrum.« less

Birkhoffian symplectic algorithms derived from Hamiltonian symplectic algorithms

NASA Astrophysics Data System (ADS)

Xin-Lei, Kong; Hui-Bin, Wu; Feng-Xiang, Mei

2016-01-01

In this paper, we focus on the construction of structure preserving algorithms for Birkhoffian systems, based on existing symplectic schemes for the Hamiltonian equations. The key of the method is to seek an invertible transformation which drives the Birkhoffian equations reduce to the Hamiltonian equations. When there exists such a transformation, applying the corresponding inverse map to symplectic discretization of the Hamiltonian equations, then resulting difference schemes are verified to be Birkhoffian symplectic for the original Birkhoffian equations. To illustrate the operation process of the method, we construct several desirable algorithms for the linear damped oscillator and the single pendulum with linear dissipation respectively. All of them exhibit excellent numerical behavior, especially in preserving conserved quantities. Project supported by the National Natural Science Foundation of China (Grant No. 11272050), the Excellent Young Teachers Program of North China University of Technology (Grant No. XN132), and the Construction Plan for Innovative Research Team of North China University of Technology (Grant No. XN129).

Effective Hamiltonian for protected edge states in graphene

DOE PAGES

Winkler, R.; Deshpande, H.

2017-06-15

Edge states in topological insulators (TIs) disperse symmetrically about one of the time-reversal invariant momenta Λ in the Brillouin zone (BZ) with protected degeneracies at Λ. Commonly TIs are distinguished from trivial insulators by the values of one or multiple topological invariants that require an analysis of the bulk band structure across the BZ. We propose an effective two-band Hamiltonian for the electronic states in graphene based on a Taylor expansion of the tight-binding Hamiltonian about the time-reversal invariant M point at the edge of the BZ. This Hamiltonian provides a faithful description of the protected edge states for bothmore » zigzag and armchair ribbons, though the concept of a BZ is not part of such an effective model. In conclusion, we show that the edge states are determined by a band inversion in both reciprocal and real space, which allows one to select Λ for the edge states without affecting the bulk spectrum.« less

Lagrangian-Hamiltonian unified formalism for autonomous higher order dynamical systems

NASA Astrophysics Data System (ADS)

Prieto-Martínez, Pedro Daniel; Román-Roy, Narciso

2011-09-01

The Lagrangian-Hamiltonian unified formalism of Skinner and Rusk was originally stated for autonomous dynamical systems in classical mechanics. It has been generalized for non-autonomous first-order mechanical systems, as well as for first-order and higher order field theories. However, a complete generalization to higher order mechanical systems is yet to be described. In this work, after reviewing the natural geometrical setting and the Lagrangian and Hamiltonian formalisms for higher order autonomous mechanical systems, we develop a complete generalization of the Lagrangian-Hamiltonian unified formalism for these kinds of systems, and we use it to analyze some physical models from this new point of view.

A Hamiltonian approach to Thermodynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baldiotti, M.C., E-mail: baldiotti@uel.br; Fresneda, R., E-mail: rodrigo.fresneda@ufabc.edu.br; Molina, C., E-mail: cmolina@usp.br

In the present work we develop a strictly Hamiltonian approach to Thermodynamics. A thermodynamic description based on symplectic geometry is introduced, where all thermodynamic processes can be described within the framework of Analytic Mechanics. Our proposal is constructed on top of a usual symplectic manifold, where phase space is even dimensional and one has well-defined Poisson brackets. The main idea is the introduction of an extended phase space where thermodynamic equations of state are realized as constraints. We are then able to apply the canonical transformation toolkit to thermodynamic problems. Throughout this development, Dirac’s theory of constrained systems is extensivelymore » used. To illustrate the formalism, we consider paradigmatic examples, namely, the ideal, van der Waals and Clausius gases. - Highlights: • A strictly Hamiltonian approach to Thermodynamics is proposed. • Dirac’s theory of constrained systems is extensively used. • Thermodynamic equations of state are realized as constraints. • Thermodynamic potentials are related by canonical transformations.« less

Bi-Hamiltonian structure of the Kermack-McKendrick model for epidemics

NASA Astrophysics Data System (ADS)

Nutku, Y.

1990-11-01

The dynamical system proposed by Kermack and McKendrick (1933) to model the spread of epidemics is shown to admit bi-Hamiltonian structure without any restrictions on the rate constants. These two inequivalent Hamiltonian structures are compatible.

Gapped two-body Hamiltonian for continuous-variable quantum computation.

PubMed

Aolita, Leandro; Roncaglia, Augusto J; Ferraro, Alessandro; Acín, Antonio

2011-03-04

We introduce a family of Hamiltonian systems for measurement-based quantum computation with continuous variables. The Hamiltonians (i) are quadratic, and therefore two body, (ii) are of short range, (iii) are frustration-free, and (iv) possess a constant energy gap proportional to the squared inverse of the squeezing. Their ground states are the celebrated Gaussian graph states, which are universal resources for quantum computation in the limit of infinite squeezing. These Hamiltonians constitute the basic ingredient for the adiabatic preparation of graph states and thus open new venues for the physical realization of continuous-variable quantum computing beyond the standard optical approaches. We characterize the correlations in these systems at thermal equilibrium. In particular, we prove that the correlations across any multipartition are contained exactly in its boundary, automatically yielding a correlation area law.

Multidimensional supersymmetric quantum mechanics: spurious states for the tensor sector two Hamiltonian.

PubMed

Chou, Chia-Chun; Kouri, Donald J

2013-04-25

We show that there exist spurious states for the sector two tensor Hamiltonian in multidimensional supersymmetric quantum mechanics. For one-dimensional supersymmetric quantum mechanics on an infinite domain, the sector one and two Hamiltonians have identical spectra with the exception of the ground state of the sector one. For tensorial multidimensional supersymmetric quantum mechanics, there exist normalizable spurious states for the sector two Hamiltonian with energy equal to the ground state energy of the sector one. These spurious states are annihilated by the adjoint charge operator, and hence, they do not correspond to physical states for the original Hamiltonian. The Hermitian property of the sector two Hamiltonian implies the orthogonality between spurious and physical states. In addition, we develop a method for construction of a specific form of the spurious states for any quantum system and also generate several spurious states for a two-dimensional anharmonic oscillator system and for the hydrogen atom.

Recursion Operators and Tri-Hamiltonian Structure of the First Heavenly Equation of Plebański

NASA Astrophysics Data System (ADS)

Sheftel, Mikhail; Yazıcı, Devrim

2016-09-01

We present first heavenly equation of Plebański in a two-component evolutionary form and obtain Lagrangian and Hamiltonian representations of this system. We study all point symmetries of the two-component system and, using the inverse Noether theorem in the Hamiltonian form, obtain all the integrals of motion corresponding to each variational (Noether) symmetry. We derive two linearly independent recursion operators for symmetries of this system related by a discrete symmetry of both the two-component system and its symmetry condition. Acting by these operators on the first Hamiltonian operator J_0 we obtain second and third Hamiltonian operators. However, we were not able to find Hamiltonian densities corresponding to the latter two operators. Therefore, we construct two recursion operators, which are either even or odd, respectively, under the above-mentioned discrete symmetry. Acting with them on J_0, we generate another two Hamiltonian operators J_+ and J_- and find the corresponding Hamiltonian densities, thus obtaining second and third Hamiltonian representations for the first heavenly equation in a two-component form. Using P. Olver's theory of the functional multi-vectors, we check that the linear combination of J_0, J_+ and J_- with arbitrary constant coefficients satisfies Jacobi identities. Since their skew symmetry is obvious, these three operators are compatible Hamiltonian operators and hence we obtain a tri-Hamiltonian representation of the first heavenly equation. Our well-founded conjecture applied here is that P. Olver's method works fine for nonlocal operators and our proof of the Jacobi identities and bi-Hamiltonian structures crucially depends on the validity of this conjecture.

Hamiltonian stability for weighted measure and generalized Lagrangian mean curvature flow

NASA Astrophysics Data System (ADS)

Kajigaya, Toru; Kunikawa, Keita

2018-06-01

In this paper, we generalize several results for the Hamiltonian stability and the mean curvature flow of Lagrangian submanifolds in a Kähler-Einstein manifold to more general Kähler manifolds including a Fano manifold equipped with a Kähler form ω ∈ 2 πc1(M) by using the method proposed by Behrndt (2011). Namely, we first consider a weighted measure on a Lagrangian submanifold L in a Kähler manifold M and investigate the variational problem of L for the weighted volume functional. We call a stationary point of the weighted volume functional f-minimal, and define the notion of Hamiltonian f-stability as a local minimizer under Hamiltonian deformations. We show such examples naturally appear in a toric Fano manifold. Moreover, we consider the generalized Lagrangian mean curvature flow in a Fano manifold which is introduced by Behrndt and Smoczyk-Wang. We generalize the result of H. Li, and show that if the initial Lagrangian submanifold is a small Hamiltonian deformation of an f-minimal and Hamiltonian f-stable Lagrangian submanifold, then the generalized MCF converges exponentially fast to an f-minimal Lagrangian submanifold.

Hamiltonian dynamics of thermostated systems: two-temperature heat-conducting phi4 chains.

PubMed

Hoover, Wm G; Hoover, Carol G

2007-04-28

We consider and compare four Hamiltonian formulations of thermostated mechanics, three of them kinetic, and the other one configurational. Though all four approaches "work" at equilibrium, their application to many-body nonequilibrium simulations can fail to provide a proper flow of heat. All the Hamiltonian formulations considered here are applied to the same prototypical two-temperature "phi4" model of a heat-conducting chain. This model incorporates nearest-neighbor Hooke's-Law interactions plus a quartic tethering potential. Physically correct results, obtained with the isokinetic Gaussian and Nose-Hoover thermostats, are compared with two other Hamiltonian results. The latter results, based on constrained Hamiltonian thermostats, fail to model correctly the flow of heat.

Regime of validity of the pairing Hamiltonian in the study of Fermi gases

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chang, S. Y.; Pandharipande, V. R.

2006-06-01

The ground state energy and pairing gap of the interacting Fermi gases calculated by the ab initio stochastic method are compared with those estimated from the Bardeen-Cooper-Schrieffer pairing Hamiltonian. We discuss the ingredients of this Hamiltonian in various regimes of interaction strength. In the weakly interacting (1/ak{sub F}<<0) regime the BCS Hamiltonian should describe Landau quasiparticle energies and interactions, on the other hand, in the strongly pairing regime, that is, 1/ak{sub F} > or approx. 0, it becomes part of the bare Hamiltonian. However, the bare BCS Hamiltonian is not adequate for describing atomic gases in the regime of weakmore » to moderate interaction strength -{infinity}<1/ak{sub F}<0 such as ak{sub F}{approx}-1.« less

On time-dependent Hamiltonian realizations of planar and nonplanar systems

NASA Astrophysics Data System (ADS)

Esen, Oğul; Guha, Partha

2018-04-01

In this paper, we elucidate the key role played by the cosymplectic geometry in the theory of time dependent Hamiltonian systems in 2 D. We generalize the cosymplectic structures to time-dependent Nambu-Poisson Hamiltonian systems and corresponding Jacobi's last multiplier for 3 D systems. We illustrate our constructions with various examples.

Hamiltonian methods: BRST, BFV

DOE Office of Scientific and Technical Information (OSTI.GOV)

Garcia, J. Antonio

2006-09-25

The range of applicability of Hamiltonian methods to gauge theories is very diverse and cover areas of research from phenomenology to mathematical physics. We review some of the areas developed in Mexico in the last decades. They cover the study of symplectic methods, BRST-BFV and BV approaches, Klauder projector program, and non perturbative technics used in the study of bound states in relativistic field theories.

Hamiltonian methods: BRST, BFV

NASA Astrophysics Data System (ADS)

García, J. Antonio

2006-09-01

The range of applicability of Hamiltonian methods to gauge theories is very diverse and cover areas of research from phenomenology to mathematical physics. We review some of the areas developed in México in the last decades. They cover the study of symplectic methods, BRST-BFV and BV approaches, Klauder projector program, and non perturbative technics used in the study of bound states in relativistic field theories.

Error Suppression for Hamiltonian-Based Quantum Computation Using Subsystem Codes

NASA Astrophysics Data System (ADS)

Marvian, Milad; Lidar, Daniel A.

2017-01-01

We present general conditions for quantum error suppression for Hamiltonian-based quantum computation using subsystem codes. This involves encoding the Hamiltonian performing the computation using an error detecting subsystem code and the addition of a penalty term that commutes with the encoded Hamiltonian. The scheme is general and includes the stabilizer formalism of both subspace and subsystem codes as special cases. We derive performance bounds and show that complete error suppression results in the large penalty limit. To illustrate the power of subsystem-based error suppression, we introduce fully two-local constructions for protection against local errors of the swap gate of adiabatic gate teleportation and the Ising chain in a transverse field.

Error Suppression for Hamiltonian-Based Quantum Computation Using Subsystem Codes.

PubMed

Marvian, Milad; Lidar, Daniel A

2017-01-20

We present general conditions for quantum error suppression for Hamiltonian-based quantum computation using subsystem codes. This involves encoding the Hamiltonian performing the computation using an error detecting subsystem code and the addition of a penalty term that commutes with the encoded Hamiltonian. The scheme is general and includes the stabilizer formalism of both subspace and subsystem codes as special cases. We derive performance bounds and show that complete error suppression results in the large penalty limit. To illustrate the power of subsystem-based error suppression, we introduce fully two-local constructions for protection against local errors of the swap gate of adiabatic gate teleportation and the Ising chain in a transverse field.

New and emerging patient-centered CT imaging and image-guided treatment paradigms for maxillofacial trauma.

PubMed

Dreizin, David; Nam, Arthur J; Hirsch, Jeffrey; Bernstein, Mark P

2018-06-20

This article reviews the conceptual framework, available evidence, and practical considerations pertaining to nascent and emerging advances in patient-centered CT-imaging and CT-guided surgery for maxillofacial trauma. These include cinematic rendering-a novel method for advanced 3D visualization, incorporation of quantitative CT imaging into the assessment of orbital fractures, low-dose CT imaging protocols made possible with contemporary scanners and reconstruction techniques, the rapidly growing use of cone-beam CT, virtual fracture reduction with design software for surgical pre-planning, the use of 3D printing for fabricating models and implants, and new avenues in CT-guided computer-aided surgery.

ESHRE's good practice guide for cross-border reproductive care for centers and practitioners.

PubMed

Shenfield, F; Pennings, G; De Mouzon, J; Ferraretti, A P; Goossens, V

2011-07-01

This paper outlines ESHRE's guidance for centers and physicians providing fertility treatment to foreign patients. This guide aims to ensure high-quality and safe assisted reproduction treatment, taking into account the patients, their future child and the interests of third-party collaborators such as gametes donors and surrogates. This is achieved by including considerations of equity, safety, efficiency, effectiveness (including evidence-based care), timeliness and patient centeredness.

Divide and conquer approach to quantum Hamiltonian simulation

NASA Astrophysics Data System (ADS)

Hadfield, Stuart; Papageorgiou, Anargyros

2018-04-01

We show a divide and conquer approach for simulating quantum mechanical systems on quantum computers. We can obtain fast simulation algorithms using Hamiltonian structure. Considering a sum of Hamiltonians we split them into groups, simulate each group separately, and combine the partial results. Simulation is customized to take advantage of the properties of each group, and hence yield refined bounds to the overall simulation cost. We illustrate our results using the electronic structure problem of quantum chemistry, where we obtain significantly improved cost estimates under very mild assumptions.

Simple model for deriving sdg interacting boson model Hamiltonians: 150Nd example

NASA Astrophysics Data System (ADS)

Devi, Y. D.; Kota, V. K. B.

1993-07-01

A simple and yet useful model for deriving sdg interacting boson model (IBM) Hamiltonians is to assume that single-boson energies derive from identical particle (pp and nn) interactions and proton, neutron single-particle energies, and that the two-body matrix elements for bosons derive from pn interaction, with an IBM-2 to IBM-1 projection of the resulting p-n sdg IBM Hamiltonian. The applicability of this model in generating sdg IBM Hamiltonians is demonstrated, using a single-j-shell Otsuka-Arima-Iachello mapping of the quadrupole and hexadecupole operators in proton and neutron spaces separately and constructing a quadrupole-quadrupole plus hexadecupole-hexadecupole Hamiltonian in the analysis of the spectra, B(E2)'s, and E4 strength distribution in the example of 150Nd.

A Hamiltonian electromagnetic gyrofluid model

NASA Astrophysics Data System (ADS)

Waelbroeck, F. L.; Hazeltine, R. D.; Morrison, P. J.

2009-03-01

An isothermal truncation of the electromagnetic gyrofluid model of Snyder and Hammett [Phys. Plasmas 8, 3199 (2001)] is shown to be Hamiltonian. The corresponding noncanonical Lie-Poisson bracket and its Casimir invariants are presented. The invariants are used to obtain a set of coupled Grad-Shafranov equations describing equilibria and propagating coherent structures.

Effective Hamiltonian Approach to Optical Activity in Weyl Spin–Orbit System

NASA Astrophysics Data System (ADS)

Kawaguchi, Hideo; Tatara, Gen

2018-06-01

Chirality or handedness in condensed matter induces anomalous optical responses such as natural optical activity, rotation of the plane of light polarization, as a result of breaking of spatial-inversion symmetry. In this study, optical properties of a Weyl spin-orbit system with quadratic dispersion, a typical chiral system invariant under time-reversal, are investigated theoretically by deriving an effective Hamiltonian based on an imaginary-time path-integral formalism. We show that the effective Hamiltonian can indeed be written in terms of an optical chirality order parameter suggested by Lipkin. The natural optical activity is discussed on the basis of the Hamiltonian.

Quantum error suppression with commuting Hamiltonians: two local is too local.

PubMed

Marvian, Iman; Lidar, Daniel A

2014-12-31

We consider error suppression schemes in which quantum information is encoded into the ground subspace of a Hamiltonian comprising a sum of commuting terms. Since such Hamiltonians are gapped, they are considered natural candidates for protection of quantum information and topological or adiabatic quantum computation. However, we prove that they cannot be used to this end in the two-local case. By making the favorable assumption that the gap is infinite, we show that single-site perturbations can generate a degeneracy splitting in the ground subspace of this type of Hamiltonian which is of the same order as the magnitude of the perturbation, and is independent of the number of interacting sites and their Hilbert space dimensions, just as in the absence of the protecting Hamiltonian. This splitting results in decoherence of the ground subspace, and we demonstrate that for natural noise models the coherence time is proportional to the inverse of the degeneracy splitting. Our proof involves a new version of the no-hiding theorem which shows that quantum information cannot be approximately hidden in the correlations between two quantum systems. The main reason that two-local commuting Hamiltonians cannot be used for quantum error suppression is that their ground subspaces have only short-range (two-body) entanglement.

Solving a Hamiltonian Path Problem with a bacterial computer

PubMed Central

Baumgardner, Jordan; Acker, Karen; Adefuye, Oyinade; Crowley, Samuel Thomas; DeLoache, Will; Dickson, James O; Heard, Lane; Martens, Andrew T; Morton, Nickolaus; Ritter, Michelle; Shoecraft, Amber; Treece, Jessica; Unzicker, Matthew; Valencia, Amanda; Waters, Mike; Campbell, A Malcolm; Heyer, Laurie J; Poet, Jeffrey L; Eckdahl, Todd T

2009-01-01

Background The Hamiltonian Path Problem asks whether there is a route in a directed graph from a beginning node to an ending node, visiting each node exactly once. The Hamiltonian Path Problem is NP complete, achieving surprising computational complexity with modest increases in size. This challenge has inspired researchers to broaden the definition of a computer. DNA computers have been developed that solve NP complete problems. Bacterial computers can be programmed by constructing genetic circuits to execute an algorithm that is responsive to the environment and whose result can be observed. Each bacterium can examine a solution to a mathematical problem and billions of them can explore billions of possible solutions. Bacterial computers can be automated, made responsive to selection, and reproduce themselves so that more processing capacity is applied to problems over time. Results We programmed bacteria with a genetic circuit that enables them to evaluate all possible paths in a directed graph in order to find a Hamiltonian path. We encoded a three node directed graph as DNA segments that were autonomously shuffled randomly inside bacteria by a Hin/hixC recombination system we previously adapted from Salmonella typhimurium for use in Escherichia coli. We represented nodes in the graph as linked halves of two different genes encoding red or green fluorescent proteins. Bacterial populations displayed phenotypes that reflected random ordering of edges in the graph. Individual bacterial clones that found a Hamiltonian path reported their success by fluorescing both red and green, resulting in yellow colonies. We used DNA sequencing to verify that the yellow phenotype resulted from genotypes that represented Hamiltonian path solutions, demonstrating that our bacterial computer functioned as expected. Conclusion We successfully designed, constructed, and tested a bacterial computer capable of finding a Hamiltonian path in a three node directed graph. This proof

A projection-free method for representing plane-wave DFT results in an atom-centered basis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dunnington, Benjamin D.; Schmidt, J. R., E-mail: schmidt@chem.wisc.edu

2015-09-14

Plane wave density functional theory (DFT) is a powerful tool for gaining accurate, atomic level insight into bulk and surface structures. Yet, the delocalized nature of the plane wave basis set hinders the application of many powerful post-computation analysis approaches, many of which rely on localized atom-centered basis sets. Traditionally, this gap has been bridged via projection-based techniques from a plane wave to atom-centered basis. We instead propose an alternative projection-free approach utilizing direct calculation of matrix elements of the converged plane wave DFT Hamiltonian in an atom-centered basis. This projection-free approach yields a number of compelling advantages, including strictmore » orthonormality of the resulting bands without artificial band mixing and access to the Hamiltonian matrix elements, while faithfully preserving the underlying DFT band structure. The resulting atomic orbital representation of the Kohn-Sham wavefunction and Hamiltonian provides a gateway to a wide variety of analysis approaches. We demonstrate the utility of the approach for a diverse set of chemical systems and example analysis approaches.« less

Combining symmetry collective states with coupled-cluster theory: Lessons from the Agassi model Hamiltonian

NASA Astrophysics Data System (ADS)

Hermes, Matthew R.; Dukelsky, Jorge; Scuseria, Gustavo E.

2017-06-01

The failures of single-reference coupled-cluster theory for strongly correlated many-body systems is flagged at the mean-field level by the spontaneous breaking of one or more physical symmetries of the Hamiltonian. Restoring the symmetry of the mean-field determinant by projection reveals that coupled-cluster theory fails because it factorizes high-order excitation amplitudes incorrectly. However, symmetry-projected mean-field wave functions do not account sufficiently for dynamic (or weak) correlation. Here we pursue a merger of symmetry projection and coupled-cluster theory, following previous work along these lines that utilized the simple Lipkin model system as a test bed [J. Chem. Phys. 146, 054110 (2017), 10.1063/1.4974989]. We generalize the concept of a symmetry-projected mean-field wave function to the concept of a symmetry projected state, in which the factorization of high-order excitation amplitudes in terms of low-order ones is guided by symmetry projection and is not exponential, and combine them with coupled-cluster theory in order to model the ground state of the Agassi Hamiltonian. This model has two separate channels of correlation and two separate physical symmetries which are broken under strong correlation. We show how the combination of symmetry collective states and coupled-cluster theory is effective in obtaining correlation energies and order parameters of the Agassi model throughout its phase diagram.

A Note on Hamiltonian Graphs

ERIC Educational Resources Information Center

Skurnick, Ronald; Davi, Charles; Skurnick, Mia

2005-01-01

Since 1952, several well-known graph theorists have proven numerous results regarding Hamiltonian graphs. In fact, many elementary graph theory textbooks contain the theorems of Ore, Bondy and Chvatal, Chvatal and Erdos, Posa, and Dirac, to name a few. In this note, the authors state and prove some propositions of their own concerning Hamiltonian…

Quantum finance Hamiltonian for coupon bond European and barrier options.

PubMed

Baaquie, Belal E

2008-03-01

Coupon bond European and barrier options are financial derivatives that can be analyzed in the Hamiltonian formulation of quantum finance. Forward interest rates are modeled as a two-dimensional quantum field theory and its Hamiltonian and state space is defined. European and barrier options are realized as transition amplitudes of the time integrated Hamiltonian operator. The double barrier option for a financial instrument is "knocked out" (terminated with zero value) if the price of the underlying instrument exceeds or falls below preset limits; the barrier option is realized by imposing boundary conditions on the eigenfunctions of the forward interest rates' Hamiltonian. The price of the European coupon bond option and the zero coupon bond barrier option are calculated. It is shown that, is general, the constraint function for a coupon bond barrier option can -- to a good approximation -- be linearized. A calculation using an overcomplete set of eigenfunctions yields an approximate price for the coupon bond barrier option, which is given in the form of an integral of a factor that results from the barrier condition times another factor that arises from the payoff function.

Global stability and quadratic Hamiltonian structure in Lotka-Volterra and quasi-polynomial systems

NASA Astrophysics Data System (ADS)

Szederkényi, Gábor; Hangos, Katalin M.

2004-04-01

We show that the global stability of quasi-polynomial (QP) and Lotka-Volterra (LV) systems with the well-known logarithmic Lyapunov function is equivalent to the existence of a local generalized dissipative Hamiltonian description of the LV system with a diagonal quadratic form as a Hamiltonian function. The Hamiltonian function can be calculated and the quadratic dissipativity neighborhood of the origin can be estimated by solving linear matrix inequalities.

Hamiltonian BVMs (HBVMs): Implementation Details and Applications

NASA Astrophysics Data System (ADS)

Brugnano, Luigi; Iavernaro, Felice; Susca, Tiziana

2009-09-01

Hamiltonian Boundary Value Methods are one step schemes of high order where the internal stages are partly exploited to impose the order conditions (fundamental stages) and partly to confer the formula the property of conserving the Hamiltonian function when this is a polynomial with a given degree v. The term "silent stages" has been coined for these latter set of extra-stages to mean that their presence does not cause an increase of the dimension of the associated nonlinear system to be solved at each step. By considering a specific method in this class, we give some details about how the solution of the nonlinear system may be conveniently carried out and how to compensate the effect of roundoff errors.

Can model Hamiltonians describe the electron-electron interaction in π-conjugated systems?: PAH and graphene

NASA Astrophysics Data System (ADS)

Chiappe, G.; Louis, E.; San-Fabián, E.; Vergés, J. A.

2015-11-01

Model Hamiltonians have been, and still are, a valuable tool for investigating the electronic structure of systems for which mean field theories work poorly. This review will concentrate on the application of Pariser-Parr-Pople (PPP) and Hubbard Hamiltonians to investigate some relevant properties of polycyclic aromatic hydrocarbons (PAH) and graphene. When presenting these two Hamiltonians we will resort to second quantisation which, although not the way chosen in its original proposal of the former, is much clearer. We will not attempt to be comprehensive, but rather our objective will be to try to provide the reader with information on what kinds of problems they will encounter and what tools they will need to solve them. One of the key issues concerning model Hamiltonians that will be treated in detail is the choice of model parameters. Although model Hamiltonians reduce the complexity of the original Hamiltonian, they cannot be solved in most cases exactly. So, we shall first consider the Hartree-Fock approximation, still the only tool for handling large systems, besides density functional theory (DFT) approaches. We proceed by discussing to what extent one may exactly solve model Hamiltonians and the Lanczos approach. We shall describe the configuration interaction (CI) method, a common technology in quantum chemistry but one rarely used to solve model Hamiltonians. In particular, we propose a variant of the Lanczos method, inspired by CI, that has the novelty of using as the seed of the Lanczos process a mean field (Hartree-Fock) determinant (the method will be named LCI). Two questions of interest related to model Hamiltonians will be discussed: (i) when including long-range interactions, how crucial is including in the Hamiltonian the electronic charge that compensates ion charges? (ii) Is it possible to reduce a Hamiltonian incorporating Coulomb interactions (PPP) to an ‘effective’ Hamiltonian including only on-site interactions (Hubbard)? The

Hamiltonian approach to second order gauge invariant cosmological perturbations

NASA Astrophysics Data System (ADS)

Domènech, Guillem; Sasaki, Misao

2018-01-01

In view of growing interest in tensor modes and their possible detection, we clarify the definition of tensor modes up to 2nd order in perturbation theory within the Hamiltonian formalism. Like in gauge theory, in cosmology the Hamiltonian is a suitable and consistent approach to reduce the gauge degrees of freedom. In this paper we employ the Faddeev-Jackiw method of Hamiltonian reduction. An appropriate set of gauge invariant variables that describe the dynamical degrees of freedom may be obtained by suitable canonical transformations in the phase space. We derive a set of gauge invariant variables up to 2nd order in perturbation expansion and for the first time we reduce the 3rd order action without adding gauge fixing terms. In particular, we are able to show the relation between the uniform-ϕ and Newtonian slicings, and study the difference in the definition of tensor modes in these two slicings.

Integrated Hamiltonian sampling: a simple and versatile method for free energy simulations and conformational sampling.

PubMed

Mori, Toshifumi; Hamers, Robert J; Pedersen, Joel A; Cui, Qiang

2014-07-17

Motivated by specific applications and the recent work of Gao and co-workers on integrated tempering sampling (ITS), we have developed a novel sampling approach referred to as integrated Hamiltonian sampling (IHS). IHS is straightforward to implement and complementary to existing methods for free energy simulation and enhanced configurational sampling. The method carries out sampling using an effective Hamiltonian constructed by integrating the Boltzmann distributions of a series of Hamiltonians. By judiciously selecting the weights of the different Hamiltonians, one achieves rapid transitions among the energy landscapes that underlie different Hamiltonians and therefore an efficient sampling of important regions of the conformational space. Along this line, IHS shares similar motivations as the enveloping distribution sampling (EDS) approach of van Gunsteren and co-workers, although the ways that distributions of different Hamiltonians are integrated are rather different in IHS and EDS. Specifically, we report efficient ways for determining the weights using a combination of histogram flattening and weighted histogram analysis approaches, which make it straightforward to include many end-state and intermediate Hamiltonians in IHS so as to enhance its flexibility. Using several relatively simple condensed phase examples, we illustrate the implementation and application of IHS as well as potential developments for the near future. The relation of IHS to several related sampling methods such as Hamiltonian replica exchange molecular dynamics and λ-dynamics is also briefly discussed.

Arts and Crafts Centers

DTIC Science & Technology

1976-08-01

This guide contains design criteria for Army Arts and Crafts Centers which are in some Instances referred to as Skill Development Centers. The term...useful in planning improvements or in better utilizing existing Arts and Crafts Centers or other suitable facilities. d. This guide is directed

Hermitian Hamiltonian equivalent to a given non-Hermitian one: manifestation of spectral singularity.

PubMed

Samsonov, Boris F

2013-04-28

One of the simplest non-Hermitian Hamiltonians, first proposed by Schwartz in 1960, that may possess a spectral singularity is analysed from the point of view of the non-Hermitian generalization of quantum mechanics. It is shown that the η operator, being a second-order differential operator, has supersymmetric structure. Asymptotic behaviour of the eigenfunctions of a Hermitian Hamiltonian equivalent to the given non-Hermitian one is found. As a result, the corresponding scattering matrix and cross section are given explicitly. It is demonstrated that the possible presence of a spectral singularity in the spectrum of the non-Hermitian Hamiltonian may be detected as a resonance in the scattering cross section of its Hermitian counterpart. Nevertheless, just at the singular point, the equivalent Hermitian Hamiltonian becomes undetermined.

Optimal feedback scheme and universal time scaling for Hamiltonian parameter estimation.

PubMed

Yuan, Haidong; Fung, Chi-Hang Fred

2015-09-11

Time is a valuable resource and it is expected that a longer time period should lead to better precision in Hamiltonian parameter estimation. However, recent studies in quantum metrology have shown that in certain cases more time may even lead to worse estimations, which puts this intuition into question. In this Letter we show that by including feedback controls this intuition can be restored. By deriving asymptotically optimal feedback controls we quantify the maximal improvement feedback controls can provide in Hamiltonian parameter estimation and show a universal time scaling for the precision limit under the optimal feedback scheme. Our study reveals an intriguing connection between noncommutativity in the dynamics and the gain of feedback controls in Hamiltonian parameter estimation.

Multiple Time-Step Dual-Hamiltonian Hybrid Molecular Dynamics — Monte Carlo Canonical Propagation Algorithm

PubMed Central

Weare, Jonathan; Dinner, Aaron R.; Roux, Benoît

2016-01-01

A multiple time-step integrator based on a dual Hamiltonian and a hybrid method combining molecular dynamics (MD) and Monte Carlo (MC) is proposed to sample systems in the canonical ensemble. The Dual Hamiltonian Multiple Time-Step (DHMTS) algorithm is based on two similar Hamiltonians: a computationally expensive one that serves as a reference and a computationally inexpensive one to which the workload is shifted. The central assumption is that the difference between the two Hamiltonians is slowly varying. Earlier work has shown that such dual Hamiltonian multiple time-step schemes effectively precondition nonlinear differential equations for dynamics by reformulating them into a recursive root finding problem that can be solved by propagating a correction term through an internal loop, analogous to RESPA. Of special interest in the present context, a hybrid MD-MC version of the DHMTS algorithm is introduced to enforce detailed balance via a Metropolis acceptance criterion and ensure consistency with the Boltzmann distribution. The Metropolis criterion suppresses the discretization errors normally associated with the propagation according to the computationally inexpensive Hamiltonian, treating the discretization error as an external work. Illustrative tests are carried out to demonstrate the effectiveness of the method. PMID:26918826

Hamiltonian Cycle Enumeration via Fermion-Zeon Convolution

NASA Astrophysics Data System (ADS)

Staples, G. Stacey

2017-12-01

Beginning with a simple graph having finite vertex set V, operators are induced on fermion and zeon algebras by the action of the graph's adjacency matrix and combinatorial Laplacian on the vector space spanned by the graph's vertices. When the graph is simple (undirected with no loops or multiple edges), the matrices are symmetric and the induced operators are self-adjoint. The goal of the current paper is to recover a number of known graph-theoretic results from quantum observables constructed as linear operators on fermion and zeon Fock spaces. By considering an "indeterminate" fermion/zeon Fock space, a fermion-zeon convolution operator is defined whose trace recovers the number of Hamiltonian cycles in the graph. This convolution operator is a quantum observable whose expectation reveals the number of Hamiltonian cycles in the graph.

The mathematics of a quantum Hamiltonian computing half adder Boolean logic gate.

PubMed

Dridi, G; Julien, R; Hliwa, M; Joachim, C

2015-08-28

The mathematics behind the quantum Hamiltonian computing (QHC) approach of designing Boolean logic gates with a quantum system are given. Using the quantum eigenvalue repulsion effect, the QHC AND, NAND, OR, NOR, XOR, and NXOR Hamiltonian Boolean matrices are constructed. This is applied to the construction of a QHC half adder Hamiltonian matrix requiring only six quantum states to fullfil a half Boolean logical truth table. The QHC design rules open a nano-architectronic way of constructing Boolean logic gates inside a single molecule or atom by atom at the surface of a passivated semi-conductor.

Construction of Hamiltonians by supervised learning of energy and entanglement spectra

NASA Astrophysics Data System (ADS)

Fujita, Hiroyuki; Nakagawa, Yuya O.; Sugiura, Sho; Oshikawa, Masaki

2018-02-01

Correlated many-body problems ubiquitously appear in various fields of physics such as condensed matter, nuclear, and statistical physics. However, due to the interplay of the large number of degrees of freedom, it is generically impossible to treat these problems from first principles. Thus the construction of a proper model, namely, effective Hamiltonian, is essential. Here, we propose a simple supervised learning algorithm for constructing Hamiltonians from given energy or entanglement spectra. We apply the proposed scheme to the Hubbard model at the half-filling, and compare the obtained effective low-energy spin model with several analytic results based on the high-order perturbation theory, which have been inconsistent with each other. We also show that our approach can be used to construct the entanglement Hamiltonian of a quantum many-body state from its entanglement spectrum as well. We exemplify this using the ground states of the S =1 /2 two-leg Heisenberg ladders. We observe a qualitative difference between the entanglement Hamiltonians of the two phases (the Haldane and the rung singlet phase) of the model due to the different origin of the entanglement. In the Haldane phase, we find that the entanglement Hamiltonian is nonlocal by nature, and the locality can be restored by introducing the anisotropy and turning the ground state into the large-D phase. Possible applications to the model construction from experimental data and to various problems of strongly correlated systems are discussed.

Symmetries of SU(2) Skyrmion in Hamiltonian and Lagrangian Approaches

NASA Astrophysics Data System (ADS)

Hong, Soon-Tae; Kim, Yong-Wan; Park, Young-Jai

We apply the Batalin-Fradkin-Tyutin (BFT) method to the SU(2) Skyrmion to study the full symmetry structure of the model at the first-class Hamiltonian level. On the other hand, we also analyze the symmetry structure of the action having the WZ term, which corresponds to this Hamiltonian, in the framework of the Lagrangian approach. Furthermore, following the BFV formalism we derive the BRST invariant gauge fixed Lagrangian from the above extended action.

The Hamiltonian structure of the (2+1)-dimensional Ablowitz--Kaup--Newell--Segur hierarchy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Athorne, C.; Dorfman, I.Y.

1993-08-01

By considering Hamiltonian theory over a suitable (noncommutative) ring the nonlinear evolution equations of the Ablowitz--Kaup--Newell--Segur (2+1) hierarchy are incorporated into a Hamiltonian framework and a modified Lenard scheme.

Hamiltonian structure of Dubrovin's equation of associativity in 2-d topological field theory

NASA Astrophysics Data System (ADS)

Galvão, C. A. P.; Nutku, Y.

1996-12-01

A third order Monge-Ampère type equation of associativity that Dubrovin has obtained in 2-d topological field theory is formulated in terms of a variational principle subject to second class constraints. Using Dirac's theory of constraints this degenerate Lagrangian system is cast into Hamiltonian form and the Hamiltonian operator is obtained from the Dirac bracket. There is a new type of Kac-Moody algebra that corresponds to this Hamiltonian operator. In particular, it is not a W-algebra.

Hamiltonian thermodynamics of charged three-dimensional dilatonic black holes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dias, Goncalo A. S.; Lemos, Jose P. S.; Centro Multidisciplinar de Astrofisica-CENTRA, Departamento de Fisica, Instituto Superior Tecnico-IST, Universidade Tecnica de Lisboa-UTL, Avenida Rovisco Pais 1, 1049-001 Lisboa

2008-10-15

The action for a class of three-dimensional dilaton-gravity theories, with an electromagnetic Maxwell field and a cosmological constant, can be recast in a Brans-Dicke-Maxwell type action, with its free {omega} parameter. For a negative cosmological constant, these theories have static, electrically charged, and spherically symmetric black hole solutions. Those theories with well formulated asymptotics are studied through a Hamiltonian formalism, and their thermodynamical properties are found out. The theories studied are general relativity ({omega}{yields}{+-}{infinity}), a dimensionally reduced cylindrical four-dimensional general relativity theory ({omega}=0), and a theory representing a class of theories ({omega}=-3), all with a Maxwell term. The Hamiltonian formalismmore » is set up in three dimensions through foliations on the right region of the Carter-Penrose diagram, with the bifurcation 1-sphere as the left boundary, and anti-de Sitter infinity as the right boundary. The metric functions on the foliated hypersurfaces and the radial component of the vector potential one-form are the canonical coordinates. The Hamiltonian action is written, the Hamiltonian being a sum of constraints. One finds a new action which yields an unconstrained theory with two pairs of canonical coordinates (M,P{sub M};Q,P{sub Q}), where M is the mass parameter, which for {omega}<-(3/2) and for {omega}={+-}{infinity} needs a careful renormalization, P{sub M} is the conjugate momenta of M, Q is the charge parameter, and P{sub Q} is its conjugate momentum. The resulting Hamiltonian is a sum of boundary terms only. A quantization of the theory is performed. The Schroedinger evolution operator is constructed, the trace is taken, and the partition function of the grand canonical ensemble is obtained, where the chemical potential is the scalar electric field {phi}. Like the uncharged cases studied previously, the charged black hole entropies differ, in general, from the usual quarter of

The Schwinger Model on S 1: Hamiltonian Formulation, Vacuum and Anomaly

NASA Astrophysics Data System (ADS)

Stuart, David

2014-12-01

We present a Hamiltonian formulation of the Schwinger model with spatial domain taken to be the circle. It is shown that, in Coulomb gauge, the Hamiltonian is a semi-bounded, self-adjoint operator which is invariant under the group of large gauge transformations. There is a nontrivial action of on fermionic Fock space and its vacuum. This action plays a role analogous to that played by the spectral flow in the infinite Dirac sea formalism. The formulation allows (1) a description of the anomaly and its relation to the group action, and (2) an explicit identification of the vacuum. The anomaly in the chiral conservation law appears as a consequence of insisting upon semi-boundedness and gauge invariance of the quantized Hamiltonian.

Gathering the Dreamers: The Transformation Process to a Learner-Centered School. The Reinventing School Series. Part Two and Viewing Guide. Videotape.

ERIC Educational Resources Information Center

Burrello, Leonard C.; DiLaura, Nancy

This videotape and viewing guide present an emerging learner-centered paradigm of teaching and learning and answer questions of why and how a staff changes its practices. The viewing guide describes the elementary school in the videotape, noting the full inclusion of 50 students identified as disabled, the team approach in which teachers are…

Finite-error metrological bounds on multiparameter Hamiltonian estimation

NASA Astrophysics Data System (ADS)

Kura, Naoto; Ueda, Masahito

2018-01-01

Estimation of multiple parameters in an unknown Hamiltonian is investigated. We present upper and lower bounds on the time required to complete the estimation within a prescribed error tolerance δ . The lower bound is given on the basis of the Cramér-Rao inequality, where the quantum Fisher information is bounded by the squared evolution time. The upper bound is obtained by an explicit construction of estimation procedures. By comparing the cases with different numbers of Hamiltonian channels, we also find that the few-channel procedure with adaptive feedback and the many-channel procedure with entanglement are equivalent in the sense that they require the same amount of time resource up to a constant factor.

Reverse engineering of a Hamiltonian by designing the evolution operators

NASA Astrophysics Data System (ADS)

Kang, Yi-Hao; Chen, Ye-Hong; Wu, Qi-Cheng; Huang, Bi-Hua; Xia, Yan; Song, Jie

2016-07-01

We propose an effective and flexible scheme for reverse engineering of a Hamiltonian by designing the evolution operators to eliminate the terms of Hamiltonian which are hard to be realized in practice. Different from transitionless quantum driving (TQD), the present scheme is focus on only one or parts of moving states in a D-dimension (D ≥ 3) system. The numerical simulation shows that the present scheme not only contains the results of TQD, but also has more free parameters, which make this scheme more flexible. An example is given by using this scheme to realize the population transfer for a Rydberg atom. The influences of various decoherence processes are discussed by numerical simulation and the result shows that the scheme is fast and robust against the decoherence and operational imperfection. Therefore, this scheme may be used to construct a Hamiltonian which can be realized in experiments.

Riemannian geometry of Hamiltonian chaos: hints for a general theory.

PubMed

Cerruti-Sola, Monica; Ciraolo, Guido; Franzosi, Roberto; Pettini, Marco

2008-10-01

We aim at assessing the validity limits of some simplifying hypotheses that, within a Riemmannian geometric framework, have provided an explanation of the origin of Hamiltonian chaos and have made it possible to develop a method of analytically computing the largest Lyapunov exponent of Hamiltonian systems with many degrees of freedom. Therefore, a numerical hypotheses testing has been performed for the Fermi-Pasta-Ulam beta model and for a chain of coupled rotators. These models, for which analytic computations of the largest Lyapunov exponents have been carried out in the mentioned Riemannian geometric framework, appear as paradigmatic examples to unveil the reason why the main hypothesis of quasi-isotropy of the mechanical manifolds sometimes breaks down. The breakdown is expected whenever the topology of the mechanical manifolds is nontrivial. This is an important step forward in view of developing a geometric theory of Hamiltonian chaos of general validity.

Hyperfine Sublevel Correlation (HYSCORE) Spectra for Paramagnetic Centers with Nuclear Spin I = 1 Having Isotropic Hyperfine Interactions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maryasov, Alexander G.; Bowman, Michael K.

2004-07-08

It is shown that HYSCORE spectra of paramagnetic centers having nuclei of spin I=1 with isotropic hfi and arbitrary NQI consist of ridges having zero width. A parametric presentation of these ridges is found which shows the range of possible frequencies in the HYSCORE spectrum and aids in spectral assignments and rapid estimation of spin Hamiltonian parameters. An alternative approach for the spectral density calculation is presented that is based on spectral decomposition of the Hamiltonian. Only the eigenvalues of the Hamiltonian are needed in this approach. An atlas of HYSCORE spectra is given in the Supporting Information. This approachmore » is applied to the estimation of the spin Hamiltonian parameters of the oxovanadium-EDTA complex.« less

Extended hamiltonian formalism and Lorentz-violating lagrangians

NASA Astrophysics Data System (ADS)

Colladay, Don

2017-09-01

A new perspective on the classical mechanical formulation of particle trajectories in Lorentz-violating theories is presented. Using the extended hamiltonian formalism, a Legendre Transformation between the associated covariant lagrangian and hamiltonian varieties is constructed. This approach enables calculation of trajectories using Hamilton's equations in momentum space and the Euler-Lagrange equations in velocity space away from certain singular points that arise in the theory. Singular points are naturally de-singularized by requiring the trajectories to be smooth functions of both velocity and momentum variables. In addition, it is possible to identify specific sheets of the dispersion relations that correspond to specific solutions for the lagrangian. Examples corresponding to bipartite Finsler functions are computed in detail. A direct connection between the lagrangians and the field-theoretic solutions to the Dirac equation is also established for a special case.

On the exactness of effective Floquet Hamiltonians employed in solid-state NMR spectroscopy

NASA Astrophysics Data System (ADS)

Garg, Rajat; Ramachandran, Ramesh

2017-05-01

Development of theoretical models based on analytic theory has remained an active pursuit in molecular spectroscopy for its utility both in the design of experiments as well as in the interpretation of spectroscopic data. In particular, the role of "Effective Hamiltonians" in the evolution of theoretical frameworks is well known across all forms of spectroscopy. Nevertheless, a constant revalidation of the approximations employed in the theoretical frameworks is necessitated by the constant improvements on the experimental front in addition to the complexity posed by the systems under study. Here in this article, we confine our discussion to the derivation of effective Floquet Hamiltonians based on the contact transformation procedure. While the importance of the effective Floquet Hamiltonians in the qualitative description of NMR experiments has been realized in simpler cases, its extension in quantifying spectral data deserves a cautious approach. With this objective, the validity of the approximations employed in the derivation of the effective Floquet Hamiltonians is re-examined through a comparison with exact numerical methods under differing experimental conditions. The limitations arising from the existing analytic methods are outlined along with remedial measures for improving the accuracy of the derived effective Floquet Hamiltonians.

Volpe Center Acoustics Facility time-space-position-information system differential global positioning system user's guide, version 1.2

DOT National Transportation Integrated Search

2000-07-01

This document is a users guide for the VolpeCenter AcousticsFacilitys(VCAF)Time-Space-Position-Information : (TSPI) System. The VCAF TSPI system is a differential global positioning system (dGPS) which may be utilized : for highly accurate vehi...

Dietary intakes at child-care centers in central Texas fail to meet Food Guide Pyramid recommendations.

PubMed

Padget, Alison; Briley, Margaret E

2005-05-01

The purpose of this study was to compare the dietary intakes of children who attend child-care centers with the recommendations of the Food Guide Pyramid for Young Children. Three-day dietary records were obtained for 50 children ages 3 to 5 years old who attended nine child-care centers in central Texas. Dietary intakes during child care were measured by a researcher, and dietary intakes at home were recorded by a parent. During child care, the 3-year-old children consumed sufficient fruits and meat/alternates, but not sufficient grains, vegetables, or dairy to meet two thirds of Food Guide Pyramid for Young Children recommendations. The 4- and 5-year-old children only consumed sufficient dairy. Ninety-one percent (20 of 22) of the 3-year-old children met two thirds of their estimated energy requirements during child care, compared with 5% (1 of 20) of 4-year-old children and 25% (2 of 8) of 5-year-old children. Intakes at home did not compensate for lack of grain and vegetable consumption during child care.

Hamiltonian General Relativity in Finite Space and Cosmological Potential Perturbations

NASA Astrophysics Data System (ADS)

Barbashov, B. M.; Pervushin, V. N.; Zakharov, A. F.; Zinchuk, V. A.

The Hamiltonian formulation of general relativity is considered in finite space-time and a specific reference frame given by the diffeo-invariant components of the Fock simplex in terms of the Dirac-ADM variables. The evolution parameter and energy invariant with respect to the time-coordinate transformations are constructed by the separation of the cosmological scale factor a(x0) and its identification with the spatial averaging of the metric determinant, so that the dimension of the kinemetric group of diffeomorphisms coincides with the dimension of a set of variables whose velocities are removed by the Gauss-type constraints in accordance with the second Nöther theorem. This coincidence allows us to solve the energy constraint, fulfil Dirac's Hamiltonian reduction, and to describe the potential perturbations in terms of the Lichnerowicz scale-invariant variables distinguished by the absence of the time derivatives of the spatial metric determinant. It was shown that the Hamiltonian version of the cosmological perturbation theory acquires attributes of the theory of superfluid liquid, and it leads to a generalization of the Schwarzschild solution. The astrophysical application of this approach to general relativity is considered under supposition that the Dirac-ADM Hamiltonian frame is identified with that of the Cosmic Microwave Background radiation distinguished by its dipole component in the frame of an Earth observer.

A Teacher's Guide to Resource - Use Outdoor Education Center.

ERIC Educational Resources Information Center

Taylor County Board of Public Instruction, Perry, FL.

Included in this guide are ideas on evaluation and conduct of outdoor education classes and unit guides and lesson plans. An interdisciplinary approach is emphasized and the unit guides and lesson plans present activities related to science, mathematics, social studies, art, and music relevant to outdoor education in general. Unit guides for soil,…

Guiding center model to interpret neutral particle analyzer results

NASA Technical Reports Server (NTRS)

Englert, G. W.; Reinmann, J. J.; Lauver, M. R.

1974-01-01

The theoretical model is discussed, which accounts for drift and cyclotron components of ion motion in a partially ionized plasma. Density and velocity distributions are systematically precribed. The flux into the neutral particle analyzer (NPA) from this plasma is determined by summing over all charge exchange neutrals in phase space which are directed into apertures. Especially detailed data, obtained by sweeping the line of sight of the apertures across the plasma of the NASA Lewis HIP-1 burnout device, are presented. Selection of randomized cyclotron velocity distributions about mean azimuthal drift yield energy distributions which compared well with experiment. Use of data obtained with a bending magnet on the NPA showed that separation between energy distribution curves of various mass species correlate well with a drift divided by mean cyclotron energy parameter of the theory. Use of the guiding center model in conjunction with NPA scans across the plasma aid in estimates of ion density and E field variation with plasma radius.

A 2-dimensional optical architecture for solving Hamiltonian path problem based on micro ring resonators

NASA Astrophysics Data System (ADS)

Shakeri, Nadim; Jalili, Saeed; Ahmadi, Vahid; Rasoulzadeh Zali, Aref; Goliaei, Sama

2015-01-01

The problem of finding the Hamiltonian path in a graph, or deciding whether a graph has a Hamiltonian path or not, is an NP-complete problem. No exact solution has been found yet, to solve this problem using polynomial amount of time and space. In this paper, we propose a two dimensional (2-D) optical architecture based on optical electronic devices such as micro ring resonators, optical circulators and MEMS based mirror (MEMS-M) to solve the Hamiltonian Path Problem, for undirected graphs in linear time. It uses a heuristic algorithm and employs n+1 different wavelengths of a light ray, to check whether a Hamiltonian path exists or not on a graph with n vertices. Then if a Hamiltonian path exists, it reports the path. The device complexity of the proposed architecture is O(n2).

The Beginnings of a Nature Center.

ERIC Educational Resources Information Center

Cherem, Gabriel J.; And Others

This guide is a comprehensive interpretive plan for the development of a nature center. Although the plan centers on a proposed nature center, the ideas included in the guide can be applied to other situations. The guide deals with all aspects of planning and is divided into seven chapters. Chapter 1, Visitorship, looks at the people who attend…

The period function of the generalized Lotka-Volterra centers

NASA Astrophysics Data System (ADS)

Villadelprat, J.

2008-05-01

The present paper deals with the period function of the quadratic centers. In the literature different terminologies are used to classify these centers, but essentially there are four families: Hamiltonian, reversible , codimension four Q4 and generalized Lotka-Volterra systems . Chicone [C. Chicone, Review in MathSciNet, Ref. 94h:58072] conjectured that the reversible centers have at most two critical periods, and that the centers of the three other families have a monotonic period function. With regard to the second part of this conjecture, only the monotonicity of the Hamiltonian and Q4 families [W.A. Coppel, L. Gavrilov, The period function of a Hamiltonian quadratic system, Differential Integral Equations 6 (1993) 1357-1365; Y. Zhao, The monotonicity of period function for codimension four quadratic system Q4, J. Differential Equations 185 (2002) 370-387] has been proved. Concerning the family, no substantial progress has been made since the middle 80s, when several authors showed independently the monotonicity of the classical Lotka-Volterra centers [F. Rothe, The periods of the Volterra-Lokta system, J. Reine Angew. Math. 355 (1985) 129-138; R. Schaaf, Global behaviour of solution branches for some Neumann problems depending on one or several parameters, J. Reine Angew. Math. 346 (1984) 1-31; J. Waldvogel, The period in the Lotka-Volterra system is monotonic, J. Math. Anal. Appl. 114 (1986) 178-184]. By means of the first period constant one can easily conclude that the period function of the centers in the family is monotone increasing near the inner boundary of its period annulus (i.e., the center itself). Thus, according to Chicone's conjecture, it should be also monotone increasing near the outer boundary, which in the Poincaré disc is a polycycle. In this paper we show that this is true. In addition we prove that, except for a zero measure subset of the parameter plane, there is no bifurcation of critical periods from the outer boundary. Finally we

Bounded Hamiltonian in the Fourth-Order Extension of the Chern-Simons Theory

NASA Astrophysics Data System (ADS)

Abakumova, V. A.; Kaparulin, D. S.; Lyakhovich, S. L.

2018-04-01

The problem of constructing alternative Hamiltonian formulations in the extended Chern-Simons theory with higher derivatives is considered. It is shown that the fourth-order extended theory admits a four-parameter series of alternative Hamiltonians which can be bounded from below, even if the canonical energy of the model is unbounded from below.

Hamiltonian models for topological phases of matter in three spatial dimensions

NASA Astrophysics Data System (ADS)

Williamson, Dominic J.; Wang, Zhenghan

2017-02-01

We present commuting projector Hamiltonian realizations of a large class of (3 + 1)D topological models based on mathematical objects called unitary G-crossed braided fusion categories. This construction comes with a wealth of examples from the literature of symmetry-enriched topological phases. The spacetime counterparts to our Hamiltonians are unitary state sum topological quantum fields theories (TQFTs) that appear to capture all known constructions in the literature, including the Crane-Yetter-Walker-Wang and 2-Group gauge theory models. We also present Hamiltonian realizations of a state sum TQFT recently constructed by Kashaev whose relation to existing models was previously unknown. We argue that this TQFT is captured as a special case of the Crane-Yetter-Walker-Wang model, with a premodular input category in some instances.

Paramagnetic centers in two phases of manganese-doped lanthanum gallate

NASA Astrophysics Data System (ADS)

Vazhenin, V. A.; Potapov, A. P.; Guseva, V. B.; Artyomov, M. Yu.

2009-05-01

An EPR study of two phases of manganese-doped lanthanum gallate (with a first-order structural transition occurring at 430 K) has revealed Gd3+, Fe3+, and Mn4+ centers at room temperature and 438 K. The parameters of spin Hamiltonians are determined for the Gd3+, Fe3+, and Mn4+ rhombohedral centers in the high-temperature phase (with no other centers found here) and for the monoclinic center Gd3+ in the low-temperature phase. Both in the orthorhombic and in the rhombohedral phase, crystallographic twins (or ferroelastic domains) are observed.

Hamiltonian formalism for f (T ) gravity

NASA Astrophysics Data System (ADS)

Ferraro, Rafael; Guzmán, María José

2018-05-01

We present the Hamiltonian formalism for f (T ) gravity, and prove that the theory has n/(n -3 ) 2 +1 degrees of freedom (d.o.f.) in n dimensions. We start from a scalar-tensor action for the theory, which represents a scalar field minimally coupled with the torsion scalar T that defines the teleparallel equivalent of general relativity (TEGR) Lagrangian. T is written as a quadratic form of the coefficients of anholonomy of the vierbein. We obtain the primary constraints through the analysis of the structure of the eigenvalues of the multi-index matrix involved in the definition of the canonical momenta. The auxiliary scalar field generates one extra primary constraint when compared with the TEGR case. The secondary constraints are the super-Hamiltonian and supermomenta constraints, that are preserved from the Arnowitt-Deser-Misner formulation of GR. There is a set of n/(n -1 ) 2 primary constraints that represent the local Lorentz transformations of the theory, which can be combined to form a set of n/(n -1 ) 2 -1 first-class constraints, while one of them becomes second class. This result is irrespective of the dimension, due to the structure of the matrix of the brackets between the constraints. The first-class canonical Hamiltonian is modified due to this local Lorentz violation, and the only one local Lorentz transformation that becomes second-class pairs up with the second-class constraint π ≈0 to remove one d.o.f. from the n2+1 pairs of canonical variables. The remaining n/(n -1 ) 2 +2 n -1 primary constraints remove the same number of d.o.f., leaving the theory with n/(n -3 ) 2 +1 d.o.f. This means that f (T ) gravity has only one extra d.o.f., which could be interpreted as a scalar d.o.f.

Hamiltonian vs Lagrangian Embedding of a Massive Spin-One Theory Involving Two-Form Field

NASA Astrophysics Data System (ADS)

Harikumar, E.; Sivakumar, M.

We consider the Hamiltonian and Lagrangian embedding of a first-order, massive spin-one, gauge noninvariant theory involving antisymmetric tensor field. We apply the BFV-BRST generalized canonical approach to convert the model to a first class system and construct nilpotent BFV-BRST charge and a unitarizing Hamiltonian. The canonical analysis of the Stückelberg formulation of this model is presented. We bring out the contrasting feature in the constraint structure, specifically with respect to the reducibility aspect, of the Hamiltonian and the Lagrangian embedded model. We show that to obtain manifestly covariant Stückelberg Lagrangian from the BFV embedded Hamiltonian, phase space has to be further enlarged and show how the reducible gauge structure emerges in the embedded model.

Hamiltonian Anomalies from Extended Field Theories

NASA Astrophysics Data System (ADS)

Monnier, Samuel

2015-09-01

We develop a proposal by Freed to see anomalous field theories as relative field theories, namely field theories taking value in a field theory in one dimension higher, the anomaly field theory. We show that when the anomaly field theory is extended down to codimension 2, familiar facts about Hamiltonian anomalies can be naturally recovered, such as the fact that the anomalous symmetry group admits only a projective representation on the Hilbert space, or that the latter is really an abelian bundle gerbe over the moduli space. We include in the discussion the case of non-invertible anomaly field theories, which is relevant to six-dimensional (2, 0) superconformal theories. In this case, we show that the Hamiltonian anomaly is characterized by a degree 2 non-abelian group cohomology class, associated to the non-abelian gerbe playing the role of the state space of the anomalous theory. We construct Dai-Freed theories, governing the anomalies of chiral fermionic theories, and Wess-Zumino theories, governing the anomalies of Wess-Zumino terms and self-dual field theories, as extended field theories down to codimension 2.

Separate spatial Holographic-Hamiltonian soliton pairs and solitons interaction in an unbiased series photorefractive crystal circuit.

PubMed

Cai, Xin; Liu, Jinsong; Wang, Shenglie

2009-02-16

This paper presents calculations for an idea in photorefractive spatial soliton, namely, a dissipative holographic soliton and a Hamiltonian soliton in one dimension form in an unbiased series photorefractive crystal circuit consisting of two photorefractive crystals of which at least one must be photovoltaic. The two solitons are known collectively as a separate Holographic-Hamiltonian spatial soliton pair and there are two types: dark-dark and bright-dark if only one crystal of the circuit is photovoltaic. The numerical results show that the Hamiltonian soliton in a soliton pair can affect the holographic one by the light-induced current whereas the effect of the holographic soliton on the Hamiltonian soliton is too weak to be ignored, i.e., the holographic soliton cannot affect the Hamiltonian one.

Phase equilibria in polymer blend thin films: A Hamiltonian approach

NASA Astrophysics Data System (ADS)

Souche, M.; Clarke, N.

2009-12-01

We propose a Hamiltonian formulation of the Flory-Huggins-de Gennes theory describing a polymer blend thin film. We then focus on the case of 50:50 polymer blends confined between antisymmetric walls. The different phases of the system and the transitions between them, including finite-size effects, are systematically studied through their relation with the geometry of the Hamiltonian flow in phase space. This method provides an easy and efficient way, with strong graphical insight, to infer the qualitative physical behavior of polymer blend thin films.

Modeling local structure using crystal field and spin Hamiltonian parameters: the tetragonal FeK3+-OI2- defect center in KTaO3 crystal

NASA Astrophysics Data System (ADS)

Gnutek, P.; Y Yang, Z.; Rudowicz, C.

2009-11-01

The local structure and the spin Hamiltonian (SH) parameters, including the zero-field-splitting (ZFS) parameters D and (a+2F/3), and the Zeeman g factors g_{\\parallel } and g_{\\perp } , are theoretically investigated for the FeK3+-OI2- center in KTaO3 crystal. The microscopic SH (MSH) parameters are modeled within the framework of the crystal field (CF) theory employing the CF analysis (CFA) package, which also incorporates the MSH modules. Our approach takes into account the spin-orbit interaction as well as the spin-spin and spin-other-orbit interactions omitted in previous studies. The superposition model (SPM) calculations are carried out to provide input CF parameters for the CFA/MSH package. The combined SPM-CFA/MSH approach is used to consider various structural models for the FeK3+-OI2- defect center in KTaO3. This modeling reveals that the off-center displacement of the Fe3+ ions, Δ1(Fe3+), combined with an inward relaxation of the nearest oxygen ligands, Δ2(O2-), and the existence of the interstitial oxygen OI2- give rise to a strong tetragonal crystal field. This finding may explain the large ZFS experimentally observed for the FeK3+-OI2- center in KTaO3. Matching the theoretical MSH predictions with the available structural data as well as electron magnetic resonance (EMR) and optical spectroscopy data enables predicting reasonable ranges of values of Δ1(Fe3+) and Δ2(O2-) as well as the possible location of OI2- ligands around Fe3+ ions in KTaO3. The defect structure model obtained using the SPM-CFA/MSH approach reproduces very well the ranges of the experimental SH parameters D, g_{\\parallel } and g_{\\perp } and importantly yields not only the correct magnitude of D but also the sign, unlike previous studies. More reliable predictions may be achieved when experimental data on (a+2F/3) and/or crystal field energy levels become available. Comparison of our results with those arising from alternative models existing in the literature indicates

An integrable family of Monge-Ampère equations and their multi-Hamiltonian structure

NASA Astrophysics Data System (ADS)

Nutku, Y.; Sarioǧlu, Ö.

1993-02-01

We have identified a completely integrable family of Monge-Ampère equations through an examination of their Hamiltonian structure. Starting with a variational formulation of the Monge-Ampère equations we have constructed the first Hamiltonian operator through an application of Dirac's theory of constraints. The completely integrable class of Monge-Ampère equations are then obtained by solving the Jacobi identities for a sufficiently general form of the second Hamiltonian operator that is compatible with the first.

Higher-dimensional Wannier functions of multiparameter Hamiltonians

NASA Astrophysics Data System (ADS)

Hanke, Jan-Philipp; Freimuth, Frank; Blügel, Stefan; Mokrousov, Yuriy

2015-05-01

When using Wannier functions to study the electronic structure of multiparameter Hamiltonians H(k ,λ ) carrying a dependence on crystal momentum k and an additional periodic parameter λ , one usually constructs several sets of Wannier functions for a set of values of λ . We present the concept of higher-dimensional Wannier functions (HDWFs), which provide a minimal and accurate description of the electronic structure of multiparameter Hamiltonians based on a single set of HDWFs. The obstacle of nonorthogonality of Bloch functions at different λ is overcome by introducing an auxiliary real space, which is reciprocal to the parameter λ . We derive a generalized interpolation scheme and emphasize the essential conceptual and computational simplifications in using the formalism, for instance, in the evaluation of linear response coefficients. We further implement the necessary machinery to construct HDWFs from ab initio within the full potential linearized augmented plane-wave method (FLAPW). We apply our implementation to accurately interpolate the Hamiltonian of a one-dimensional magnetic chain of Mn atoms in two important cases of λ : (i) the spin-spiral vector q and (ii) the direction of the ferromagnetic magnetization m ̂. Using the generalized interpolation of the energy, we extract the corresponding values of magnetocrystalline anisotropy energy, Heisenberg exchange constants, and spin stiffness, which compare very well with the values obtained from direct first principles calculations. For toy models we demonstrate that the method of HDWFs can also be used in applications such as the virtual crystal approximation, ferroelectric polarization, and spin torques.

The Jarzynski identity derived from general Hamiltonian or non-Hamiltonian dynamics reproducing NVT or NPT ensembles

NASA Astrophysics Data System (ADS)

Cuendet, Michel A.

2006-10-01

The Jarzynski identity (JI) relates nonequilibrium work averages to thermodynamic free energy differences. It was shown in a recent contribution [M. A. Cuendet, Phys. Rev. Lett. 96, 120602 (2006)] that the JI can, in particular, be derived directly from the Nosé-Hoover thermostated dynamics. This statistical mechanical derivation is particularly relevant in the framework of molecular dynamics simulation, because it is based solely on the equations of motion considered and is free of any additional assumptions on system size or bath coupling. Here, this result is generalized to a variety of dynamics, along two directions. On the one hand, specific improved thermostating schemes used in practical applications are treated. These include Nosé-Hoover chains, higher moment thermostats, as well as an isothermal-isobaric scheme yielding the JI in the NPT ensemble. On the other hand, the theoretical generality of the new derivation is explored. Generic dynamics with arbitrary coupling terms and an arbitrary number of thermostating variables, both non-Hamiltonian and Hamiltonian, are shown to imply the JI. In particular, a nonautonomous formulation of the generalized Nosé-Poincaré thermostat is proposed. Finally, general conditions required for the JI derivation are briefly discussed.

Hamiltonian formulation of systems with balanced loss-gain and exactly solvable models

NASA Astrophysics Data System (ADS)

Ghosh, Pijush K.; Sinha, Debdeep

2018-01-01

A Hamiltonian formulation of generic many-body systems with balanced loss and gain is presented. It is shown that a Hamiltonian formulation is possible only if the balancing of loss and gain terms occurs in a pairwise fashion. It is also shown that with the choice of a suitable co-ordinate, the Hamiltonian can always be reformulated in the background of a pseudo-Euclidean metric. If the equations of motion of some of the well-known many-body systems like Calogero models are generalized to include balanced loss and gain, it appears that the same may not be amenable to a Hamiltonian formulation. A few exactly solvable systems with balanced loss and gain, along with a set of integrals of motion are constructed. The examples include a coupled chain of nonlinear oscillators and a many-particle Calogero-type model with four-body inverse square plus two-body pair-wise harmonic interactions. For the case of nonlinear oscillators, stable solution exists even if the loss and gain parameter has unbounded upper range. Further, the range of the parameter for which the stable solutions are obtained is independent of the total number of the oscillators. The set of coupled nonlinear equations are solved exactly for the case when the values of all the constants of motions except the Hamiltonian are equal to zero. Exact, analytical classical solutions are presented for all the examples considered.

Representation of the exact relativistic electronic Hamiltonian within the regular approximation

NASA Astrophysics Data System (ADS)

Filatov, Michael; Cremer, Dieter

2003-12-01

The exact relativistic Hamiltonian for electronic states is expanded in terms of energy-independent linear operators within the regular approximation. An effective relativistic Hamiltonian has been obtained, which yields in lowest order directly the infinite-order regular approximation (IORA) rather than the zeroth-order regular approximation method. Further perturbational expansion of the exact relativistic electronic energy utilizing the effective Hamiltonian leads to new methods based on ordinary (IORAn) or double [IORAn(2)] perturbation theory (n: order of expansion), which provide improved energies in atomic calculations. Energies calculated with IORA4 and IORA3(2) are accurate up to c-20. Furthermore, IORA is improved by using the IORA wave function to calculate the Rayleigh quotient, which, if minimized, leads to the exact relativistic energy. The outstanding performance of this new IORA method coined scaled IORA is documented in atomic and molecular calculations.

Hamiltonian structure of three-dimensional gravity in Vielbein formalism

NASA Astrophysics Data System (ADS)

Hajihashemi, Mahdi; Shirzad, Ahmad

2018-01-01

Considering Chern-Simons like gravity theories in three dimensions as first order systems, we analyze the Hamiltonian structure of three theories Topological massive gravity, New massive gravity, and Zwei-Dreibein Gravity. We show that these systems demonstrate a new feature of the constrained systems in which a new kind of constraints emerge due to factorization of determinant of the matrix of Poisson brackets of constraints. We find the desired number of degrees of freedom as well as the generating functional of local Lorentz transformations and diffeomorphism through canonical structure of the system. We also compare the Hamiltonian structure of linearized version of the considered models with the original ones.

Multisymplectic Lagrangian and Hamiltonian Formalisms of Classical Field Theories

NASA Astrophysics Data System (ADS)

Román-Roy, Narciso

2009-11-01

This review paper is devoted to presenting the standard multisymplectic formulation for describing geometrically classical field theories, both the regular and singular cases. First, the main features of the Lagrangian formalism are revisited and, second, the Hamiltonian formalism is constructed using Hamiltonian sections. In both cases, the variational principles leading to the Euler-Lagrange and the Hamilton-De Donder-Weyl equations, respectively, are stated, and these field equations are given in different but equivalent geometrical ways in each formalism. Finally, both are unified in a new formulation (which has been developed in the last years), following the original ideas of Rusk and Skinner for mechanical systems.

Centrifugal distortion coefficients of asymmetric-top molecules: Reduction of the octic terms of the rotational Hamiltonian

NASA Astrophysics Data System (ADS)

Ramachandra Rao, Ch. V. S.

1983-11-01

The rotational Hamiltonian of an asymmetric-top molecule in its standard form, containing terms up to eighth degree in the components of the total angular momentum, is transformed by a unitary transformation with parameters Spqr to a reduced Hamiltonian so as to avoid the indeterminacies inherent in fitting the complete Hamiltonian to observed energy levels. Expressions are given for the nine determinable combinations of octic constants Θ' i ( i = 1 to 9) which are invariant under the unitary transformation. A method of reduction suitable for energy calculations by matrix diagonalization is considered. The relations between the coefficients of the transformed Hamiltonian, for suitable choice of the parameters Spqr, and those of the reduced Hamiltonian are given. This enables the determination of the nine octic constants Θ' i in terms of the experimental constants.

Entanglement Entropy of Eigenstates of Quadratic Fermionic Hamiltonians.

PubMed

Vidmar, Lev; Hackl, Lucas; Bianchi, Eugenio; Rigol, Marcos

2017-07-14

In a seminal paper [D. N. Page, Phys. Rev. Lett. 71, 1291 (1993)PRLTAO0031-900710.1103/PhysRevLett.71.1291], Page proved that the average entanglement entropy of subsystems of random pure states is S_{ave}≃lnD_{A}-(1/2)D_{A}^{2}/D for 1≪D_{A}≤sqrt[D], where D_{A} and D are the Hilbert space dimensions of the subsystem and the system, respectively. Hence, typical pure states are (nearly) maximally entangled. We develop tools to compute the average entanglement entropy ⟨S⟩ of all eigenstates of quadratic fermionic Hamiltonians. In particular, we derive exact bounds for the most general translationally invariant models lnD_{A}-(lnD_{A})^{2}/lnD≤⟨S⟩≤lnD_{A}-[1/(2ln2)](lnD_{A})^{2}/lnD. Consequently, we prove that (i) if the subsystem size is a finite fraction of the system size, then ⟨S⟩Hamiltonian departs from the result for typical pure states, and (ii) in the limit in which the subsystem size is a vanishing fraction of the system size, the average entanglement entropy is maximal; i.e., typical eigenstates of such Hamiltonians exhibit eigenstate thermalization.

Quantum recurrence and fractional dynamic localization in ac-driven perfect state transfer Hamiltonians

DOE Office of Scientific and Technical Information (OSTI.GOV)

Longhi, Stefano, E-mail: stefano.longhi@fisi.polimi.it

Quantum recurrence and dynamic localization are investigated in a class of ac-driven tight-binding Hamiltonians, the Krawtchouk quantum chain, which in the undriven case provides a paradigmatic Hamiltonian model that realizes perfect quantum state transfer and mirror inversion. The equivalence between the ac-driven single-particle Krawtchouk Hamiltonian H{sup -hat} (t) and the non-interacting ac-driven bosonic junction Hamiltonian enables to determine in a closed form the quasi energy spectrum of H{sup -hat} (t) and the conditions for exact wave packet reconstruction (dynamic localization). In particular, we show that quantum recurrence, which is predicted by the general quantum recurrence theorem, is exact for themore » Krawtchouk quantum chain in a dense range of the driving amplitude. Exact quantum recurrence provides perfect wave packet reconstruction at a frequency which is fractional than the driving frequency, a phenomenon that can be referred to as fractional dynamic localization.« less

Continuation of periodic orbits in symmetric Hamiltonian and conservative systems

NASA Astrophysics Data System (ADS)

Galan-Vioque, J.; Almaraz, F. J. M.; Macías, E. F.

2014-12-01

We present and review results on the continuation and bifurcation of periodic solutions in conservative, reversible and Hamiltonian systems in the presence of symmetries. In particular we show how two-point boundary value problem continuation software can be used to compute families of periodic solutions of symmetric Hamiltonian systems. The technique is introduced with a very simple model example (the mathematical pendulum), justified with a theoretical continuation result and then applied to two non trivial examples: the non integrable spring pendulum and the continuation of the figure eight solution of the three body problem.

Equilibrium Solutions of the Logarithmic Hamiltonian Leapfrog for the N-body Problem

NASA Astrophysics Data System (ADS)

Minesaki, Yukitaka

2018-04-01

We prove that a second-order logarithmic Hamiltonian leapfrog for the classical general N-body problem (CGNBP) designed by Mikkola and Tanikawa and some higher-order logarithmic Hamiltonian methods based on symmetric multicompositions of the logarithmic algorithm exactly reproduce the orbits of elliptic relative equilibrium solutions in the original CGNBP. These methods are explicit symplectic methods. Before this proof, only some implicit discrete-time CGNBPs proposed by Minesaki had been analytically shown to trace the orbits of elliptic relative equilibrium solutions. The proof is therefore the first existence proof for explicit symplectic methods. Such logarithmic Hamiltonian methods with a variable time step can also precisely retain periodic orbits in the classical general three-body problem, which generic numerical methods with a constant time step cannot do.

A unified theoretical framework for mapping models for the multi-state Hamiltonian.

PubMed

Liu, Jian

2016-11-28

We propose a new unified theoretical framework to construct equivalent representations of the multi-state Hamiltonian operator and present several approaches for the mapping onto the Cartesian phase space. After mapping an F-dimensional Hamiltonian onto an F+1 dimensional space, creation and annihilation operators are defined such that the F+1 dimensional space is complete for any combined excitation. Commutation and anti-commutation relations are then naturally derived, which show that the underlying degrees of freedom are neither bosons nor fermions. This sets the scene for developing equivalent expressions of the Hamiltonian operator in quantum mechanics and their classical/semiclassical counterparts. Six mapping models are presented as examples. The framework also offers a novel way to derive such as the well-known Meyer-Miller model.

A Synthetical Two-Component Model with Peakon Solutions: One More Bi-Hamiltonian Case

NASA Astrophysics Data System (ADS)

Mengxia, Zhang; Xiaomin, Yang

2018-05-01

Compatible pairs of Hamiltonian operators for the synthetical two-component model of Xia, Qiao, and Zhou are derived systematically by means of the spectral gradient method. A new two-component system, which is bi-Hamiltonian, is presented. For this new system, the construction of its peakon solutions is considered.

Tsallis thermostatistics for finite systems: a Hamiltonian approach

NASA Astrophysics Data System (ADS)

Adib, Artur B.; Moreira, Andrã© A.; Andrade, José S., Jr.; Almeida, Murilo P.

2003-05-01

The derivation of the Tsallis generalized canonical distribution from the traditional approach of the Gibbs microcanonical ensemble is revisited (Phys. Lett. A 193 (1994) 140). We show that finite systems whose Hamiltonians obey a generalized homogeneity relation rigorously follow the nonextensive thermostatistics of Tsallis. In the thermodynamical limit, however, our results indicate that the Boltzmann-Gibbs statistics is always recovered, regardless of the type of potential among interacting particles. This approach provides, moreover, a one-to-one correspondence between the generalized entropy and the Hamiltonian structure of a wide class of systems, revealing a possible origin for the intrinsic nonlinear features present in the Tsallis formalism that lead naturally to power-law behavior. Finally, we confirm these exact results through extensive numerical simulations of the Fermi-Pasta-Ulam chain of anharmonic oscillators.

An Exact Separation of the Spin-Free and Spin-Dependent Terms of the Dirac-Coulomb-Breit Hamiltonian

NASA Technical Reports Server (NTRS)

Dyall, Kenneth G.

1994-01-01

The Dirac Hamiltonian is transformed by extracting the operator (sigma x p)/2mc from the small component of the wave function and applying it to the operators of the original Hamiltonian. The resultant operators contain products of Paull matrices that can be rearranged to give spin-free and spin-dependent operators. These operators are the ones encountered in the Breit-Pauli Hamiltonian, as well as some of higher order in alpha(sup 2). However, since the transformation of the original Dirac Hamiltonian is exact, the new Hamiltonian can be used in variational calculations, with or without the spin-dependent terms. The new small component functions have the same symmetry properties as the large component. Use of only the spin-free terms of the new Hamiltonian permits the same factorization over spin variables as in nonrelativistic theory, and therefore all the post-Self-Consistent Field (SCF) machinery of nonrelativistic calculations can be applied. However, the single-particle functions are two-component orbitals having a large and small component, and the SCF methods must be modified accordingly. Numerical examples are presented, and comparisons are made with the spin-free second-order Douglas-Kroll transformed Hamiltonian of Hess.

Iterated Hamiltonian type systems and applications

NASA Astrophysics Data System (ADS)

Tiba, Dan

2018-04-01

We discuss, in arbitrary dimension, certain Hamiltonian type systems and prove existence, uniqueness and regularity properties, under the independence condition. We also investigate the critical case, define a class of generalized solutions and prove existence and basic properties. Relevant examples and counterexamples are also indicated. The applications concern representations of implicitly defined manifolds and their perturbations, motivated by differential systems involving unknown geometries.

Conformal killing tensors and covariant Hamiltonian dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cariglia, M., E-mail: marco@iceb.ufop.br; Gibbons, G. W., E-mail: G.W.Gibbons@damtp.cam.ac.uk; LE STUDIUM, Loire Valley Institute for Advanced Studies, Tours and Orleans

2014-12-15

A covariant algorithm for deriving the conserved quantities for natural Hamiltonian systems is combined with the non-relativistic framework of Eisenhart, and of Duval, in which the classical trajectories arise as geodesics in a higher dimensional space-time, realized by Brinkmann manifolds. Conserved quantities which are polynomial in the momenta can be built using time-dependent conformal Killing tensors with flux. The latter are associated with terms proportional to the Hamiltonian in the lower dimensional theory and with spectrum generating algebras for higher dimensional quantities of order 1 and 2 in the momenta. Illustrations of the general theory include the Runge-Lenz vector formore » planetary motion with a time-dependent gravitational constant G(t), motion in a time-dependent electromagnetic field of a certain form, quantum dots, the Hénon-Heiles and Holt systems, respectively, providing us with Killing tensors of rank that ranges from one to six.« less

Two-layer interfacial flows beyond the Boussinesq approximation: a Hamiltonian approach

NASA Astrophysics Data System (ADS)

Camassa, R.; Falqui, G.; Ortenzi, G.

2017-02-01

The theory of integrable systems of Hamiltonian PDEs and their near-integrable deformations is used to study evolution equations resulting from vertical-averages of the Euler system for two-layer stratified flows in an infinite two-dimensional channel. The Hamiltonian structure of the averaged equations is obtained directly from that of the Euler equations through the process of Hamiltonian reduction. Long-wave asymptotics together with the Boussinesq approximation of neglecting the fluids’ inertia is then applied to reduce the leading order vertically averaged equations to the shallow-water Airy system, albeit in a non-trivial way. The full non-Boussinesq system for the dispersionless limit can then be viewed as a deformation of this well known equation. In a perturbative study of this deformation, a family of approximate constants of the motion are explicitly constructed and used to find local solutions of the evolution equations by means of hodograph-like formulae.

Reductions of topologically massive gravity I: Hamiltonian analysis of second order degenerate Lagrangians

NASA Astrophysics Data System (ADS)

Ćaǧatay Uçgun, Filiz; Esen, Oǧul; Gümral, Hasan

2018-01-01

We present Skinner-Rusk and Hamiltonian formalisms of second order degenerate Clément and Sarıoğlu-Tekin Lagrangians. The Dirac-Bergmann constraint algorithm is employed to obtain Hamiltonian realizations of Lagrangian theories. The Gotay-Nester-Hinds algorithm is used to investigate Skinner-Rusk formalisms of these systems.

On the Existence of Star Products on Quotient Spaces of Linear Hamiltonian Torus Actions

NASA Astrophysics Data System (ADS)

Herbig, Hans-Christian; Iyengar, Srikanth B.; Pflaum, Markus J.

2009-08-01

We discuss BFV deformation quantization (Bordemann et al. in A homological approach to singular reduction in deformation quantization, singularity theory, pp. 443-461. World Scientific, Hackensack, 2007) in the special case of a linear Hamiltonian torus action. In particular, we show that the Koszul complex on the moment map of an effective linear Hamiltonian torus action is acyclic. We rephrase the nonpositivity condition of Arms and Gotay (Adv Math 79(1):43-103, 1990) for linear Hamiltonian torus actions. It follows that reduced spaces of such actions admit continuous star products.

Universal adiabatic quantum computation via the space-time circuit-to-Hamiltonian construction.

PubMed

Gosset, David; Terhal, Barbara M; Vershynina, Anna

2015-04-10

We show how to perform universal adiabatic quantum computation using a Hamiltonian which describes a set of particles with local interactions on a two-dimensional grid. A single parameter in the Hamiltonian is adiabatically changed as a function of time to simulate the quantum circuit. We bound the eigenvalue gap above the unique ground state by mapping our model onto the ferromagnetic XXZ chain with kink boundary conditions; the gap of this spin chain was computed exactly by Koma and Nachtergaele using its q-deformed version of SU(2) symmetry. We also discuss a related time-independent Hamiltonian which was shown by Janzing to be capable of universal computation. We observe that in the limit of large system size, the time evolution is equivalent to the exactly solvable quantum walk on Young's lattice.

Universal Adiabatic Quantum Computation via the Space-Time Circuit-to-Hamiltonian Construction

NASA Astrophysics Data System (ADS)

Gosset, David; Terhal, Barbara M.; Vershynina, Anna

2015-04-01

We show how to perform universal adiabatic quantum computation using a Hamiltonian which describes a set of particles with local interactions on a two-dimensional grid. A single parameter in the Hamiltonian is adiabatically changed as a function of time to simulate the quantum circuit. We bound the eigenvalue gap above the unique ground state by mapping our model onto the ferromagnetic X X Z chain with kink boundary conditions; the gap of this spin chain was computed exactly by Koma and Nachtergaele using its q -deformed version of SU(2) symmetry. We also discuss a related time-independent Hamiltonian which was shown by Janzing to be capable of universal computation. We observe that in the limit of large system size, the time evolution is equivalent to the exactly solvable quantum walk on Young's lattice.

Complete Hamiltonian analysis of cosmological perturbations at all orders II: non-canonical scalar field

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nandi, Debottam; Shankaranarayanan, S., E-mail: debottam@iisertvm.ac.in, E-mail: shanki@iisertvm.ac.in

2016-10-01

In this work, we present a consistent Hamiltonian analysis of cosmological perturbations for generalized non-canonical scalar fields. In order to do so, we introduce a new phase-space variable that is uniquely defined for different non-canonical scalar fields. We also show that this is the simplest and efficient way of expressing the Hamiltonian. We extend the Hamiltonian approach of [1] to non-canonical scalar field and obtain an unique expression of speed of sound in terms of phase-space variable. In order to invert generalized phase-space Hamilton's equations to Euler-Lagrange equations of motion, we prescribe a general inversion formulae and show that ourmore » approach for non-canonical scalar field is consistent. We also obtain the third and fourth order interaction Hamiltonian for generalized non-canonical scalar fields and briefly discuss the extension of our method to generalized Galilean scalar fields.« less

Columbia County Kindergarten Center Environmental Study Area Guide.

ERIC Educational Resources Information Center

Florida State Dept. of Education, Tallahassee. Office of Environment Education.

The guide lists seven program objectives and 15 activities guides for meeting the objectives. Included in each activity is an introduction, outdoor activity, classroom activity, and evaluation. Sample activities are: Animals Use Natural Materials to Provide Food and Shelter, Differences in Soil, Decomposition, Man-made or Natural Objects, Food…

Witnessing eigenstates for quantum simulation of Hamiltonian spectra

PubMed Central

Santagati, Raffaele; Wang, Jianwei; Gentile, Antonio A.; Paesani, Stefano; Wiebe, Nathan; McClean, Jarrod R.; Morley-Short, Sam; Shadbolt, Peter J.; Bonneau, Damien; Silverstone, Joshua W.; Tew, David P.; Zhou, Xiaoqi; O’Brien, Jeremy L.; Thompson, Mark G.

2018-01-01

The efficient calculation of Hamiltonian spectra, a problem often intractable on classical machines, can find application in many fields, from physics to chemistry. We introduce the concept of an “eigenstate witness” and, through it, provide a new quantum approach that combines variational methods and phase estimation to approximate eigenvalues for both ground and excited states. This protocol is experimentally verified on a programmable silicon quantum photonic chip, a mass-manufacturable platform, which embeds entangled state generation, arbitrary controlled unitary operations, and projective measurements. Both ground and excited states are experimentally found with fidelities >99%, and their eigenvalues are estimated with 32 bits of precision. We also investigate and discuss the scalability of the approach and study its performance through numerical simulations of more complex Hamiltonians. This result shows promising progress toward quantum chemistry on quantum computers. PMID:29387796

Integrable Time-Dependent Quantum Hamiltonians

NASA Astrophysics Data System (ADS)

Sinitsyn, Nikolai A.; Yuzbashyan, Emil A.; Chernyak, Vladimir Y.; Patra, Aniket; Sun, Chen

2018-05-01

We formulate a set of conditions under which the nonstationary Schrödinger equation with a time-dependent Hamiltonian is exactly solvable analytically. The main requirement is the existence of a non-Abelian gauge field with zero curvature in the space of system parameters. Known solvable multistate Landau-Zener models satisfy these conditions. Our method provides a strategy to incorporate time dependence into various quantum integrable models while maintaining their integrability. We also validate some prior conjectures, including the solution of the driven generalized Tavis-Cummings model.

Modular Hamiltonians on the null plane and the Markov property of the vacuum state

NASA Astrophysics Data System (ADS)

Casini, Horacio; Testé, Eduardo; Torroba, Gonzalo

2017-09-01

We compute the modular Hamiltonians of regions having the future horizon lying on a null plane. For a CFT this is equivalent to regions with a boundary of arbitrary shape lying on the null cone. These Hamiltonians have a local expression on the horizon formed by integrals of the stress tensor. We prove this result in two different ways, and show that the modular Hamiltonians of these regions form an infinite dimensional Lie algebra. The corresponding group of unitary transformations moves the fields on the null surface locally along the null generators with arbitrary null line dependent velocities, but act non-locally outside the null plane. We regain this result in greater generality using more abstract tools on the algebraic quantum field theory. Finally, we show that modular Hamiltonians on the null surface satisfy a Markov property that leads to the saturation of the strong sub-additive inequality for the entropies and to the strong super-additivity of the relative entropy.

Model many-body Stoner Hamiltonian for binary FeCr alloys

NASA Astrophysics Data System (ADS)

Nguyen-Manh, D.; Dudarev, S. L.

2009-09-01

We derive a model tight-binding many-body d -electron Stoner Hamiltonian for FeCr binary alloys and investigate the sensitivity of its mean-field solutions to the choice of hopping integrals and the Stoner exchange parameters. By applying the local charge-neutrality condition within a self-consistent treatment we show that the negative enthalpy-of-mixing anomaly characterizing the alloy in the low chromium concentration limit is due entirely to the presence of the on-site exchange Stoner terms and that the occurrence of this anomaly is not specifically related to the choice of hopping integrals describing conventional chemical bonding between atoms in the alloy. The Bain transformation pathway computed, using the proposed model Hamiltonian, for the Fe15Cr alloy configuration is in excellent agreement with ab initio total-energy calculations. Our investigation also shows how the parameters of a tight-binding many-body model Hamiltonian for a magnetic alloy can be derived from the comparison of its mean-field solutions with other, more accurate, mean-field approximations (e.g., density-functional calculations), hence stimulating the development of large-scale computational algorithms for modeling radiation damage effects in magnetic alloys and steels.

Multi-Hamiltonian structure of Plebanski's second heavenly equation

NASA Astrophysics Data System (ADS)

Neyzi, F.; Nutku, Y.; Sheftel, M. B.

2005-09-01

We show that Plebanski's second heavenly equation, when written as a first-order nonlinear evolutionary system, admits multi-Hamiltonian structure. Therefore by Magri's theorem it is a completely integrable system. Thus it is an example of a completely integrable system in four dimensions.

Hydrodynamic blade guide

DOEpatents

Blaedel, Kenneth L.; Davis, Pete J.; Landram, Charles S.

2000-01-01

A saw having a self-pumped hydrodynamic blade guide or bearing for retaining the saw blade in a centered position in the saw kerf (width of cut made by the saw). The hydrodynamic blade guide or bearing utilizes pockets or grooves incorporated into the sides of the blade. The saw kerf in the workpiece provides the guide or bearing stator surface. Both sides of the blade entrain cutting fluid as the blade enters the kerf in the workpiece, and the trapped fluid provides pressure between the blade and the workpiece as an inverse function of the gap between the blade surface and the workpiece surface. If the blade wanders from the center of the kerf, then one gap will increase and one gap will decrease and the consequent pressure difference between the two sides of the blade will cause the blade to re-center itself in the kerf. Saws using the hydrodynamic blade guide or bearing have particular application in slicing slabs from boules of single crystal materials, for example, as well as for cutting other difficult to saw materials such as ceramics, glass, and brittle composite materials.

Thermalization Time Bounds for Pauli Stabilizer Hamiltonians

NASA Astrophysics Data System (ADS)

Temme, Kristan

2017-03-01

We prove a general lower bound to the spectral gap of the Davies generator for Hamiltonians that can be written as the sum of commuting Pauli operators. These Hamiltonians, defined on the Hilbert space of N-qubits, serve as one of the most frequently considered candidates for a self-correcting quantum memory. A spectral gap bound on the Davies generator establishes an upper limit on the life time of such a quantum memory and can be used to estimate the time until the system relaxes to thermal equilibrium when brought into contact with a thermal heat bath. The bound can be shown to behave as {λ ≥ O(N^{-1} exp(-2β overline{ɛ}))}, where {overline{ɛ}} is a generalization of the well known energy barrier for logical operators. Particularly in the low temperature regime we expect this bound to provide the correct asymptotic scaling of the gap with the system size up to a factor of N -1. Furthermore, we discuss conditions and provide scenarios where this factor can be removed and a constant lower bound can be proven.

The Modified Hartmann Potential Effects on γ-rigid Bohr Hamiltonian

NASA Astrophysics Data System (ADS)

Suparmi, A.; Cari, C.; Nur Pratiwi, Beta

2018-04-01

In this paper, we present the solution of Bohr Hamiltonian in the case of γ-rigid for the modified Hartmann potential. The modified Hartmann potential was formed from the original Hartmann potential, consists of β function and θ function. By using the separation method, the three-dimensional Bohr Hamiltonian equation was reduced into three one-dimensional Schrodinger-like equation which was solved analytically. The results for the wavefunction were shown in mathematically, while for the binding energy was solved numerically. The numerical binding energy for the presence of the modified Hartmann potential is lower than the binding energy value in the absence of modified Hartmann potential effect.

Nonholonomic Hamiltonian Method for Meso-macroscale Simulations of Reacting Shocks

NASA Astrophysics Data System (ADS)

Fahrenthold, Eric; Lee, Sangyup

2015-06-01

The seamless integration of macroscale, mesoscale, and molecular scale models of reacting shock physics has been hindered by dramatic differences in the model formulation techniques normally used at different scales. In recent research the authors have developed the first unified discrete Hamiltonian approach to multiscale simulation of reacting shock physics. Unlike previous work, the formulation employs reacting themomechanical Hamiltonian formulations at all scales, including the continuum. Unlike previous work, the formulation employs a nonholonomic modeling approach to systematically couple the models developed at all scales. Example applications of the method show meso-macroscale shock to detonation simulations in nitromethane and RDX. Research supported by the Defense Threat Reduction Agency.

Steepest entropy ascent for two-state systems with slowly varying Hamiltonians

NASA Astrophysics Data System (ADS)

Militello, Benedetto

2018-05-01

The steepest entropy ascent approach is considered and applied to two-state systems. When the Hamiltonian of the system is time-dependent, the principle of maximum entropy production can still be exploited; arguments to support this fact are given. In the limit of slowly varying Hamiltonians, which allows for the adiabatic approximation for the unitary part of the dynamics, the system exhibits significant robustness to the thermalization process. Specific examples such as a spin in a rotating field and a generic two-state system undergoing an avoided crossing are considered.

Field Testing Competency-Based Vocational Education Student Learning Guides Developed at Ridge Vocational-Technical Center. From August 1, 1981 to June 30, 1982. Final Report.

ERIC Educational Resources Information Center

Andreyka, Robert E.

This project's main objective was to field test competency-based vocational education (CBVE) student learning guides developed during 1979-1981 at Ridge Vocational-Technical Center (RVTC) (Florida). The learning guides were for six programs: clerical occupations, cosmetology, heavy duty truck/bus mechanics, industrial electricity, masonry, and…

Dynamics, integrability and topology for some classes of Kolmogorov Hamiltonian systems in R+4

NASA Astrophysics Data System (ADS)

Llibre, Jaume; Xiao, Dongmei

2017-02-01

In this paper we first give the sufficient and necessary conditions in order that two classes of polynomial Kolmogorov systems in R+4 are Hamiltonian systems. Then we study the integrability of these Hamiltonian systems in the Liouville sense. Finally, we investigate the global dynamics of the completely integrable Lotka-Volterra Hamiltonian systems in R+4. As an application of the invariant subsets of these systems, we obtain topological classifications of the 3-submanifolds in R+4 defined by the hypersurfaces axy + bzw + cx2 y + dxy2 + ez2 w + fzw2 = h, where a , b , c , d , e , f , w and h are real constants.

Interprofessional education and practice guide No. 4: Developing and sustaining interprofessional education at an academic health center.

PubMed

Willgerodt, Mayumi A; Abu-Rish Blakeney, Erin; Brock, Douglas M; Liner, Debra; Murphy, Nanci; Zierler, Brenda

2015-01-01

Increasingly health professions schools and academic health centers are required to include interprofessional education (IPE) as a standard part of their core curricula to maintain accreditation. However, challenges continue to surface as faculty struggle to develop and participate in IPE activities while balancing increasing workloads and limited resources, and also trying to keep current in the changing profession-specific accreditation and standards. This guide shares lessons learned from developing and sustaining IPE activities at the University of Washington (UW) based in the United States. In 2008, the UW Schools of Nursing and Medicine were awarded funds to develop, implement, and evaluate an interprofessional program focused on team communication. This funding supported the creation of two annual large-scale IPE events, provided infrastructure support for the Center for Health Sciences Interprofessional Education, Research and Practice (CHSIERP), and supported numerous interprofessional activities and initiatives in the health professions curricula. Our experiences over the years have yielded several key lessons that are important to consider in any IPE effort. In this guide we report on these lessons learned and provide pragmatic suggestions for designing and implementing IPE in order to maximize long-term success.

Controlling effect of geometrically defined local structural changes on chaotic Hamiltonian systems.

PubMed

Ben Zion, Yossi; Horwitz, Lawrence

2010-04-01

An effective characterization of chaotic conservative Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor derived from the structure of the Hamiltonian has been extended to a wide class of potential models of standard form through definition of a conformal metric. The geodesic equations reproduce the Hamilton equations of the original potential model through an inverse map in the tangent space. The second covariant derivative of the geodesic deviation in this space generates a dynamical curvature, resulting in (energy-dependent) criteria for unstable behavior different from the usual Lyapunov criteria. We show here that this criterion can be constructively used to modify locally the potential of a chaotic Hamiltonian model in such a way that stable motion is achieved. Since our criterion for instability is local in coordinate space, these results provide a minimal method for achieving control of a chaotic system.

Similarity-transformed dyson mapping and SDG-interacting boson hamiltonian

NASA Astrophysics Data System (ADS)

Navrátil, P.; Dobeš, J.

1991-10-01

The sdg-interacting boson hamiltonian is constructed from the fermion shell-model input. The seniority boson mapping as given by the similarity-transformed Dyson boson mapping is used. The s, d, and g collective boson amplitudes are determined consistently from the mapped hamiltonian. Influence of the starting shell-model parameters is discussed. Calculations for the Sm isotopic chain and for the 148Sm, 150Nd, and 196Pt nuclei are presented. Calculated energy levels as well as E2 and E4 properties agree rather well with experimental ones. To obtain such agreement, the input shell-model parameters cannot be fixed at a constant set for several nuclei but have to be somewhat varied, especially in the deformed region. Possible reasons for this variation are discussed. Effects of the explicit g-boson consideration are shown.

BRST quantization of Yang-Mills theory: A purely Hamiltonian approach on Fock space

NASA Astrophysics Data System (ADS)

Öttinger, Hans Christian

2018-04-01

We develop the basic ideas and equations for the BRST quantization of Yang-Mills theories in an explicit Hamiltonian approach, without any reference to the Lagrangian approach at any stage of the development. We present a new representation of ghost fields that combines desirable self-adjointness properties with canonical anticommutation relations for ghost creation and annihilation operators, thus enabling us to characterize the physical states on a well-defined Fock space. The Hamiltonian is constructed by piecing together simple BRST invariant operators to obtain a minimal invariant extension of the free theory. It is verified that the evolution equations implied by the resulting minimal Hamiltonian provide a quantum version of the classical Yang-Mills equations. The modifications and requirements for the inclusion of matter are discussed in detail.

Hamiltonian Effective Field Theory Study of the N^{*}(1535) Resonance in Lattice QCD.

PubMed

Liu, Zhan-Wei; Kamleh, Waseem; Leinweber, Derek B; Stokes, Finn M; Thomas, Anthony W; Wu, Jia-Jun

2016-02-26

Drawing on experimental data for baryon resonances, Hamiltonian effective field theory (HEFT) is used to predict the positions of the finite-volume energy levels to be observed in lattice QCD simulations of the lowest-lying J^{P}=1/2^{-} nucleon excitation. In the initial analysis, the phenomenological parameters of the Hamiltonian model are constrained by experiment and the finite-volume eigenstate energies are a prediction of the model. The agreement between HEFT predictions and lattice QCD results obtained on volumes with spatial lengths of 2 and 3 fm is excellent. These lattice results also admit a more conventional analysis where the low-energy coefficients are constrained by lattice QCD results, enabling a determination of resonance properties from lattice QCD itself. Finally, the role and importance of various components of the Hamiltonian model are examined.

Charged dust in planetary magnetospheres: Hamiltonian dynamics and numerical simulations for highly charged grains

NASA Technical Reports Server (NTRS)

Schaffer, L.; Burns, J. A.

1994-01-01

We use a combination of analytical and numerical methods to investigate the dynamics of charged dust grains in planetary magnetospheres. Our emphasis is on obtaining results valid for particles that are not necessarily dominated either by gravitational or electromagnetic forces. A Hamiltonian formulation of the problem yields exact results, for all values of charge-to-mass ratio, when we introduce two constraints: particles remain in the equatorial plane and the magnetic field is taken as axially symmetric. In particular, we obtain locations of equilibrium points, the frequencies of stable periodic orbits, the topology of separatrices in phase space, and the rate of longitudinal drift. These results are significant for specific applications: motion in the nearly aligned dipolar field of Saturn, and the trajectories of arbitrarily charged particles in complex magnetic fields for limited periods of time after ejection from parent bodies. Since the model is restrictive, we also use numerical integrations of the full three-dimensional equations of motion and illustrate under what conditions the constrained problem yields reasonable results. We show that a large fraction of the intermediately charged and highly charged (gyrating) particles will always be lost to a planet's atmosphere within a few hundred hours, for motion through tilted-dipole magnetic fields. We find that grains must have a very high charge-to-mass ratio in order to be mirrored back to the ring plane. Thus, except perhaps at Saturn where the dipole tilt is very small, the likely inhabitants of the dusty ring systems are those particles that are either nearly Keplerian (weakly charged) grains or grains whose charges place them in the lower end of the intermediate charge zone. Fianlly, we demonstrate the effect of plasma drag on the orbits of gyrating particles to be a rapid decrease in gyroradius followed by a slow radial evolution of the guiding center.

A complex guided spectral transform Lanczos method for studying quantum resonance states

DOE PAGES

Yu, Hua-Gen

2014-12-28

A complex guided spectral transform Lanczos (cGSTL) algorithm is proposed to compute both bound and resonance states including energies, widths and wavefunctions. The algorithm comprises of two layers of complex-symmetric Lanczos iterations. A short inner layer iteration produces a set of complex formally orthogonal Lanczos (cFOL) polynomials. They are used to span the guided spectral transform function determined by a retarded Green operator. An outer layer iteration is then carried out with the transform function to compute the eigen-pairs of the system. The guided spectral transform function is designed to have the same wavefunctions as the eigenstates of the originalmore » Hamiltonian in the spectral range of interest. Therefore the energies and/or widths of bound or resonance states can be easily computed with their wavefunctions or by using a root-searching method from the guided spectral transform surface. The new cGSTL algorithm is applied to bound and resonance states of HO₂, and compared to previous calculations.« less

Quadratic time dependent Hamiltonians and separation of variables

NASA Astrophysics Data System (ADS)

Anzaldo-Meneses, A.

2017-06-01

Time dependent quantum problems defined by quadratic Hamiltonians are solved using canonical transformations. The Green's function is obtained and a comparison with the classical Hamilton-Jacobi method leads to important geometrical insights like exterior differential systems, Monge cones and time dependent Gaussian metrics. The Wei-Norman approach is applied using unitary transformations defined in terms of generators of the associated Lie groups, here the semi-direct product of the Heisenberg group and the symplectic group. A new explicit relation for the unitary transformations is given in terms of a finite product of elementary transformations. The sequential application of adequate sets of unitary transformations leads naturally to a new separation of variables method for time dependent Hamiltonians, which is shown to be related to the Inönü-Wigner contraction of Lie groups. The new method allows also a better understanding of interacting particles or coupled modes and opens an alternative way to analyze topological phases in driven systems.

Quantum gates by inverse engineering of a Hamiltonian

NASA Astrophysics Data System (ADS)

Santos, Alan C.

2018-01-01

Inverse engineering of a Hamiltonian (IEH) from an evolution operator is a useful technique for the protocol of quantum control with potential applications in quantum information processing. In this paper we introduce a particular protocol to perform IEH and we show how this scheme can be used to implement a set of quantum gates by using minimal quantum resources (such as entanglement, interactions between more than two qubits or auxiliary qubits). Remarkably, while previous protocols request three-qubit interactions and/or auxiliary qubits to implement such gates, our protocol requires just two-qubit interactions and no auxiliary qubits. By using this approach we can obtain a large class of Hamiltonians that allow us to implement single and two-qubit gates necessary for quantum computation. To conclude this article we analyze the performance of our scheme against systematic errors related to amplitude noise, where we show that the free parameters introduced in our scheme can be useful for enhancing the robustness of the protocol against such errors.

Hamiltonian analysis of non-relativistic non-BPS Dp-brane

NASA Astrophysics Data System (ADS)

Klusoň, J.

2017-07-01

We perform Hamiltonian analysis of non-relativistic non-BPS Dp-brane. We find the constraint structure of this theory and determine corresponding equations of motion. We further discuss property of this theory at the tachyon vacuum.

Weak hamiltonian Wilson Coefficients from Lattice QCD

NASA Astrophysics Data System (ADS)

Bruno, Mattia

2018-03-01

n this work we present a calculation of the Wilson Coefficients C1 and C2 of the Effective Weak Hamiltonian to all-orders in αs, using lattice simulations. Given the current availability of lattice spacings we restrict our calculation to unphysically light W bosons around 2 GeV and we study the systematic uncertainties of the two Wilson Coefficients.

Effective Hamiltonian approach to the Kerr nonlinearity in an optomechanical system

NASA Astrophysics Data System (ADS)

Gong, Z. R.; Ian, H.; Liu, Yu-Xi; Sun, C. P.; Nori, Franco

2009-12-01

Using the Born-Oppenheimer approximation, we derive an effective Hamiltonian for an optomechanical system that leads to a nonlinear Kerr effect in the system’s vacuum. The oscillating mirror at one edge of the optomechanical system induces a squeezing effect in the intensity spectrum of the cavity field. A near-resonant laser field is applied at the other edge to drive the cavity field in order to enhance the Kerr effect. We also propose a quantum-nondemolition-measurement setup to monitor a system with two cavities separated by a common oscillating mirror based on our effective Hamiltonian approach.

Trojan dynamics well approximated by a new Hamiltonian normal form

NASA Astrophysics Data System (ADS)

Páez, Rocío Isabel; Locatelli, Ugo

2015-10-01

We revisit a classical perturbative approach to the Hamiltonian related to the motions of Trojan bodies, in the framework of the planar circular restricted three-body problem, by introducing a number of key new ideas in the formulation. In some sense, we adapt the approach of Garfinkel to the context of the normal form theory and its modern techniques. First, we make use of Delaunay variables for a physically accurate representation of the system. Therefore, we introduce a novel manipulation of the variables so as to respect the natural behaviour of the model. We develop a normalization procedure over the fast angle which exploits the fact that singularities in this model are essentially related to the slow angle. Thus, we produce a new normal form, i.e. an integrable approximation to the Hamiltonian. We emphasize some practical examples of the applicability of our normalizing scheme, e.g. the estimation of the stable libration region. Finally, we compare the level curves produced by our normal form with surfaces of section provided by the integration of the non-normalized Hamiltonian, with very good agreement. Further precision tests are also provided. In addition, we give a step-by-step description of the algorithm, allowing for extensions to more complicated models.

Stability of Inhomogeneous Equilibria of Hamiltonian Continuous Media Field Theories

NASA Astrophysics Data System (ADS)

Hagstrom, George

2013-10-01

There are a wide variety of 1 + 1 Hamiltonian continuous media field theories that exhibit phase space pattern formation. In plasma physics, the most famous of these is the Vlasov-Poisson equation, but other examples include the incompressible Euler equation in two-dimensions and the Hamiltonian Mean Field (or XY) model. One of the characteristic phenomenon that occurs in systems described by these equations is the formation of cat's eye patterns in phase space as a result of the nonlinear saturation of instabilities. Corresponding to each of these cat's eyes is a spatially inhomogeneous equilibrium solution of the underlying model, in plasma physics these are called BGK modes, but analogous solutions exist in all of the above systems. Here we analyze the stability of inhomogeneous equilibria in the Hamiltonian Mean Field model and in the Single Wave model, which is an equation that was derived to provide a model of the formation of electron holes in plasmas. We use action angle variables and the properties of elliptic functions to analyze the resulting dispersion relation construct linearly stable inhomogeneous equilibria for in the limit of small numbers of particles and study the behavior of solutions near these equilibria. Work supported by USDOE grant no. DE-FG02-ER53223.

Hamiltonian model and dynamic analyses for a hydro-turbine governing system with fractional item and time-lag

NASA Astrophysics Data System (ADS)

Xu, Beibei; Chen, Diyi; Zhang, Hao; Wang, Feifei; Zhang, Xinguang; Wu, Yonghong

2017-06-01

This paper focus on a Hamiltonian mathematical modeling for a hydro-turbine governing system including fractional item and time-lag. With regards to hydraulic pressure servo system, a universal dynamical model is proposed, taking into account the viscoelastic properties and low-temperature impact toughness of constitutive materials as well as the occurrence of time-lag in the signal transmissions. The Hamiltonian model of the hydro-turbine governing system is presented using the method of orthogonal decomposition. Furthermore, a novel Hamiltonian function that provides more detailed energy information is presented, since the choice of the Hamiltonian function is the key issue by putting the whole dynamical system to the theory framework of the generalized Hamiltonian system. From the numerical experiments based on a real large hydropower station, we prove that the Hamiltonian function can describe the energy variation of the hydro-turbine suitably during operation. Moreover, the effect of the fractional α and the time-lag τ on the dynamic variables of the hydro-turbine governing system are explored and their change laws identified, respectively. The physical meaning between fractional calculus and time-lag are also discussed in nature. All of the above theories and numerical results are expected to provide a robust background for the safe operation and control of large hydropower stations.

Split Orthogonal Group: A Guiding Principle for Sign-Problem-Free Fermionic Simulations

NASA Astrophysics Data System (ADS)

Wang, Lei; Liu, Ye-Hua; Iazzi, Mauro; Troyer, Matthias; Harcos, Gergely

2015-12-01

We present a guiding principle for designing fermionic Hamiltonians and quantum Monte Carlo (QMC) methods that are free from the infamous sign problem by exploiting the Lie groups and Lie algebras that appear naturally in the Monte Carlo weight of fermionic QMC simulations. Specifically, rigorous mathematical constraints on the determinants involving matrices that lie in the split orthogonal group provide a guideline for sign-free simulations of fermionic models on bipartite lattices. This guiding principle not only unifies the recent solutions of the sign problem based on the continuous-time quantum Monte Carlo methods and the Majorana representation, but also suggests new efficient algorithms to simulate physical systems that were previously prohibitive because of the sign problem.

Entree Production Guides for Modified Diets at Walter Reed Army Medical Center. Part 4. Meat Substitute Entrees

DTIC Science & Technology

1979-06-01

numbers of vegetarian patients. Part V, Renal Diets , consists of eight very carefully weighed entrees and one dessert. These items are designed to give...WORDS (Conthmae an, revee side It nocesary and Identify by black number) \\ ~FOOD PREPARATION MEAT SUBSTITUTE MODIFIED DIETS COOK-FEEZE SYSTEMS SENSORY...Unsrfnounced I:! I *1C: -r Lii ENTREE PRODUCTION GUIDES FOR MODIFIED DIETS AT WALTER REED ARMY MEDICAL CENTER PART III: DENTAL LIQUID ENTREES FOREWORD

The Three Roots and Papa's Advice. A Puerto Rican Migration Story. A Learner-Centered Model Guide for Teachers.

ERIC Educational Resources Information Center

Herendeen, Noemi Carrera; Mitchell, Alaire; Dinos, Carmen

This document is part of a series of guides for teachers in which the Division of Bilingual Education of the New York City Board of Education presents a learner-centered model in which the learner sees himself or herself in the story. Learners are able to relive their own experiences or those of their parents or grandparents as they left their own…

Hamiltonian structure of Dubrovin{close_quote}s equation of associativity in 2-d topological field theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Galvao, C.A.; Nutku, Y.

1996-12-01

mA third order Monge-Amp{grave e}re type equation of associativity that Dubrovin has obtained in 2-d topological field theory is formulated in terms of a variational principle subject to second class constraints. Using Dirac{close_quote}s theory of constraints this degenerate Lagrangian system is cast into Hamiltonian form and the Hamiltonian operator is obtained from the Dirac bracket. There is a new type of Kac-Moody algebra that corresponds to this Hamiltonian operator. In particular, it is not a W-algebra. {copyright} {ital 1996 American Institute of Physics.}

On the paradoxical evolution of the number of photons in a new model of interpolating Hamiltonians

NASA Astrophysics Data System (ADS)

Valverde, Clodoaldo; Baseia, Basílio

2018-01-01

We introduce a new Hamiltonian model which interpolates between the Jaynes-Cummings model (JCM) and other types of such Hamiltonians. It works with two interpolating parameters, rather than one as traditional. Taking advantage of this greater degree of freedom, we can perform continuous interpolation between the various types of these Hamiltonians. As applications, we discuss a paradox raised in literature and compare the time evolution of the photon statistics obtained in the various interpolating models. The role played by the average excitation in these comparisons is also highlighted.

Learner-centered teaching in the college science classroom: a practical guide for teaching assistants, instructors, and professors

NASA Astrophysics Data System (ADS)

Dominguez, Margaret Z.; Vorndran, Shelby

2014-09-01

The Office of Instruction and Assessment at the University of Arizona currently offers a Certificate in College Teaching Program. The objective of this program is to develop the competencies necessary to teach effectively in higher education today, with an emphasis on learner-centered teaching. This type of teaching methodology has repeatedly shown to have superior effects compared to traditional teacher-centered approaches. The success of this approach has been proven in both short term and long term teaching scenarios. Students must actively participate in class, which allows for the development of depth of understanding, acquisition of critical thinking, and problem-solving skills. As optical science graduate students completing the teaching program certificate, we taught a recitation class for OPTI 370: Photonics and Lasers for two consecutive years. The recitation was an optional 1-hour long session to supplement the course lectures. This recitation received positive feedback and learner-centered teaching was shown to be a successful method for engaging students in science, specifically in optical sciences following an inquiry driven format. This paper is intended as a guide for interactive, multifaceted teaching, due to the fact that there are a variety of learning styles found in every classroom. The techniques outlined can be implemented in many formats: a full course, recitation session, office hours and tutoring. This guide is practical and includes only the most effective and efficient strategies learned while also addressing the challenges faced, such as formulating engaging questions, using wait time and encouraging shy students.

Size Reduction of Hamiltonian Matrix for Large-Scale Energy Band Calculations Using Plane Wave Bases

NASA Astrophysics Data System (ADS)

Morifuji, Masato

2018-01-01

We present a method of reducing the size of a Hamiltonian matrix used in calculations of electronic states. In the electronic states calculations using plane wave basis functions, a large number of plane waves are often required to obtain precise results. Even using state-of-the-art techniques, the Hamiltonian matrix often becomes very large. The large computational time and memory necessary for diagonalization limit the widespread use of band calculations. We show a procedure of deriving a reduced Hamiltonian constructed using a small number of low-energy bases by renormalizing high-energy bases. We demonstrate numerically that the significant speedup of eigenstates evaluation is achieved without losing accuracy.

Sqeezing generated by a nonlinear master equation and by amplifying-dissipative Hamiltonians

NASA Technical Reports Server (NTRS)

Dodonov, V. V.; Marchiolli, M. A.; Mizrahi, Solomon S.; Moussa, M. H. Y.

1994-01-01

In the first part of this contribution we show that the master equation derived from the generalized version of the nonlinear Doebner-Goldin equation leads to the squeezing of one of the quadratures. In the second part we consider two familiar Hamiltonians, the Bateman- Caldirola-Kanai and the optical parametric oscillator; going back to their classical Lagrangian form we introduce a stochastic force and a dissipative factor. From this new Lagrangian we obtain a modified Hamiltonian that treats adequately the simultaneous amplification and dissipation phenomena, presenting squeezing, too.

Construction of Lagrangians and Hamiltonians from the Equation of Motion

ERIC Educational Resources Information Center

Yan, C. C.

1978-01-01

Demonstrates that infinitely many Lagrangians and Hamiltonians can be constructed from a given equation of motion. Points out the lack of an established criterion for making a proper selection. (Author/GA)

Experimental quantification of decoherence via the Loschmidt echo in a many spin system with scaled dipolar Hamiltonians

DOE Office of Scientific and Technical Information (OSTI.GOV)

Buljubasich, Lisandro; Dente, Axel D.; Levstein, Patricia R.

2015-10-28

We performed Loschmidt echo nuclear magnetic resonance experiments to study decoherence under a scaled dipolar Hamiltonian by means of a symmetrical time-reversal pulse sequence denominated Proportionally Refocused Loschmidt (PRL) echo. The many-spin system represented by the protons in polycrystalline adamantane evolves through two steps of evolution characterized by the secular part of the dipolar Hamiltonian, scaled down with a factor |k| and opposite signs. The scaling factor can be varied continuously from 0 to 1/2, giving access to a range of complexity in the dynamics. The experimental results for the Loschmidt echoes showed a spreading of the decay rates thatmore » correlate directly to the scaling factors |k|, giving evidence that the decoherence is partially governed by the coherent dynamics. The average Hamiltonian theory was applied to give an insight into the spin dynamics during the pulse sequence. The calculations were performed for every single radio frequency block in contrast to the most widely used form. The first order of the average Hamiltonian numerically computed for an 8-spin system showed decay rates that progressively decrease as the secular dipolar Hamiltonian becomes weaker. Notably, the first order Hamiltonian term neglected by conventional calculations yielded an explanation for the ordering of the experimental decoherence rates. However, there is a strong overall decoherence observed in the experiments which is not reflected by the theoretical results. The fact that the non-inverted terms do not account for this effect is a challenging topic. A number of experiments to further explore the relation of the complete Hamiltonian with this dominant decoherence rate are proposed.« less

ESL VI Curriculum Guide.

ERIC Educational Resources Information Center

Flander, Leonard

This curriculum guide for English as a Second Language (ESL) Level VI is the sixth of six in a Guam Community College ESL project series. The other five guides, a companion teacher's guide and pre- and post-tests are available separately (see note). The entire project centers around the Peabody Kits P, Level P, Level 1, Level 2, Level 3, and the…

ESL V Curriculum Guide.

ERIC Educational Resources Information Center

Flander, Leonard

This curriculum guide for English as a Second Language (ESL) Level V is the fifth of six in the Guam Community College ESL project series. The other five guides, a companion teacher's guide, and pre- and post-tests are available separately (see note). The entire project centers around the Peabody Kits P, Level P, Level 1, Level 2, Level 3, and the…

Léon Rosenfeld's general theory of constrained Hamiltonian dynamics

NASA Astrophysics Data System (ADS)

Salisbury, Donald

Léon Rosenfeld published in Annalen der Physik in 1930 a groundbreaking paper showing how to construct a Hamiltonian formalism for Lagrangian theories which admitted an underlying local gauge symmetry. The theory included both ``internal'' transformations such as the U(1) symmetry group of electromagnetism, and ``external'' symmetries typified by Einstein's general theory of relativity. His comprehensive analysis predated by two decades the formalism known as the Dirac-Bergmann approach, and I will present evidence that each of these giants were to some extent influenced by Rosenfeld's theory. Of particular significance is Rosenfeld's incorporation of arbitrary functions into the phase space generator of temporal evolution, and his construction of the phase space generator of symmetry transformations. The existing Hamiltonian formalisms have of course played a central role both in the demonstration of the renormalizability of Yang-Mills theories and current efforts in constructing a quantum theory of gravity.

Entangled trajectories Hamiltonian dynamics for treating quantum nuclear effects

NASA Astrophysics Data System (ADS)

Smith, Brendan; Akimov, Alexey V.

2018-04-01

A simple and robust methodology, dubbed Entangled Trajectories Hamiltonian Dynamics (ETHD), is developed to capture quantum nuclear effects such as tunneling and zero-point energy through the coupling of multiple classical trajectories. The approach reformulates the classically mapped second-order Quantized Hamiltonian Dynamics (QHD-2) in terms of coupled classical trajectories. The method partially enforces the uncertainty principle and facilitates tunneling. The applicability of the method is demonstrated by studying the dynamics in symmetric double well and cubic metastable state potentials. The methodology is validated using exact quantum simulations and is compared to QHD-2. We illustrate its relationship to the rigorous Bohmian quantum potential approach, from which ETHD can be derived. Our simulations show a remarkable agreement of the ETHD calculation with the quantum results, suggesting that ETHD may be a simple and inexpensive way of including quantum nuclear effects in molecular dynamics simulations.

Gyroaverage effects on nontwist Hamiltonians: Separatrix reconnection and chaos suppression

DOE Office of Scientific and Technical Information (OSTI.GOV)

Del-Castillo-Negrete, Diego B; Martinell, J.

2012-01-01

A study of finite Larmor radius (FLR) effects on E x B test particle chaotic transport in non-monotonic zonal flows with drift waves in magnetized plasmas is presented. Due to the non-monotonicity of the zonal flow, the Hamiltonian does not satisfy the twist condition. The electrostatic potential is modeled as a linear superposition of a zonal flow and the regular neutral modes of the Hasegawa-Mima equation. FLR effects are incorporated by gyro-averaging the E x B Hamiltonian. It is shown that there is a critical value of the Larmor radius for which the zonal flow transitions from a profile withmore » one maximum to a profile with two maxima and a minimum. This bifurcation leads to the creation of additional shearless curves and resonances. The gyroaveraged nontwist Hamiltonian exhibits complex patterns of separatrix reconnection. A change in the Larmor radius can lead to heteroclinic-homoclinic bifurcations and dipole formation. For Larmor radii for which the zonal flow has bifurcated, double heteroclinic-heteroclinic, homoclinic-homoclinic and heteroclinic-homoclinic separatrix topologies are observed. It is also shown that chaotic transport is typically reduced as the Larmor radius increases. Poincare sections show that, for large enough Larmor radius, chaos can be practically suppressed. In particular, changes of the Larmor radius can restore the shearless curve.« less

Gyroaverage effects on nontwist Hamiltonians: separatrix reconnection and chaos suppression

DOE Office of Scientific and Technical Information (OSTI.GOV)

Del-Castillo-Negrete, Diego B; Martinell, J.

2012-01-01

A study of nite Larmor radius (FLR) eects on E B test particle chaotic transport in non- monotonic zonal ows with drift waves in magnetized plasmas is presented. Due to the non- monotonicity of the zonal ow, the Hamiltonian does not satisfy the twist condition. The electro- static potential is modeled as a linear superposition of a zonal ow and regular neutral modes of the Hasegawa-Mima equation. FLR eects are incorporated by gyro-averaging the EB Hamiltonian. It is shown that there is a critical value the Larmor radius for which the zonal ow transitions from a prole with one maximummore » to a prole with two maxima and a minimum. This bifurcation leads to the creation of additional shearless curves and resonances. The gyroaveraged nontwist Hamiltonian exhibits complex patterns of separatrix reconnection. A change in the Larmor ra- dius can lead to heteroclinic-homoclinic bifurcations and dipole formation. For Larmor radii for which the zonal ow has bifurcated, double heteroclinic-heteroclinic, homoclinic-homoclinic and heteroclinic-homoclinic topologies are observed. It is also shown that chaotic transport is typically reduced as the Larmor radius increases. Poincare sections shows that, for large enough Larmor radius, chaos can be practically suppressed. In particular, small changes on the Larmor radius can restore the shearless curve.« less

On the chaotic diffusion in multidimensional Hamiltonian systems

NASA Astrophysics Data System (ADS)

Cincotta, P. M.; Giordano, C. M.; Martí, J. G.; Beaugé, C.

2018-01-01

We present numerical evidence that diffusion in the herein studied multidimensional near-integrable Hamiltonian systems departs from a normal process, at least for realistic timescales. Therefore, the derivation of a diffusion coefficient from a linear fit on the variance evolution of the unperturbed integrals fails. We review some topics on diffusion in the Arnold Hamiltonian and yield numerical and theoretical arguments to show that in the examples we considered, a standard coefficient would not provide a good estimation of the speed of diffusion. However, numerical experiments concerning diffusion would provide reliable information about the stability of the motion within chaotic regions of the phase space. In this direction, we present an extension of previous results concerning the dynamical structure of the Laplace resonance in Gliese-876 planetary system considering variations of the orbital parameters accordingly to the error introduced by the radial velocity determination. We found that a slight variation of the eccentricity of planet c would destabilize the inner region of the resonance that, though chaotic, shows stable when adopting the best fit values for the parameters.

Hamiltonian derivation of the nonhydrostatic pressure-coordinate model

NASA Astrophysics Data System (ADS)

Salmon, Rick; Smith, Leslie M.

1994-07-01

In 1989, the Miller-Pearce (MP) model for nonhydrostatic fluid motion governed by equations written in pressure coordinates was extended by removing the prescribed reference temperature, T(sub s)(p), while retaining the conservation laws and other desirable properties. It was speculated that this extension of the MP model had a Hamiltonian structure and that a slick derivation of the Ertel property could be constructed if the relevant Hamiltonian were known. In this note, the extended equations are derived using Hamilton's principle. The potential vorticity law arises from the usual particle-relabeling symmetry of the Lagrangian, and even the absence of sound waves is anticipated from the fact that the pressure inside the free energy G(p, theta) in the derived equation is hydrostatic and thus G is insensitive to local pressure fluctuations. The model extension is analogous to the semigeostrophic equations for nearly geostrophic flow, which do not incorporate a prescribed reference state, while the earlier MP model is analogous to the quasigeostrophic equations, which become highly inaccurate when the flow wanders from a prescribed state with nearly flat isothermal surfaces.

Modular Hamiltonians for deformed half-spaces and the averaged null energy condition

NASA Astrophysics Data System (ADS)

Faulkner, Thomas; Leigh, Robert G.; Parrikar, Onkar; Wang, Huajia

2016-09-01

We study modular Hamiltonians corresponding to the vacuum state for deformed half-spaces in relativistic quantum field theories on {{R}}^{1,d-1} . We show that in addition to the usual boost generator, there is a contribution to the modular Hamiltonian at first order in the shape deformation, proportional to the integral of the null components of the stress tensor along the Rindler horizon. We use this fact along with monotonicity of relative entropy to prove the averaged null energy condition in Minkowski space-time. This subsequently gives a new proof of the Hofman-Maldacena bounds on the parameters appearing in CFT three-point functions. Our main technical advance involves adapting newly developed perturbative methods for calculating entanglement entropy to the problem at hand. These methods were recently used to prove certain results on the shape dependence of entanglement in CFTs and here we generalize these results to excited states and real time dynamics. We also discuss the AdS/CFT counterpart of this result, making connection with the recently proposed gravitational dual for modular Hamiltonians in holographic theories.

Magnetic anisotropy in binuclear complexes in the weak-exchange limit: From the multispin to the giant-spin Hamiltonian

NASA Astrophysics Data System (ADS)

Maurice, Rémi; de Graaf, Coen; Guihéry, Nathalie

2010-06-01

This paper studies the physical basis of the giant-spin Hamiltonian, which is usually used to describe the anisotropy of single-molecule magnets. A rigorous extraction of the model has been performed in the weak-exchange limit of a binuclear centrosymmetric Ni(II) complex, using correlated ab initio calculations and effective Hamiltonian theory. It is shown that the giant-spin Hamiltonian is not appropriate to describe polynuclear complexes as soon as spin mixing becomes non-negligible. A relevant model is proposed involving fourth-order operators, different from the traditionally used Stevens operators. The new giant-spin Hamiltonian correctly reproduces the effects of the spin mixing in the weak-exchange limit. A procedure to switch on and off the spin mixing in the extraction has been implemented in order to separate this effect from other anisotropic effects and to numerically evaluate both contributions to the tunnel splitting. Furthermore, the new giant-spin Hamiltonian has been derived analytically from the multispin Hamiltonian at the second order of perturbation and the theoretical link between the two models is studied to gain understanding concerning the microscopic origin of the fourth-order interaction in terms of axial, rhombic, or mixed (axial-rhombic) character. Finally, an adequate method is proposed to extract the proper magnetic axes frame for polynuclear anisotropic systems.

Bifurcation of Limit Cycles in a Near-Hamiltonian System with a Cusp of Order Two and a Saddle

NASA Astrophysics Data System (ADS)

Bakhshalizadeh, Ali; Zangeneh, Hamid R. Z.; Kazemi, Rasool

In this paper, the asymptotic expansion of first-order Melnikov function of a heteroclinic loop connecting a cusp of order two and a hyperbolic saddle for a planar near-Hamiltonian system is given. Next, we consider the limit cycle bifurcations of a hyper-elliptic Liénard system with this kind of heteroclinic loop and study the least upper bound of limit cycles bifurcated from the period annulus inside the heteroclinic loop, from the heteroclinic loop itself and the center. We find that at most three limit cycles can be bifurcated from the period annulus, also we present different distributions of bifurcated limit cycles.

COLLABORATIVE GUIDE: A REEF MANAGER'S GUIDE TO ...

EPA Pesticide Factsheets

Innovative strategies to conserve the world's coral reefs are included in a new guide released today by NOAA, and the Australian Great Barrier Reef Marine Park Authority, with author contributions from a variety of international partners from government agencies, non-governmental organizations, and academic institutions. Referred to as A Reef Manager's Guide to Coral Bleaching, the guide will provide coral reef managers with the latest scientific information on the causes of coral bleaching and new management strategies for responding to this significant threat to coral reef ecosystems. Innovative strategies to conserve the world's coral reefs are included in a new guide released today by NOAA, and the Australian Great Barrier Reef Marine Park Authority, with author contributions from a variety of international partners from government agencies, non-governmental organizations, and academic institutions. Dr. Jordan West, of the National Center for Environmental Assessment, was a major contributor to the guide. Referred to as

Hamiltonian approach to continuum dynamics

NASA Astrophysics Data System (ADS)

Isaev, A. A.; Kovalevskii, M. Yu.; Peletminskii, S. V.

1995-02-01

A study is made of the problem of obtaining the Poisson-bracket algebra of the dynamical variables of continuous media on the basis of specification of the kinematic part of the Lagrangian in terms of generalized coordinates and momenta. Within this algebra, subalgebras of variables corresponding to the description of elastic media, the hydrodynamics of ordinary liquids, and the dynamics of some phases of liquid crystals are identified. The differential conservation laws associated with the symmetries of the Hamiltonian of the system are studied. The dynamics of nematics is considered, and features of the dynamics of the cholesteric, smectic, and discotic phases are noted.

Exact decoupling of the Dirac Hamiltonian. II. The generalized Douglas-Kroll-Hess transformation up to arbitrary order.

PubMed

Reiher, Markus; Wolf, Alexander

2004-12-08

In order to achieve exact decoupling of the Dirac Hamiltonian within a unitary transformation scheme, we have discussed in part I of this series that either a purely numerical iterative technique (the Barysz-Sadlej-Snijders method) or a stepwise analytic approach (the Douglas-Kroll-Hess method) are possible. For the evaluation of Douglas-Kroll-Hess Hamiltonians up to a pre-defined order it was shown that a symbolic scheme has to be employed. In this work, an algorithm for this analytic derivation of Douglas-Kroll-Hess Hamiltonians up to any arbitrary order in the external potential is presented. We discuss how an estimate for the necessary order for exact decoupling (within machine precision) for a given system can be determined from the convergence behavior of the Douglas-Kroll-Hess expansion prior to a quantum chemical calculation. Once this maximum order has been accomplished, the spectrum of the positive-energy part of the decoupled Hamiltonian, e.g., for electronic bound states, cannot be distinguished from the corresponding part of the spectrum of the Dirac operator. An efficient scalar-relativistic implementation of the symbolic operations for the evaluation of the positive-energy part of the block-diagonal Hamiltonian is presented, and its accuracy is tested for ground-state energies of one-electron ions over the whole periodic table. Furthermore, the first many-electron calculations employing sixth up to fourteenth order DKH Hamiltonians are presented. (c) 2004 American Institute of Physics.

Exact decoupling of the Dirac Hamiltonian. II. The generalized Douglas-Kroll-Hess transformation up to arbitrary order

DOE Office of Scientific and Technical Information (OSTI.GOV)

Reiher, Markus; Wolf, Alexander

In order to achieve exact decoupling of the Dirac Hamiltonian within a unitary transformation scheme, we have discussed in part I of this series that either a purely numerical iterative technique (the Barysz-Sadlej-Snijders method) or a stepwise analytic approach (the Douglas-Kroll-Hess method) are possible. For the evaluation of Douglas-Kroll-Hess Hamiltonians up to a pre-defined order it was shown that a symbolic scheme has to be employed. In this work, an algorithm for this analytic derivation of Douglas-Kroll-Hess Hamiltonians up to any arbitrary order in the external potential is presented. We discuss how an estimate for the necessary order for exactmore » decoupling (within machine precision) for a given system can be determined from the convergence behavior of the Douglas-Kroll-Hess expansion prior to a quantum chemical calculation. Once this maximum order has been accomplished, the spectrum of the positive-energy part of the decoupled Hamiltonian, e.g., for electronic bound states, cannot be distinguished from the corresponding part of the spectrum of the Dirac operator. An efficient scalar-relativistic implementation of the symbolic operations for the evaluation of the positive-energy part of the block-diagonal Hamiltonian is presented, and its accuracy is tested for ground-state energies of one-electron ions over the whole periodic table. Furthermore, the first many-electron calculations employing sixth up to fourteenth order DKH Hamiltonians are presented.« less

On the Perturbative Equivalence Between the Hamiltonian and Lagrangian Quantizations

NASA Astrophysics Data System (ADS)

Batalin, I. A.; Tyutin, I. V.

The Hamiltonian (BFV) and Lagrangian (BV) quantization schemes are proved to be perturbatively equivalent to each other. It is shown in particular that the quantum master equation being treated perturbatively possesses a local formal solution.

Density-matrix based determination of low-energy model Hamiltonians from ab initio wavefunctions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Changlani, Hitesh J.; Zheng, Huihuo; Wagner, Lucas K.

2015-09-14

We propose a way of obtaining effective low energy Hubbard-like model Hamiltonians from ab initio quantum Monte Carlo calculations for molecular and extended systems. The Hamiltonian parameters are fit to best match the ab initio two-body density matrices and energies of the ground and excited states, and thus we refer to the method as ab initio density matrix based downfolding. For benzene (a finite system), we find good agreement with experimentally available energy gaps without using any experimental inputs. For graphene, a two dimensional solid (extended system) with periodic boundary conditions, we find the effective on-site Hubbard U{sup ∗}/t tomore » be 1.3 ± 0.2, comparable to a recent estimate based on the constrained random phase approximation. For molecules, such parameterizations enable calculation of excited states that are usually not accessible within ground state approaches. For solids, the effective Hamiltonian enables large-scale calculations using techniques designed for lattice models.« less

Fermion bag approach to Hamiltonian lattice field theories in continuous time

NASA Astrophysics Data System (ADS)

Huffman, Emilie; Chandrasekharan, Shailesh

2017-12-01

We extend the idea of fermion bags to Hamiltonian lattice field theories in the continuous time formulation. Using a class of models we argue that the temperature is a parameter that splits the fermion dynamics into small spatial regions that can be used to identify fermion bags. Using this idea we construct a continuous time quantum Monte Carlo algorithm and compute critical exponents in the 3 d Ising Gross-Neveu universality class using a single flavor of massless Hamiltonian staggered fermions. We find η =0.54 (6 ) and ν =0.88 (2 ) using lattices up to N =2304 sites. We argue that even sizes up to N =10 ,000 sites should be accessible with supercomputers available today.

Implementation of the SU(2) Hamiltonian Symmetry for the DMRG Algorithm

DOE Office of Scientific and Technical Information (OSTI.GOV)

Alvarez, Gonzalo

2012-01-01

In the Density Matrix Renormalization Group (DMRG) algorithm (White, 1992, 1993) and Hamiltonian symmetries play an important role. Using symmetries, the matrix representation of the Hamiltonian can be blocked. Diagonalizing each matrix block is more efficient than diagonalizing the original matrix. This paper explains how the the DMRG++ code (Alvarez, 2009) has been extended to handle the non-local SU(2) symmetry in a model independent way. Improvements in CPU times compared to runs with only local symmetries are discussed for the one-orbital Hubbard model, and for a two-orbital Hubbard model for iron-based superconductors. The computational bottleneck of the algorithm and themore » use of shared memory parallelization are also addressed.« less

University guide to NASA, 1993

NASA Technical Reports Server (NTRS)

1992-01-01

This guide provides brief descriptions of the two NASA Headquarters program offices through which NASA primarily funds universities, the Office of Space Science and Applications and the Office of Aeronautics and Space Technology. It also describes NASA's Office of Commercial Programs, which funds the Centers for the Commercial Development of Space and the Small Business Innovation Research Program. This guide explains the roles played by NASA's eight field centers and the Jet Propulsion Laboratory, and gives a sampling of ongoing NASA-wide educational programs and services. Most importantly, this guide provides practical information in the form of names and telephone numbers of NASA contacts.

University guide to NASA, 1993

NASA Astrophysics Data System (ADS)

1992-10-01

This guide provides brief descriptions of the two NASA Headquarters program offices through which NASA primarily funds universities, the Office of Space Science and Applications and the Office of Aeronautics and Space Technology. It also describes NASA's Office of Commercial Programs, which funds the Centers for the Commercial Development of Space and the Small Business Innovation Research Program. This guide explains the roles played by NASA's eight field centers and the Jet Propulsion Laboratory, and gives a sampling of ongoing NASA-wide educational programs and services. Most importantly, this guide provides practical information in the form of names and telephone numbers of NASA contacts.

Léon Rosenfeld's general theory of constrained Hamiltonian dynamics

NASA Astrophysics Data System (ADS)

Salisbury, Donald; Sundermeyer, Kurt

2017-04-01

This commentary reflects on the 1930 general theory of Léon Rosenfeld dealing with phase-space constraints. We start with a short biography of Rosenfeld and his motivation for this article in the context of ideas pursued by W. Pauli, F. Klein, E. Noether. We then comment on Rosenfeld's General Theory dealing with symmetries and constraints, symmetry generators, conservation laws and the construction of a Hamiltonian in the case of phase-space constraints. It is remarkable that he was able to derive expressions for all phase space symmetry generators without making explicit reference to the generator of time evolution. In his Applications, Rosenfeld treated the general relativistic example of Einstein-Maxwell-Dirac theory. We show, that although Rosenfeld refrained from fully applying his general findings to this example, he could have obtained the Hamiltonian. Many of Rosenfeld's discoveries were re-developed or re-discovered by others two decades later, yet as we show there remain additional firsts that are still not recognized in the community.

Applications of the trilinear Hamiltonian with three trapped ions

NASA Astrophysics Data System (ADS)

Hablutzel Marrero, Roland Esteban; Ding, Shiqian; Maslennikov, Gleb; Gan, Jaren; Nimmrichter, Stefan; Roulet, Alexandre; Dai, Jibo; Scarani, Valerio; Matsukevich, Dzmitry

2017-04-01

The trilinear Hamiltonian a† bc + ab†c† , which describes a nonlinear interaction between harmonic oscillators, can be implemented to study different phenomena ranging from simple quantum models to quantum thermodynamics. We engineer this coupling between three modes of motion of three trapped 171Yb+ ions, where the interaction arises naturally from their mutual (anharmonic) Coulomb repulsion. By tuning our trapping parameters we are able to turn on / off resonant exchange of energy between the modes on demand. We present applications of this Hamiltonian for simulations of the parametric down conversion process in the regime of depleted pump, a simple model of Hawking radiation, and the Tavis-Cummings model. We also discuss the implementation of the quantum absorption refrigerator in such system and experimentally study effects of quantum coherence on its performance. This research is supported by the National Research Foundation, Prime Minister's Office, Singapore and the Ministry of Education, Singapore under the Research Centres of Excellence programme.

Clocks in Feynman's computer and Kitaev's local Hamiltonian: Bias, gaps, idling, and pulse tuning

NASA Astrophysics Data System (ADS)

Caha, Libor; Landau, Zeph; Nagaj, Daniel

2018-06-01

We present a collection of results about the clock in Feynman's computer construction and Kitaev's local Hamiltonian problem. First, by analyzing the spectra of quantum walks on a line with varying end-point terms, we find a better lower bound on the gap of the Feynman Hamiltonian, which translates into a less strict promise gap requirement for the quantum-Merlin-Arthur-complete local Hamiltonian problem. We also translate this result into the language of adiabatic quantum computation. Second, introducing an idling clock construction with a large state space but fast Cesaro mixing, we provide a way for achieving an arbitrarily high success probability of computation with Feynman's computer with only a logarithmic increase in the number of clock qubits. Finally, we tune and thus improve the costs (locality and gap scaling) of implementing a (pulse) clock with a single excitation.

Isospectral Hamiltonian for position-dependent mass for an arbitrary quantum system and coherent states

NASA Astrophysics Data System (ADS)

Yahiaoui, Sid-Ahmed; Bentaiba, Mustapha

2017-06-01

By means of the unitary transformation, a new way for discussing the ordering prescription of the Schrödinger equation with a position-dependent mass (PDM) for isospectral Hamiltonian operators is presented. We show that the ambiguity parameter choices in the kinetic part of the Hamiltonian can be explained through an exact SUSY QM symmetry as well as a consequence of an accidental symmetry under the Z2 action. By making use of the unitary transformation, we construct coherent states for a family of PDM isospectral Hamiltonians from a suitable choice of ladder operators. We show that these states preserve the usual structure of Klauder-Perelomov's states and thus saturate and minimize the position-momentum uncertainty relation (PMUR) under some special restrictions. We show that PMUR properties can be used to determine the sign of the superpotential.

Hamiltonian description and quantization of dissipative systems

NASA Astrophysics Data System (ADS)

Enz, Charles P.

1994-09-01

Dissipative systems are described by a Hamiltonian, combined with a “dynamical matrix” which generalizes the simplectic form of the equations of motion. Criteria for dissipation are given and the examples of a particle with friction and of the Lotka-Volterra model are presented. Quantization is first introduced by translating generalized Poisson brackets into commutators and anticommutators. Then a generalized Schrödinger equation expressed by a dynamical matrix is constructed and discussed.

Nonlinear dynamics of a semiquantum Hamiltonian in the vicinity of quantum unstable regimes

NASA Astrophysics Data System (ADS)

Kowalski, A. M.; Rossignoli, R.

2018-04-01

We examine the emergence of chaos in a non-linear model derived from a semiquantum Hamiltonian describing the coupling between a classical field and a quantum system. The latter corresponds to a bosonic version of a BCS-like Hamiltonian, and possesses stable and unstable regimes. The dynamics of the whole system is shown to be strongly influenced by the quantum subsystem. In particular, chaos is seen to arise in the vicinity of a quantum critical case, which separates the stable and unstable regimes of the bosonic system.

A finite-temperature Hartree-Fock code for shell-model Hamiltonians

NASA Astrophysics Data System (ADS)

Bertsch, G. F.; Mehlhaff, J. M.

2016-10-01

The codes HFgradZ.py and HFgradT.py find axially symmetric minima of a Hartree-Fock energy functional for a Hamiltonian supplied in a shell model basis. The functional to be minimized is the Hartree-Fock energy for zero-temperature properties or the Hartree-Fock grand potential for finite-temperature properties (thermal energy, entropy). The minimization may be subjected to additional constraints besides axial symmetry and nucleon numbers. A single-particle operator can be used to constrain the minimization by adding it to the single-particle Hamiltonian with a Lagrange multiplier. One can also constrain its expectation value in the zero-temperature code. Also the orbital filling can be constrained in the zero-temperature code, fixing the number of nucleons having given Kπ quantum numbers. This is particularly useful to resolve near-degeneracies among distinct minima.

De Donder-Weyl Hamiltonian formalism of MacDowell-Mansouri gravity

NASA Astrophysics Data System (ADS)

Berra-Montiel, Jasel; Molgado, Alberto; Serrano-Blanco, David

2017-12-01

We analyse the behaviour of the MacDowell-Mansouri action with internal symmetry group SO(4, 1) under the De Donder-Weyl Hamiltonian formulation. The field equations, known in this formalism as the De Donder-Weyl equations, are obtained by means of the graded Poisson-Gerstenhaber bracket structure present within the De Donder-Weyl formulation. The decomposition of the internal algebra so(4, 1)≃so(3, 1)\\oplus{R}3, 1 allows the symmetry breaking SO(4, 1)\\toSO(3, 1) , which reduces the original action to the Palatini action without the topological term. We demonstrate that, in contrast to the Lagrangian approach, this symmetry breaking can be performed indistinctly in the polysymplectic formalism either before or after the variation of the De Donder-Weyl Hamiltonian has been done, recovering Einstein’s equations via the Poisson-Gerstenhaber bracket.

The limits of hamiltonian structures in three-dimensional elasticity, shells, and rods

NASA Astrophysics Data System (ADS)

Ge, Z.; Kruse, H. P.; Marsden, J. E.

1996-01-01

This paper uses Hamiltonian structures to study the problem of the limit of three-dimensional (3D) elastic models to shell and rod models. In the case of shells, we show that the Hamiltonian structure for a three-dimensional elastic body converges, in a sense made precise, to that for a shell model described by a one-director Cosserat surface as the thickness goes to zero. We study limiting procedures that give rise to unconstrained as well as constrained Cosserat director models. The case of a rod is also considered and similar convergence results are established, with the limiting model being a geometrically exact director rod model (in the framework developed by Antman, Simo, and coworkers). The resulting model may or may not have constraints, depending on the nature of the constitutive relations and their behavior under the limiting procedure. The closeness of Hamiltonian structures is measured by the closeness of Poisson brackets on certain classes of functions, as well as the Hamiltonians. This provides one way of justifying the dynamic one-director model for shells. Another way of stating the convergence result is that there is an almost-Poisson embedding from the phase space of the shell to the phase space of the 3D elastic body, which implies that, in the sense of Hamiltonian structures, the dynamics of the elastic body is close to that of the shell. The constitutive equations of the 3D model and their behavior as the thickness tends to zero dictates whether the limiting 2D model is a constrained or an unconstrained director model. We apply our theory in the specific case of a 3D Saint Venant-Kirchhoff material and derive the corresponding limiting shell and rod theories. The limiting shell model is an interesting Kirchhoff-like shell model in which the stored energy function is explicitly derived in terms of the shell curvature. For rods, one gets (with an additional inextensibility constraint) a one-director Kirchhoff elastic rod model, which reduces to

Diagonalizing the Hamiltonian of λϕ4 theory in 2 space-time dimensions

NASA Astrophysics Data System (ADS)

Christensen, Neil

2018-01-01

We propose a new non-perturbative technique for calculating the scattering amplitudes of field-theory directly from the eigenstates of the Hamiltonian. Our method involves a discretized momentum space and a momentum cutoff, thereby truncating the Hilbert space and making numerical diagonalization of the Hamiltonian achievable. We show how to do this in the context of a simplified λϕ4 theory in two space-time dimensions. We present the results of our diagonalization, its dependence on time, its dependence on the parameters of the theory and its renormalization.

Modular Hamiltonians for deformed half-spaces and the averaged null energy condition

DOE PAGES

Faulkner, Thomas; Leigh, Robert G.; Parrikar, Onkar; ...

2016-09-08

We study modular Hamiltonians corresponding to the vacuum state for deformed half-spaces in relativistic quantum field theories on R 1,d-1. We show that in addition to the usual boost generator, there is a contribution to the modular Hamiltonian at first order in the shape deformation, proportional to the integral of the null components of the stress tensor along the Rindler horizon. We use this fact along with monotonicity of relative entropy to prove the averaged null energy condition in Minkowski space-time. This subsequently gives a new proof of the Hofman-Maldacena bounds on the parameters appearing in CFT three-point functions. Ourmore » main technical advance involves adapting newly developed perturbative methods for calculating entanglement entropy to the problem at hand. Our methods were recently used to prove certain results on the shape dependence of entanglement in CFTs and here we generalize these results to excited states and real time dynamics. Finally, we discuss the AdS/CFT counterpart of this result, making connection with the recently proposed gravitational dual for modular Hamiltonians in holographic theories.« less

Modular Hamiltonians for deformed half-spaces and the averaged null energy condition

DOE Office of Scientific and Technical Information (OSTI.GOV)

Faulkner, Thomas; Leigh, Robert G.; Parrikar, Onkar

We study modular Hamiltonians corresponding to the vacuum state for deformed half-spaces in relativistic quantum field theories on R 1,d-1. We show that in addition to the usual boost generator, there is a contribution to the modular Hamiltonian at first order in the shape deformation, proportional to the integral of the null components of the stress tensor along the Rindler horizon. We use this fact along with monotonicity of relative entropy to prove the averaged null energy condition in Minkowski space-time. This subsequently gives a new proof of the Hofman-Maldacena bounds on the parameters appearing in CFT three-point functions. Ourmore » main technical advance involves adapting newly developed perturbative methods for calculating entanglement entropy to the problem at hand. Our methods were recently used to prove certain results on the shape dependence of entanglement in CFTs and here we generalize these results to excited states and real time dynamics. Finally, we discuss the AdS/CFT counterpart of this result, making connection with the recently proposed gravitational dual for modular Hamiltonians in holographic theories.« less

Dynamics and Self-consistent Chaos in a Mean Field Hamiltonian Model

NASA Astrophysics Data System (ADS)

del-Castillo-Negrete, Diego

We study a mean field Hamiltonian model that describes the collective dynamics of marginally stable fluids and plasmas in the finite N and N-> infty kinetic limit (where N is the number of particles). The linear stability of equilibria in the kinetic model is studied as well as the initial value problem including Landau damping . Numerical simulations show the existence of coherent, rotating dipole states. We approximate the dipole as two macroparticles and show that the N=2 limit has a family of rotating integrable solutions that provide an accurate description of the dynamics. We discuss the role of self-consistent Hamiltonian chaos in the formation of coherent structures, and discuss a mechanism of "violent" mixing caused by a self-consistent elliptic-hyperbolic bifurcation in phase space.

Competition Between Two Large-Amplitude Motion Models: New Hybrid Hamiltonian Versus Old Pure-Tunneling Hamiltonian

NASA Astrophysics Data System (ADS)

Kleiner, Isabelle; Hougen, Jon T.

2017-06-01

In this talk we report on our progress in trying to make the hybrid Hamiltonian competitive with the pure-tunneling Hamiltonian for treating large-amplitude motions in methylamine. A treatment using the pure-tunneling model has the advantages of: (i) requiring relatively little computer time, (ii) working with relatively uncorrelated fitting parameters, and (iii) yielding in the vast majority of cases fits to experimental measurement accuracy. These advantages are all illustrated in the work published this past year on a gigantic v_{t} = 1 data set for the torsional fundamental band in methyl amine. A treatment using the hybrid model has the advantages of: (i) being able to carry out a global fit involving both v_{t} = 0 and v_{t} = 1 energy levels and (ii) working with fitting parameters that have a clearer physical interpretation. Unfortunately, a treatment using the hybrid model has the great disadvantage of requiring a highly correlated set of fitting parameters to achieve reasonable fitting accuracy, which complicates the search for a good set of molecular fitting parameters and a fit to experimental accuracy. At the time of writing this abstract, we have been able to carry out a fit with J up to 15 that includes all available infrared data in the v_{t} = 1-0 torsional fundamental band, all ground-state microwave data with K up to 10 and J up to 15, and about a hundred microwave lines within the v_{t} = 1 torsional state, achieving weighted root-mean-square (rms) deviations of about 1.4, 2.8, and 4.2 for these three categories of data. We will give an update of this situation at the meeting. I. Gulaczyk, M. Kreglewski, V.-M. Horneman, J. Mol. Spectrosc., in Press (2017).

PREFACE: 6th International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physics

NASA Astrophysics Data System (ADS)

Fring, Andreas; Jones, Hugh; Znojil, Miloslav

2008-06-01

Attempts to understand the quantum mechanics of non-Hermitian Hamiltonian systems can be traced back to the early days, one example being Heisenberg's endeavour to formulate a consistent model involving an indefinite metric. Over the years non-Hermitian Hamiltonians whose spectra were believed to be real have appeared from time to time in the literature, for instance in the study of strong interactions at high energies via Regge models, in condensed matter physics in the context of the XXZ-spin chain, in interacting boson models in nuclear physics, in integrable quantum field theories as Toda field theories with complex coupling constants, and also very recently in a field theoretical scenario in the quantization procedure of strings on an AdS5 x S5 background. Concrete experimental realizations of these types of systems in the form of optical lattices have been proposed in 2007. In the area of mathematical physics similar non-systematic results appeared sporadically over the years. However, intensive and more systematic investigation of these types of non- Hermitian Hamiltonians with real eigenvalue spectra only began about ten years ago, when the surprising discovery was made that a large class of one-particle systems perturbed by a simple non-Hermitian potential term possesses a real energy spectrum. Since then regular international workshops devoted to this theme have taken place. This special issue is centred around the 6th International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physics held in July 2007 at City University London. All the contributions contain significant new results or alternatively provide a survey of the state of the art of the subject or a critical assessment of the present understanding of the topic and a discussion of open problems. Original contributions from non-participants were also invited. Meanwhile many interesting results have been obtained and consensus has been reached on various central conceptual issues in the

Integrable and superintegrable Hamiltonian systems with four dimensional real Lie algebras as symmetry of the systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Abedi-Fardad, J., E-mail: j.abedifardad@bonabu.ac.ir; Rezaei-Aghdam, A., E-mail: rezaei-a@azaruniv.edu; Haghighatdoost, Gh., E-mail: gorbanali@azaruniv.edu

2014-05-15

We construct integrable and superintegrable Hamiltonian systems using the realizations of four dimensional real Lie algebras as a symmetry of the system with the phase space R{sup 4} and R{sup 6}. Furthermore, we construct some integrable and superintegrable Hamiltonian systems for which the symmetry Lie group is also the phase space of the system.

FAST TRACK COMMUNICATION: Superintegrability of the Tremblay-Turbiner-Winternitz quantum Hamiltonians on a plane for odd k

NASA Astrophysics Data System (ADS)

Quesne, C.

2010-02-01

In a recent communication paper by Tremblay et al (2009 J. Phys. A: Math. Theor. 42 205206), it has been conjectured that for any integer value of k, some novel exactly solvable and integrable quantum Hamiltonian Hk on a plane is superintegrable and that the additional integral of motion is a 2kth-order differential operator Y2k. Here we demonstrate the conjecture for the infinite family of Hamiltonians Hk with odd k >= 3, whose first member corresponds to the three-body Calogero-Marchioro-Wolfes model after elimination of the centre-of-mass motion. Our approach is based on the construction of some D2k-extended and invariant Hamiltonian {\\cal H}_k, which can be interpreted as a modified boson oscillator Hamiltonian. The latter is then shown to possess a D2k-invariant integral of motion {\\cal Y}_{2k}, from which Y2k can be obtained by projection in the D2k identity representation space.

To Rabi Hamiltonian through their Time Dependent Terms can be Reckons as Fractals

NASA Astrophysics Data System (ADS)

Rosary-Oyong, Se, Glory

2016-03-01

For light-matters interactions, ever replies by theLate HE. Mr. Prof M. Barmawi through Bose-Einstein condensates matter-waves ever retrieves [Boyce & DiPrima, 2015] instead of Richard Courant cq HE. Mr. Prof. Sudjoko Danusubroto's LKTM, Lustrum VI ITB, March 2, 1984. Follows ``Modified kernel to Quantum systems thorough Laplace inverse transformation'' whereas ``karyon'' in prokaryotes/eukaryotes meant as well as `kernel' , have been sought for `growth curve' & `potential of proton to other protons' the time dependent terms cos (ωt)exp[-iωot] whose integration y = sin ωt + c proves to be fractals h. 3 guided by Rabi Hamiltonian from Isidor Isaac Rabi,1944. Accompanying ``the Theory of Scale Relativity'' from Laurent Nottale/LUTH, the proofs of considerances whereas `time also are fractals', from Norways for Infra OMAN soughts a benchmark portfolio from Kjell Storvik, 2004: ``Socially Responsible Investment Strategies for the Norwegian Petroleum Fund'' whereas the Rabi frequency ? = 2 ɛ.deg/h can be relatively in comparisons expressed of capacitive [E.d/h]. Acknowledgment to HE. Mr. AUGUST PARENGKUAN if accepts 1995-2005 Invoicing & Fulfillments to ``KOMPAS'' cq the Prodi of Physics ITB.

Improving long time behavior of Poisson bracket mapping equation: A non-Hamiltonian approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kim, Hyun Woo; Rhee, Young Min, E-mail: ymrhee@postech.ac.kr

2014-05-14

Understanding nonadiabatic dynamics in complex systems is a challenging subject. A series of semiclassical approaches have been proposed to tackle the problem in various settings. The Poisson bracket mapping equation (PBME) utilizes a partial Wigner transform and a mapping representation for its formulation, and has been developed to describe nonadiabatic processes in an efficient manner. Operationally, it is expressed as a set of Hamilton's equations of motion, similar to more conventional classical molecular dynamics. However, this original Hamiltonian PBME sometimes suffers from a large deviation in accuracy especially in the long time limit. Here, we propose a non-Hamiltonian variant ofmore » PBME to improve its behavior especially in that limit. As a benchmark, we simulate spin-boson and photosynthetic model systems and find that it consistently outperforms the original PBME and its Ehrenfest style variant. We explain the source of this improvement by decomposing the components of the mapping Hamiltonian and by assessing the energy flow between the system and the bath. We discuss strengths and weaknesses of our scheme with a viewpoint of offering future prospects.« less

Formalism for the solution of quadratic Hamiltonians with large cosine terms

NASA Astrophysics Data System (ADS)

Ganeshan, Sriram; Levin, Michael

2016-02-01

We consider quantum Hamiltonians of the form H =H0-U ∑jcos(Cj) , where H0 is a quadratic function of position and momentum variables {x1,p1,x2,p2,⋯} and the Cj's are linear in these variables. We allow H0 and Cj to be completely general with only two restrictions: we require that (1) the Cj's are linearly independent and (2) [Cj,Ck] is an integer multiple of 2 π i for all j ,k so that the different cosine terms commute with one another. Our main result is a recipe for solving these Hamiltonians and obtaining their exact low-energy spectrum in the limit U →∞ . This recipe involves constructing creation and annihilation operators and is similar in spirit to the procedure for diagonalizing quadratic Hamiltonians. In addition to our exact solution in the infinite U limit, we also discuss how to analyze these systems when U is large but finite. Our results are relevant to a number of different physical systems, but one of the most natural applications is to understanding the effects of electron scattering on quantum Hall edge modes. To demonstrate this application, we use our formalism to solve a toy model for a fractional quantum spin Hall edge with different types of impurities.

Aviation Mechanic General, Airframe, and Powerplant Knowledge Test Guide

DOT National Transportation Integrated Search

1995-01-01

The FAA has available hundreds of computer testing centers nationwide. These testing centers offer the full range of airman knowledge tests. Refer to appendix 1 in this guide for a list of computer testing designees. This knowledge test guide was dev...

Soil-disturbance field guide

Treesearch

Carolyn Napper; Steven Howes; Deborah Page-Dumroese

2009-01-01

The San Dimas Technology and Development Center of the Forest Service, U. S. Department of Agriculture, developed the soil-disturbance field guide as a soil monitoring tool to identify soildisturbance classes. The field guide provides detailed descriptions and photographic examples - over a wide range of climatic and vegetative conditions - of the undisturbed soil...

Analysis of Franck-Condon factors for CO+ molecule using the Fourier Grid Hamiltonian method

NASA Astrophysics Data System (ADS)

Syiemiong, Arnestar; Swer, Shailes; Jha, Ashok Kumar; Saxena, Atul

2018-04-01

Franck-Condon factors (FCFs) are important parameters and it plays a very important role in determining the intensities of the vibrational bands in electronic transitions. In this paper, we illustrate the Fourier Grid Hamiltonian (FGH) method, a relatively simple method to calculate the FCFs. The FGH is a method used for calculating the vibrational eigenvalues and eigenfunctions of bound electronic states of diatomic molecules. The obtained vibrational wave functions for the ground and the excited states are used to calculate the vibrational overlap integral and then the FCFs. In this computation, we used the Morse potential and Bi-Exponential potential model for constructing and diagonalizing the molecular Hamiltonians. The effects of the change in equilibrium internuclear distance (xe), dissociation energy (De), and the nature of the excited state electronic energy curve on the FCFs have been determined. Here we present our work for the qualitative analysis of Franck-Condon Factorsusing this Fourier Grid Hamiltonian Method.

Equivalent Theories and Changing Hamiltonian Observables in General Relativity

NASA Astrophysics Data System (ADS)

Pitts, J. Brian

2018-03-01

Change and local spatial variation are missing in Hamiltonian general relativity according to the most common definition of observables as having 0 Poisson bracket with all first-class constraints. But other definitions of observables have been proposed. In pursuit of Hamiltonian-Lagrangian equivalence, Pons, Salisbury and Sundermeyer use the Anderson-Bergmann-Castellani gauge generator G, a tuned sum of first-class constraints. Kuchař waived the 0 Poisson bracket condition for the Hamiltonian constraint to achieve changing observables. A systematic combination of the two reforms might use the gauge generator but permit non-zero Lie derivative Poisson brackets for the external gauge symmetry of General Relativity. Fortunately one can test definitions of observables by calculation using two formulations of a theory, one without gauge freedom and one with gauge freedom. The formulations, being empirically equivalent, must have equivalent observables. For de Broglie-Proca non-gauge massive electromagnetism, all constraints are second-class, so everything is observable. Demanding equivalent observables from gauge Stueckelberg-Utiyama electromagnetism, one finds that the usual definition fails while the Pons-Salisbury-Sundermeyer definition with G succeeds. This definition does not readily yield change in GR, however. Should GR's external gauge freedom of general relativity share with internal gauge symmetries the 0 Poisson bracket (invariance), or is covariance (a transformation rule) sufficient? A graviton mass breaks the gauge symmetry (general covariance), but it can be restored by parametrization with clock fields. By requiring equivalent observables, one can test whether observables should have 0 or the Lie derivative as the Poisson bracket with the gauge generator G. The latter definition is vindicated by calculation. While this conclusion has been reported previously, here the calculation is given in some detail.

Equivalent Theories and Changing Hamiltonian Observables in General Relativity

NASA Astrophysics Data System (ADS)

Pitts, J. Brian

2018-05-01

Change and local spatial variation are missing in Hamiltonian general relativity according to the most common definition of observables as having 0 Poisson bracket with all first-class constraints. But other definitions of observables have been proposed. In pursuit of Hamiltonian-Lagrangian equivalence, Pons, Salisbury and Sundermeyer use the Anderson-Bergmann-Castellani gauge generator G, a tuned sum of first-class constraints. Kuchař waived the 0 Poisson bracket condition for the Hamiltonian constraint to achieve changing observables. A systematic combination of the two reforms might use the gauge generator but permit non-zero Lie derivative Poisson brackets for the external gauge symmetry of General Relativity. Fortunately one can test definitions of observables by calculation using two formulations of a theory, one without gauge freedom and one with gauge freedom. The formulations, being empirically equivalent, must have equivalent observables. For de Broglie-Proca non-gauge massive electromagnetism, all constraints are second-class, so everything is observable. Demanding equivalent observables from gauge Stueckelberg-Utiyama electromagnetism, one finds that the usual definition fails while the Pons-Salisbury-Sundermeyer definition with G succeeds. This definition does not readily yield change in GR, however. Should GR's external gauge freedom of general relativity share with internal gauge symmetries the 0 Poisson bracket (invariance), or is covariance (a transformation rule) sufficient? A graviton mass breaks the gauge symmetry (general covariance), but it can be restored by parametrization with clock fields. By requiring equivalent observables, one can test whether observables should have 0 or the Lie derivative as the Poisson bracket with the gauge generator G. The latter definition is vindicated by calculation. While this conclusion has been reported previously, here the calculation is given in some detail.

New quantum number for the many-electron Dirac-Coulomb Hamiltonian

NASA Astrophysics Data System (ADS)

Komorovsky, Stanislav; Repisky, Michal; Bučinský, Lukáš

2016-11-01

By breaking the spin symmetry in the relativistic domain, a powerful tool in physical sciences was lost. In this work, we examine an alternative of spin symmetry for systems described by the many-electron Dirac-Coulomb Hamiltonian. We show that the square of many-electron operator K+, defined as a sum of individual single-electron time-reversal (TR) operators, is a linear Hermitian operator which commutes with the Dirac-Coulomb Hamiltonian in a finite Fock subspace. In contrast to the square of a standard unitary many-electron TR operator K , the K+2 has a rich eigenspectrum having potential to substitute spin symmetry in the relativistic domain. We demonstrate that K+ is connected to K through an exponential mapping, in the same way as spin operators are mapped to the spin rotational group. Consequently, we call K+ the generator of the many-electron TR symmetry. By diagonalizing the operator K+2 in the basis of Kramers-restricted Slater determinants, we introduce the relativistic variant of configuration state functions (CSF), denoted as Kramers CSF. A new quantum number associated with K+2 has potential to be used in many areas, for instance, (a) to design effective spin Hamiltonians for electron spin resonance spectroscopy of heavy-element containing systems; (b) to increase efficiency of methods for the solution of many-electron problems in relativistic computational chemistry and physics; (c) to define Kramers contamination in unrestricted density functional and Hartree-Fock theory as a relativistic analog of the spin contamination in the nonrelativistic domain.

Resident Program Guide: Hillside Outdoor Education Center.

ERIC Educational Resources Information Center

Sommer, Bonnie

Founded in 1972 as part of the private, non-profit Edwin Gould Outdoor Education Centers, the Hillside Outdoor Education Center offers services to various educational groups by providing residential experiences for students and faculty, day-visit programs, school-site outdoor education programs, teacher workshops, college courses in outdoor…

Collaboration and Team Science Field Guide - Center for Research Strategy

Cancer.gov

Collaboration and Team Science: A Field Guide provides insight into the practices of conducting collaborative work. Since its 2010 publication, the authors have worked and learned from teams and organizations all over the world. Learn from these experiences in the second edition of the Team Science Field Guide.

Hybrid Topological Lie-Hamiltonian Learning in Evolving Energy Landscapes

NASA Astrophysics Data System (ADS)

Ivancevic, Vladimir G.; Reid, Darryn J.

2015-11-01

In this Chapter, a novel bidirectional algorithm for hybrid (discrete + continuous-time) Lie-Hamiltonian evolution in adaptive energy landscape-manifold is designed and its topological representation is proposed. The algorithm is developed within a geometrically and topologically extended framework of Hopfield's neural nets and Haken's synergetics (it is currently designed in Mathematica, although with small changes it could be implemented in Symbolic C++ or any other computer algebra system). The adaptive energy manifold is determined by the Hamiltonian multivariate cost function H, based on the user-defined vehicle-fleet configuration matrix W, which represents the pseudo-Riemannian metric tensor of the energy manifold. Search for the global minimum of H is performed using random signal differential Hebbian adaptation. This stochastic gradient evolution is driven (or, pulled-down) by `gravitational forces' defined by the 2nd Lie derivatives of H. Topological changes of the fleet matrix W are observed during the evolution and its topological invariant is established. The evolution stops when the W-topology breaks down into several connectivity-components, followed by topology-breaking instability sequence (i.e., a series of phase transitions).

Multipayer patient-centered medical home implementation guided by the chronic care model.

PubMed

Gabbay, Robert A; Bailit, Michael H; Mauger, David T; Wagner, Edward H; Siminerio, Linda

2011-06-01

A unique statewide multipayer ini Pennsylvania was undertaken to implement the Patient-Centered Medical Home (PCMH) guided by the Chronic Care Model (CCM) with diabetes as an initial target disease. This project represents the first broad-scale CCM implementation with payment reform across a diverse range of practice organizations and one of the largest PCMH multipayer initiatives. Practices implemented the CCM and PCMH through regional Breakthrough Series learning collaboratives, supported by Improving Performance in Practice (IPIP) practice coaches, with required monthly quality reporting enhanced by multipayer infrastructure payments. Some 105 practices, representing 382 primary care providers, were engaged in the four regional collaboratives. The practices from the Southeast region of Pennsylvania focused on diabetes patients (n = 10,016). During the first intervention year (May 2008-May 2009), all practices achieved at least Level 1 National Committee for Quality Assurance (NCQA) Physician Practice Connections Patient-Centered Medical Home (PPC-PCMH) recognition. There was significant improvement in the percentage of patients who had evidence-based complications screening and who were on therapies to reduce morbidity and mortality (statins, angiotensin-converting enzyme inhibitors). In addition, there were small but statistically significant improvements in key clinical parameters for blood pressure and cholesterol levels, with the greatest absolute improvement in the highest-risk patients. Transforming primary care delivery through implementation of the PCMH and CCM supported by multipayer infrastructure payments holds significant promise to improve diabetes care.

Application of Dirac's Generalized Hamiltonian Dynamics to Atomic and Molecular Systems

NASA Astrophysics Data System (ADS)

Uzer, Turgay

2002-10-01

Incorporating electronic degrees of freedom into classical treatments of atoms and molecules is a challenging problem from both the practical and fundamental points of view. Because it goes to the heart of classical-quantal correspondence, there are now a number of prescriptions which differ by the extent of quantal information that they include. We reach back to Dirac for inspiration, who, half a century ago, designed a so-called Generalized Hamiltonian Dynamics (GHD) with applications to field theory in mind. Physically, the GHD is a purely classical formalism for systems with constraints; it incorporates the constraints into the Hamiltonian. We apply the GHD to atomic and molecular physics by choosing integrals of motion as the constraints. We show that this purely classical formalism allows the derivation of energies of non-radiating states.

Quantum theory of atoms in molecules: results for the SR-ZORA Hamiltonian.

PubMed

Anderson, James S M; Ayers, Paul W

2011-11-17

The quantum theory of atoms in molecules (QTAIM) is generalized to include relativistic effects using the popular scalar-relativistic zeroth-order regular approximation (SR-ZORA). It is usually assumed that the definition of the atom as a volume bounded by a zero-flux surface of the electron density is closely linked to the form of the kinetic energy, so it is somewhat surprising that the atoms corresponding to the relativistic kinetic-energy operator in the SR-ZORA Hamiltonian are also bounded by zero-flux surfaces. The SR-ZORA Hamiltonian should be sufficient for qualitative descriptions of molecular electronic structure across the periodic table, which suggests that QTAIM-based analysis can be useful for molecules and solids containing heavy atoms.

Interacting quantum dot coupled to a kondo spin: a universal Hamiltonian study.

PubMed

Rotter, Stefan; Türeci, Hakan E; Alhassid, Y; Stone, A Douglas

2008-04-25

We study a Kondo spin coupled to a mesoscopic interacting quantum dot that is described by the "universal Hamiltonian." The problem is solved numerically by diagonalizing the system Hamiltonian in a good-spin basis and analytically in the weak and strong Kondo coupling limits. The ferromagnetic exchange interaction within the dot leads to a stepwise increase of the ground-state spin (Stoner staircase), which is modified nontrivially by the Kondo interaction. We find that the spin-transition steps move to lower values of the exchange coupling for weak Kondo interaction, but shift back up for sufficiently strong Kondo coupling. The interplay between Kondo and ferromagnetic exchange correlations can be probed with experimentally tunable parameters.

The Electromagnetic Dipole Radiation Field through the Hamiltonian Approach

ERIC Educational Resources Information Center

Likar, A.; Razpet, N.

2009-01-01

The dipole radiation from an oscillating charge is treated using the Hamiltonian approach to electrodynamics where the concept of cavity modes plays a central role. We show that the calculation of the radiation field can be obtained in a closed form within this approach by emphasizing the role of coherence between the cavity modes, which is…

Self-duality of the compactified Ruijsenaars-Schneider system from quasi-Hamiltonian reduction

NASA Astrophysics Data System (ADS)

Fehér, L.; Klimčík, C.

2012-07-01

The Delzant theorem of symplectic topology is used to derive the completely integrable compactified Ruijsenaars-Schneider IIIb system from a quasi-Hamiltonian reduction of the internally fused double SU(n)×SU(n). In particular, the reduced spectral functions depending respectively on the first and second SU(n) factor of the double engender two toric moment maps on the IIIb phase space CP(n-1) that play the roles of action-variables and particle-positions. A suitable central extension of the SL(2,Z) mapping class group of the torus with one boundary component is shown to act on the quasi-Hamiltonian double by automorphisms and, upon reduction, the standard generator S of the mapping class group is proved to descend to the Ruijsenaars self-duality symplectomorphism that exchanges the toric moment maps. We give also two new presentations of this duality map: one as the composition of two Delzant symplectomorphisms and the other as the composition of three Dehn twist symplectomorphisms realized by Goldman twist flows. Through the well-known relation between quasi-Hamiltonian manifolds and moduli spaces, our results rigorously establish the validity of the interpretation [going back to Gorsky and Nekrasov] of the IIIb system in terms of flat SU(n) connections on the one-holed torus.

National Center tour guide

USGS Publications Warehouse

,

1979-01-01

On behalf of each employee at the Geological Survey's National Center, I [H. William Menard, Director] extend a warm welcome to you during our Centennial Year. We hope that your visit to our headquarters will be a pleasant and rewarding experience. Our scientific research is directed towards helping to solve some of the critical environmental and natural resource problems that face our Nation today. We want you to see some aspects of this work, and we hope you will visit us again. As part of the Federal Government, we are deeply committed to the concept of public service. We are proud to serve you.

Gauge properties of the guiding center variational symplectic integrator

DOE Office of Scientific and Technical Information (OSTI.GOV)

Squire, J.; Tang, W. M.; Qin, H.

Variational symplectic algorithms have recently been developed for carrying out long-time simulation of charged particles in magnetic fields [H. Qin and X. Guan, Phys. Rev. Lett. 100, 035006 (2008); H. Qin, X. Guan, and W. Tang, Phys. Plasmas (2009); J. Li, H. Qin, Z. Pu, L. Xie, and S. Fu, Phys. Plasmas 18, 052902 (2011)]. As a direct consequence of their derivation from a discrete variational principle, these algorithms have very good long-time energy conservation, as well as exactly preserving discrete momenta. We present stability results for these algorithms, focusing on understanding how explicit variational integrators can be designed formore » this type of system. It is found that for explicit algorithms, an instability arises because the discrete symplectic structure does not become the continuous structure in the t{yields}0 limit. We examine how a generalized gauge transformation can be used to put the Lagrangian in the 'antisymmetric discretization gauge,' in which the discrete symplectic structure has the correct form, thus eliminating the numerical instability. Finally, it is noted that the variational guiding center algorithms are not electromagnetically gauge invariant. By designing a model discrete Lagrangian, we show that the algorithms are approximately gauge invariant as long as A and {phi} are relatively smooth. A gauge invariant discrete Lagrangian is very important in a variational particle-in-cell algorithm where it ensures current continuity and preservation of Gauss's law [J. Squire, H. Qin, and W. Tang (to be published)].« less

Focal points and principal solutions of linear Hamiltonian systems revisited

NASA Astrophysics Data System (ADS)

Šepitka, Peter; Šimon Hilscher, Roman

2018-05-01

In this paper we present a novel view on the principal (and antiprincipal) solutions of linear Hamiltonian systems, as well as on the focal points of their conjoined bases. We present a new and unified theory of principal (and antiprincipal) solutions at a finite point and at infinity, and apply it to obtain new representation of the multiplicities of right and left proper focal points of conjoined bases. We show that these multiplicities can be characterized by the abnormality of the system in a neighborhood of the given point and by the rank of the associated T-matrix from the theory of principal (and antiprincipal) solutions. We also derive some additional important results concerning the representation of T-matrices and associated normalized conjoined bases. The results in this paper are new even for completely controllable linear Hamiltonian systems. We also discuss other potential applications of our main results, in particular in the singular Sturmian theory.

Maximum Renyi entropy principle for systems with power-law Hamiltonians.

PubMed

Bashkirov, A G

2004-09-24

The Renyi distribution ensuring the maximum of Renyi entropy is investigated for a particular case of a power-law Hamiltonian. Both Lagrange parameters alpha and beta can be eliminated. It is found that beta does not depend on a Renyi parameter q and can be expressed in terms of an exponent kappa of the power-law Hamiltonian and an average energy U. The Renyi entropy for the resulting Renyi distribution reaches its maximal value at q=1/(1+kappa) that can be considered as the most probable value of q when we have no additional information on the behavior of the stochastic process. The Renyi distribution for such q becomes a power-law distribution with the exponent -(kappa+1). When q=1/(1+kappa)+epsilon (0

Hamiltonian approach to Ehrenfest expectation values and Gaussian quantum states

PubMed Central

Bonet-Luz, Esther

2016-01-01

The dynamics of quantum expectation values is considered in a geometric setting. First, expectation values of the canonical observables are shown to be equivariant momentum maps for the action of the Heisenberg group on quantum states. Then, the Hamiltonian structure of Ehrenfest’s theorem is shown to be Lie–Poisson for a semidirect-product Lie group, named the Ehrenfest group. The underlying Poisson structure produces classical and quantum mechanics as special limit cases. In addition, quantum dynamics is expressed in the frame of the expectation values, in which the latter undergo canonical Hamiltonian motion. In the case of Gaussian states, expectation values dynamics couples to second-order moments, which also enjoy a momentum map structure. Eventually, Gaussian states are shown to possess a Lie–Poisson structure associated with another semidirect-product group, which is called the Jacobi group. This structure produces the energy-conserving variant of a class of Gaussian moment models that have previously appeared in the chemical physics literature. PMID:27279764

Question and Answer Guide to OCLC.

ERIC Educational Resources Information Center

Yen, Sidney S. C.

The purpose of this guide is to provide basic factual information about the Ohio College Library Center (OCLC), its data base, its operation, and its functions. It is intended for libraries which have not yet participated in OCLC, but would be useful as a reference guide in all libraries. Presented in question and answer form, the guide consists…

A new approach in the design of an interactive environment for teaching Hamiltonian digraphs

NASA Astrophysics Data System (ADS)

Iordan, A. E.; Panoiu, M.

2014-03-01

In this article the authors present the necessary steps in object orientated design of an interactive environment that is dedicated to the process of acquaintances assimilation in Hamiltonian graphs theory domain, especially for the simulation of algorithms which determine the Hamiltonian trails and circuits. The modelling of the interactive environment is achieved through specific UML diagrams representing the steps of analysis, design and implementation. This interactive environment is very useful for both students and professors, because computer programming domain, especially digraphs theory domain is comprehended and assimilated with difficulty by students.

Hamiltonian structure of classical N-body systems of finite-size particles subject to EM interactions

NASA Astrophysics Data System (ADS)

Cremaschini, C.; Tessarotto, M.

2012-01-01

An open issue in classical relativistic mechanics is the consistent treatment of the dynamics of classical N-body systems of mutually interacting particles. This refers, in particular, to charged particles subject to EM interactions, including both binary interactions and self-interactions ( EM-interacting N- body systems). The correct solution to the question represents an overriding prerequisite for the consistency between classical and quantum mechanics. In this paper it is shown that such a description can be consistently obtained in the context of classical electrodynamics, for the case of a N-body system of classical finite-size charged particles. A variational formulation of the problem is presented, based on the N -body hybrid synchronous Hamilton variational principle. Covariant Lagrangian and Hamiltonian equations of motion for the dynamics of the interacting N-body system are derived, which are proved to be delay-type ODEs. Then, a representation in both standard Lagrangian and Hamiltonian forms is proved to hold, the latter expressed by means of classical Poisson Brackets. The theory developed retains both the covariance with respect to the Lorentz group and the exact Hamiltonian structure of the problem, which is shown to be intrinsically non-local. Different applications of the theory are investigated. The first one concerns the development of a suitable Hamiltonian approximation of the exact equations that retains finite delay-time effects characteristic of the binary interactions and self-EM-interactions. Second, basic consequences concerning the validity of Dirac generator formalism are pointed out, with particular reference to the instant-form representation of Poincaré generators. Finally, a discussion is presented both on the validity and possible extension of the Dirac generator formalism as well as the failure of the so-called Currie "no-interaction" theorem for the non-local Hamiltonian system considered here.

Collective coordinates and constrained hamiltonian systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dayi, O.F.

1992-07-01

A general method of incorporating collective coordinates (transformation of fields into an overcomplete basis) with constrained hamiltonian systems is given where the original phase space variables and collective coordinates can be bosonic or/and fermionic. This method is illustrated by applying it to the SU(2) Yang-Mills-Higgs theory and its BFV-BRST quantization is discussed. Moreover, this formalism is used to give a systematic way of converting second class constraints into effectively first class ones, by considering second class constraints as first class constraints and gauge fixing conditions. This approach is applied to the massive superparticle. Proca lagrangian, and some topological quantum fieldmore » theories.« less

Superfield Hamiltonian quantization in terms of quantum antibrackets

NASA Astrophysics Data System (ADS)

Batalin, Igor A.; Lavrov, Peter M.

2016-04-01

We develop a new version of the superfield Hamiltonian quantization. The main new feature is that the BRST-BFV charge and the gauge fixing Fermion are introduced on equal footing within the sigma model approach, which provides for the actual use of the quantum/derived antibrackets. We study in detail the generating equations for the quantum antibrackets and their primed counterparts. We discuss the finite quantum anticanonical transformations generated by the quantum antibracket.

Integrable time-dependent Hamiltonians, solvable Landau-Zener models and Gaudin magnets

NASA Astrophysics Data System (ADS)

Yuzbashyan, Emil A.

2018-05-01

We solve the non-stationary Schrödinger equation for several time-dependent Hamiltonians, such as the BCS Hamiltonian with an interaction strength inversely proportional to time, periodically driven BCS and linearly driven inhomogeneous Dicke models as well as various multi-level Landau-Zener tunneling models. The latter are Demkov-Osherov, bow-tie, and generalized bow-tie models. We show that these Landau-Zener problems and their certain interacting many-body generalizations map to Gaudin magnets in a magnetic field. Moreover, we demonstrate that the time-dependent Schrödinger equation for the above models has a similar structure and is integrable with a similar technique as Knizhnik-Zamolodchikov equations. We also discuss applications of our results to the problem of molecular production in an atomic Fermi gas swept through a Feshbach resonance and to the evaluation of the Landau-Zener transition probabilities.

Robust Online Hamiltonian Learning

NASA Astrophysics Data System (ADS)

Granade, Christopher; Ferrie, Christopher; Wiebe, Nathan; Cory, David

2013-05-01

In this talk, we introduce a machine-learning algorithm for the problem of inferring the dynamical parameters of a quantum system, and discuss this algorithm in the example of estimating the precession frequency of a single qubit in a static field. Our algorithm is designed with practicality in mind by including parameters that control trade-offs between the requirements on computational and experimental resources. The algorithm can be implemented online, during experimental data collection, or can be used as a tool for post-processing. Most importantly, our algorithm is capable of learning Hamiltonian parameters even when the parameters change from experiment-to-experiment, and also when additional noise processes are present and unknown. Finally, we discuss the performance of the our algorithm by appeal to the Cramer-Rao bound. This work was financially supported by the Canadian government through NSERC and CERC and by the United States government through DARPA. NW would like to acknowledge funding from USARO-DTO.

United States Air Force Child Care Center Infant Care Guide.

ERIC Educational Resources Information Center

Craig, Ardyn; And Others

Intended to guide Air Force infant caregivers in providing high quality group care for infants 6 weeks to 6 months of age, this infant care guide must be used in conjunction with other Air Force regulations on day care, such as AFR 215-1, Volume VI (to be renumbered AFR 215-27). After a brief introductory chapter (Chapter I), Chapter II indicates…

The use of an analytic Hamiltonian matrix for solving the hydrogenic atom

NASA Astrophysics Data System (ADS)

Bhatti, Mohammad

2001-10-01

The non-relativistic Hamiltonian corresponding to the Shrodinger equation is converted into analytic Hamiltonian matrix using the kth order B-splines functions. The Galerkin method is applied to the solution of the Shrodinger equation for bound states of hydrogen-like systems. The program Mathematica is used to create analytic matrix elements and exact integration is performed over the knot-sequence of B-splines and the resulting generalized eigenvalue problem is solved on a specified numerical grid. The complete basis set and the energy spectrum is obtained for the coulomb potential for hydrogenic systems with Z less than 100 with B-splines of order eight. Another application is given to test the Thomas-Reiche-Kuhn sum rule for the hydrogenic systems.

4 NCIC Data Acquisition Guide

USGS Publications Warehouse

,

1979-01-01

The National Cartographic Information Center (NCIC) is the information branch of the National Mapping Program. NCIC gathers descriptions of cartographic products held by Federal, State and local agencies, and private companies. Computerized information systems are used to edit, store, and distribute these descriptions. The Aerial Photography Summary Record System (APSRS) is NCIC's system for determining if photographs of a particular area, with a particular set of characteristics, are available, and if so, where they can be found. This guide defines the procedures for planning and conducting visits to potential contributors to the APSRS data base. The guide also defines acquisition responsibilities of the contributor, State affiliates, mapping centers, and NCIC headquarters. As a Data Acquisition specialist, you are encouraged to seek innovative approaches to acquiring data and to suggest additions or changes to this guide.

Asymptotic analysis on a pseudo-Hermitian Riemann-zeta Hamiltonian

NASA Astrophysics Data System (ADS)

Bender, Carl M.; Brody, Dorje C.

2018-04-01

The differential-equation eigenvalue problem associated with a recently-introduced Hamiltonian, whose eigenvalues correspond to the zeros of the Riemann zeta function, is analyzed using Fourier and WKB analysis. The Fourier analysis leads to a challenging open problem concerning the formulation of the eigenvalue problem in the momentum space. The WKB analysis gives the exact asymptotic behavior of the eigenfunction.

A Hamiltonian electromagnetic gyrofluid model

NASA Astrophysics Data System (ADS)

Waelbroeck, F. L.; Hazeltine, R. D.; Morrison, P. J.

2009-11-01

An isothermal truncation of the electromagnetic gyrofluid model of Snyder and Hammett [Phys. Plasmas 8, 3199 (2001)] is shown to be Hamiltonian. The corresponding noncanonical Lie-Poisson bracket and its Casimir invariants are presented. The model describes the evolution of the density, the electrostatic potential, and the component of the vector potential along a strong background field. This makes it suitable for describing such phenomena as the propagation of kinetic-Alfv'en modons, the nonlinear saturation of drift-tearing modes, and the diamagnetic stabilization of the internal kink. The invariants are used to obtain a set of coupled Grad-Shafranov equations describing equilibria and propagating coherent structures. They also lead to a Lagrangian formulation of the equations of motion that is well suited to solution with the PIC method.

High-spin europium and gadolinium centers in yttrium-aluminum garnet

NASA Astrophysics Data System (ADS)

Vazhenin, V. A.; Potapov, A. P.; Asatryan, G. R.; Uspenskaya, Yu. A.; Petrosyan, A. G.; Fokin, A. V.

2016-08-01

Electron-spin resonance spectra of Eu2+ and Gd3+ centers substituting Y3+ ions in single-crystal yttrium-aluminum garnet have been studied and the parameters of their rhombic spin Hamiltonian have been determined. The fine-structure parameters of the above ions have been calculated in the superposition model disregarding changes in the angular coordinates of the ligand environment of the impurity defect thus demonstrating the necessity of taking these changes into account.

People, Animals and the Environment: An Educational Simulation Game. Teacher's Guide and Student Guide.

ERIC Educational Resources Information Center

American Animal Welfare Foundation, St. Paul, MN.

This document consists of a teacher guide and a student guide to an educational simulation game that provides students with an opportunity to examine the relationship between humans and animals, and to explore the roles that animals play in daily life. The teaching technique employed is a student-centered process in which students work…

Nutrition and Meal Planning in Child-Care Programs: A Practical Guide.

ERIC Educational Resources Information Center

Edelstein, Sari

Designed to assist child care center managers in planning nutritious meals for children in centers or licensed home day care programs, this guide presents information on the nutritional requirements of infants and children, sample menus for child care centers, and resources for further information. The first part of the guide details the…

Linearly scaling and almost Hamiltonian dielectric continuum molecular dynamics simulations through fast multipole expansions

NASA Astrophysics Data System (ADS)

Lorenzen, Konstantin; Mathias, Gerald; Tavan, Paul

2015-11-01

Hamiltonian Dielectric Solvent (HADES) is a recent method [S. Bauer et al., J. Chem. Phys. 140, 104103 (2014)] which enables atomistic Hamiltonian molecular dynamics (MD) simulations of peptides and proteins in dielectric solvent continua. Such simulations become rapidly impractical for large proteins, because the computational effort of HADES scales quadratically with the number N of atoms. If one tries to achieve linear scaling by applying a fast multipole method (FMM) to the computation of the HADES electrostatics, the Hamiltonian character (conservation of total energy, linear, and angular momenta) may get lost. Here, we show that the Hamiltonian character of HADES can be almost completely preserved, if the structure-adapted fast multipole method (SAMM) as recently redesigned by Lorenzen et al. [J. Chem. Theory Comput. 10, 3244-3259 (2014)] is suitably extended and is chosen as the FMM module. By this extension, the HADES/SAMM forces become exact gradients of the HADES/SAMM energy. Their translational and rotational invariance then guarantees (within the limits of numerical accuracy) the exact conservation of the linear and angular momenta. Also, the total energy is essentially conserved—up to residual algorithmic noise, which is caused by the periodically repeated SAMM interaction list updates. These updates entail very small temporal discontinuities of the force description, because the employed SAMM approximations represent deliberately balanced compromises between accuracy and efficiency. The energy-gradient corrected version of SAMM can also be applied, of course, to MD simulations of all-atom solvent-solute systems enclosed by periodic boundary conditions. However, as we demonstrate in passing, this choice does not offer any serious advantages.

Electrostatics of proteins in dielectric solvent continua. II. Hamiltonian reaction field dynamics

NASA Astrophysics Data System (ADS)

Bauer, Sebastian; Tavan, Paul; Mathias, Gerald

2014-03-01

In Paper I of this work [S. Bauer, G. Mathias, and P. Tavan, J. Chem. Phys. 140, 104102 (2014)] we have presented a reaction field (RF) method, which accurately solves the Poisson equation for proteins embedded in dielectric solvent continua at a computational effort comparable to that of polarizable molecular mechanics (MM) force fields. Building upon these results, here we suggest a method for linearly scaling Hamiltonian RF/MM molecular dynamics (MD) simulations, which we call "Hamiltonian dielectric solvent" (HADES). First, we derive analytical expressions for the RF forces acting on the solute atoms. These forces properly account for all those conditions, which have to be self-consistently fulfilled by RF quantities introduced in Paper I. Next we provide details on the implementation, i.e., we show how our RF approach is combined with a fast multipole method and how the self-consistency iterations are accelerated by the use of the so-called direct inversion in the iterative subspace. Finally we demonstrate that the method and its implementation enable Hamiltonian, i.e., energy and momentum conserving HADES-MD, and compare in a sample application on Ac-Ala-NHMe the HADES-MD free energy landscape at 300 K with that obtained in Paper I by scanning of configurations and with one obtained from an explicit solvent simulation.

Toward Hamiltonian Adaptive QM/MM: Accurate Solvent Structures Using Many-Body Potentials.

PubMed

Boereboom, Jelle M; Potestio, Raffaello; Donadio, Davide; Bulo, Rosa E

2016-08-09

Adaptive quantum mechanical (QM)/molecular mechanical (MM) methods enable efficient molecular simulations of chemistry in solution. Reactive subregions are modeled with an accurate QM potential energy expression while the rest of the system is described in a more approximate manner (MM). As solvent molecules diffuse in and out of the reactive region, they are gradually included into (and excluded from) the QM expression. It would be desirable to model such a system with a single adaptive Hamiltonian, but thus far this has resulted in distorted structures at the boundary between the two regions. Solving this long outstanding problem will allow microcanonical adaptive QM/MM simulations that can be used to obtain vibrational spectra and dynamical properties. The difficulty lies in the complex QM potential energy expression, with a many-body expansion that contains higher order terms. Here, we outline a Hamiltonian adaptive multiscale scheme within the framework of many-body potentials. The adaptive expressions are entirely general, and complementary to all standard (nonadaptive) QM/MM embedding schemes available. We demonstrate the merit of our approach on a molecular system defined by two different MM potentials (MM/MM'). For the long-range interactions a numerical scheme is used (particle mesh Ewald), which yields energy expressions that are many-body in nature. Our Hamiltonian approach is the first to provide both energy conservation and the correct solvent structure everywhere in this system.

Discontinuous Galerkin methods for Hamiltonian ODEs and PDEs

NASA Astrophysics Data System (ADS)

Tang, Wensheng; Sun, Yajuan; Cai, Wenjun

2017-02-01

In this article, we present a unified framework of discontinuous Galerkin (DG) discretizations for Hamiltonian ODEs and PDEs. We show that with appropriate numerical fluxes the numerical algorithms deduced from DG discretizations can be combined with the symplectic methods in time to derive the multi-symplectic PRK schemes. The resulting numerical discretizations are applied to the linear and nonlinear Schrödinger equations. Some conservative properties of the numerical schemes are investigated and confirmed in the numerical experiments.

Convergence of the Ponderomotive Guiding Center approximation in the LWFA

NASA Astrophysics Data System (ADS)

Silva, Thales; Vieira, Jorge; Helm, Anton; Fonseca, Ricardo; Silva, Luis

2017-10-01

Plasma accelerators arose as potential candidates for future accelerator technology in the last few decades because of its predicted compactness and low cost. One of the proposed designs for plasma accelerators is based on Laser Wakefield Acceleration (LWFA). However, simulations performed for such systems have to solve the laser wavelength which is orders of magnitude lower than the plasma wavelength. In this context, the Ponderomotive Guiding Center (PGC) algorithm for particle-in-cell (PIC) simulations is a potent tool. The laser is approximated by its envelope which leads to a speed-up of around 100 times because the laser wavelength is not solved. The plasma response is well understood, and comparison with the full PIC code show an excellent agreement. However, for LWFA, the convergence of the self-injected beam parameters, such as energy and charge, was not studied before and has vital importance for the use of the algorithm in predicting the beam parameters. Our goal is to do a thorough investigation of the stability and convergence of the algorithm in situations of experimental relevance for LWFA. To this end, we perform simulations using the PGC algorithm implemented in the PIC code OSIRIS. To verify the PGC predictions, we compare the results with full PIC simulations. This project has received funding from the European Union's Horizon 2020 research and innovation programme under Grant agreement No 653782.

Entanglement hamiltonian and entanglement contour in inhomogeneous 1D critical systems

NASA Astrophysics Data System (ADS)

Tonni, Erik; Rodríguez-Laguna, Javier; Sierra, Germán

2018-04-01

Inhomogeneous quantum critical systems in one spatial dimension have been studied by using conformal field theory in static curved backgrounds. Two interesting examples are the free fermion gas in the harmonic trap and the inhomogeneous XX spin chain called rainbow chain. For conformal field theories defined on static curved spacetimes characterised by a metric which is Weyl equivalent to the flat metric, with the Weyl factor depending only on the spatial coordinate, we study the entanglement hamiltonian and the entanglement spectrum of an interval adjacent to the boundary of a segment where the same boundary condition is imposed at the endpoints. A contour function for the entanglement entropies corresponding to this configuration is also considered, being closely related to the entanglement hamiltonian. The analytic expressions obtained by considering the curved spacetime which characterises the rainbow model have been checked against numerical data for the rainbow chain, finding an excellent agreement.

Transition probabilities for non self-adjoint Hamiltonians in infinite dimensional Hilbert spaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bagarello, F., E-mail: fabio.bagarello@unipa.it

In a recent paper we have introduced several possible inequivalent descriptions of the dynamics and of the transition probabilities of a quantum system when its Hamiltonian is not self-adjoint. Our analysis was carried out in finite dimensional Hilbert spaces. This is useful, but quite restrictive since many physically relevant quantum systems live in infinite dimensional Hilbert spaces. In this paper we consider this situation, and we discuss some applications to well known models, introduced in the literature in recent years: the extended harmonic oscillator, the Swanson model and a generalized version of the Landau levels Hamiltonian. Not surprisingly we willmore » find new interesting features not previously found in finite dimensional Hilbert spaces, useful for a deeper comprehension of this kind of physical systems.« less

Equivalent Hamiltonian for the Lee model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jones, H. F.

2008-03-15

Using the techniques of quasi-Hermitian quantum mechanics and quantum field theory we use a similarity transformation to construct an equivalent Hermitian Hamiltonian for the Lee model. In the field theory confined to the V/N{theta} sector it effectively decouples V, replacing the three-point interaction of the original Lee model by an additional mass term for the V particle and a four-point interaction between N and {theta}. While the construction is originally motivated by the regime where the bare coupling becomes imaginary, leading to a ghost, it applies equally to the standard Hermitian regime where the bare coupling is real. In thatmore » case the similarity transformation becomes a unitary transformation.« less

Quantum Hamiltonian daemons: Unitary analogs of combustion engines

NASA Astrophysics Data System (ADS)

Thesing, Eike P.; Gilz, Lukas; Anglin, James R.

2017-07-01

Hamiltonian daemons have recently been defined classically as small, closed Hamiltonian systems which can exhibit secular energy transfer from high-frequency to low-frequency degrees of freedom (steady downconversion), analogous to the steady transfer of energy in a combustion engine from the high terahertz frequencies of molecular excitations to the low kilohertz frequencies of piston motion [L. Gilz, E. P. Thesing, and J. R. Anglin, Phys. Rev. E 94, 042127 (2016), 10.1103/PhysRevE.94.042127]. Classical daemons achieve downconversion within a small, closed system by exploiting nonlinear resonances; the adiabatic theorem permits their operation but imposes nontrivial limitations on their efficiency. Here we investigate a simple example of a quantum mechanical daemon. In the correspondence regime it obeys similar efficiency limits to its classical counterparts, but in the strongly quantum mechanical regime the daemon operates in an entirely different manner. It maintains an engine-like behavior in a distinctly quantum mechanical form: a weight is lifted at a steady average speed through a long sequence of quantum jumps in momentum, at each of which a quantum of fuel is consumed. The quantum daemon can cease downconversion at any time through nonadiabatic Landau-Zener transitions, and continuing operation of the quantum daemon is associated with steadily growing entanglement between fast and slow degrees of freedom.

Self-consistent chaos in a mean-field Hamiltonian model of fluids and plasmas

NASA Astrophysics Data System (ADS)

del-Castillo-Negrete, D.; Firpo, Marie-Christine

2002-11-01

We present a mean-field Hamiltonian model that describes the collective dynamics of marginally stable fluids and plasmas. In plasmas, the model describes the self-consistent evolution of electron holes and clumps in phase space. In fluids, the model describes the dynamics of vortices with negative and positive circulation in shear flows. The mean-field nature of the system makes it a tractable model to study the dynamics of large degrees-of-freedom, coupled Hamiltonian systems. Here we focus in the role of self-consistent chaos in the formation and destruction of phase space coherent structures. Numerical simulations in the finite N and in the Narrow kinetic limit (where N is the number of particles) show the existence of coherent, rotating dipole states. We approximate the dipole as two macroparticles, and show that the N = 2 limit has a family of rotating integrable solutions described by a one degree-of-freedom nontwist Hamiltonian. The coherence of the dipole is explained in terms of a parametric resonance between the rotation frequency of the macroparticles and the oscillation frequency of the self-consistent mean field. For a class of initial conditions, the mean field exhibits a self-consistent, elliptic-hyperbolic bifurcation that leads to the destruction of the dipole and violent mixing of the phase space.

Capillary wave Hamiltonian for the Landau-Ginzburg-Wilson density functional

NASA Astrophysics Data System (ADS)

Chacón, Enrique; Tarazona, Pedro

2016-06-01

We study the link between the density functional (DF) formalism and the capillary wave theory (CWT) for liquid surfaces, focused on the Landau-Ginzburg-Wilson (LGW) model, or square gradient DF expansion, with a symmetric double parabola free energy, which has been extensively used in theoretical studies of this problem. We show the equivalence between the non-local DF results of Parry and coworkers and the direct evaluation of the mean square fluctuations of the intrinsic surface, as is done in the intrinsic sampling method for computer simulations. The definition of effective wave-vector dependent surface tensions is reviewed and we obtain new proposals for the LGW model. The surface weight proposed by Blokhuis and the surface mode analysis proposed by Stecki provide consistent and optimal effective definitions for the extended CWT Hamiltonian associated to the DF model. A non-local, or coarse-grained, definition of the intrinsic surface provides the missing element to get the mesoscopic surface Hamiltonian from the molecular DF description, as had been proposed a long time ago by Dietrich and coworkers.

Capillary wave Hamiltonian for the Landau-Ginzburg-Wilson density functional.

PubMed

Chacón, Enrique; Tarazona, Pedro

2016-06-22

We study the link between the density functional (DF) formalism and the capillary wave theory (CWT) for liquid surfaces, focused on the Landau-Ginzburg-Wilson (LGW) model, or square gradient DF expansion, with a symmetric double parabola free energy, which has been extensively used in theoretical studies of this problem. We show the equivalence between the non-local DF results of Parry and coworkers and the direct evaluation of the mean square fluctuations of the intrinsic surface, as is done in the intrinsic sampling method for computer simulations. The definition of effective wave-vector dependent surface tensions is reviewed and we obtain new proposals for the LGW model. The surface weight proposed by Blokhuis and the surface mode analysis proposed by Stecki provide consistent and optimal effective definitions for the extended CWT Hamiltonian associated to the DF model. A non-local, or coarse-grained, definition of the intrinsic surface provides the missing element to get the mesoscopic surface Hamiltonian from the molecular DF description, as had been proposed a long time ago by Dietrich and coworkers.

Isochronous extension of the Hamiltonian describing free motion in the Poincaré half-plane: Classical and quantum treatments

NASA Astrophysics Data System (ADS)

Calogero, F. A.; Leyvraz, F.

2007-09-01

We modify (in two different manners) the Hamiltonian describing motions in the Poincaré half-plane so that the modified Hamiltonians thereby obtained are entirely isochronous: indeed, in the classical context, all the motions they entail are periodic with the same period. We then investigate suitably quantized versions of these systems and show that their spectra are equispaced.

Nonperturbative light-front Hamiltonian methods

NASA Astrophysics Data System (ADS)

Hiller, J. R.

2016-09-01

We examine the current state-of-the-art in nonperturbative calculations done with Hamiltonians constructed in light-front quantization of various field theories. The language of light-front quantization is introduced, and important (numerical) techniques, such as Pauli-Villars regularization, discrete light-cone quantization, basis light-front quantization, the light-front coupled-cluster method, the renormalization group procedure for effective particles, sector-dependent renormalization, and the Lanczos diagonalization method, are surveyed. Specific applications are discussed for quenched scalar Yukawa theory, ϕ4 theory, ordinary Yukawa theory, supersymmetric Yang-Mills theory, quantum electrodynamics, and quantum chromodynamics. The content should serve as an introduction to these methods for anyone interested in doing such calculations and as a rallying point for those who wish to solve quantum chromodynamics in terms of wave functions rather than random samplings of Euclidean field configurations.

High-precision calculations in strongly coupled quantum field theory with next-to-leading-order renormalized Hamiltonian Truncation

NASA Astrophysics Data System (ADS)

Elias-Miró, Joan; Rychkov, Slava; Vitale, Lorenzo G.

2017-10-01

Hamiltonian Truncation (a.k.a. Truncated Spectrum Approach) is an efficient numerical technique to solve strongly coupled QFTs in d = 2 spacetime dimensions. Further theoretical developments are needed to increase its accuracy and the range of applicability. With this goal in mind, here we present a new variant of Hamiltonian Truncation which exhibits smaller dependence on the UV cutoff than other existing implementations, and yields more accurate spectra. The key idea for achieving this consists in integrating out exactly a certain class of high energy states, which corresponds to performing renormalization at the cubic order in the interaction strength. We test the new method on the strongly coupled two-dimensional quartic scalar theory. Our work will also be useful for the future goal of extending Hamiltonian Truncation to higher dimensions d ≥ 3.

Multiple Intelligences Centers and Projects.

ERIC Educational Resources Information Center

Chapman, Carolyn; Freeman, Lynn

Based upon Gardner's theory of multiple intelligences, this book guides elementary school teachers through the process of using classroom learning centers and projects by providing choices for students. The guide is divided into two sections, providing the theoretical background and information on how to develop multiple intelligences learning…

Scattering matrix of arbitrary tight-binding Hamiltonians

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ramírez, C., E-mail: carlos@ciencias.unam.mx; Medina-Amayo, L.A.

2017-03-15

A novel efficient method to calculate the scattering matrix (SM) of arbitrary tight-binding Hamiltonians is proposed, including cases with multiterminal structures. In particular, the SM of two kinds of fundamental structures is given, which can be used to obtain the SM of bigger systems iteratively. Also, a procedure to obtain the SM of layer-composed periodic leads is described. This method allows renormalization approaches, which permits computations over macroscopic length systems without introducing additional approximations. Finally, the transmission coefficient of a ring-shaped multiterminal system and the transmission function of a square-lattice nanoribbon with a reduced width region are calculated.

Simple and Double Alfven Waves: Hamiltonian Aspects

NASA Astrophysics Data System (ADS)

Webb, G. M.; Zank, G. P.; Hu, Q.; le Roux, J. A.; Dasgupta, B.

2011-12-01

We discuss the nature of simple and double Alfvén waves. Simple waves depend on a single phase variable \\varphi, but double waves depend on two independent phase variables \\varphi1 and \\varphi2. The phase variables depend on the space and time coordinates x and t. Simple and double Alfvén waves have the same integrals, namely, the entropy, density, magnetic pressure, and group velocity (the sum of the Alfvén and fluid velocities) are constant throughout the flow. We present examples of both simple and double Alfvén waves, and discuss Hamiltonian formulations of the waves.

Education Leaders' Guide to Transforming Student and Learning Supports. A Center Guide

ERIC Educational Resources Information Center

Center for Mental Health in Schools at UCLA, 2014

2014-01-01

New directions for student and learning supports are key to systemically addressing barriers to learning and teaching. The aim is to unify and then develop a comprehensive and equitable system of student/learning supports at every school. This guide incorporates years of research and prototype development and a variety of examples from…

Aircraft: United States Air Force Child Care Program Activity Guide.

ERIC Educational Resources Information Center

Boggs, Juanita; Brant, Linda

General information about United States' aircraft is provided in this program activity guide for teachers and caregivers in Air Force preschools and day care centers. The guide includes basic information for teachers and caregivers, basic understandings, suggested teaching methods and group activities, vocabulary, ideas for interest centers, and…

Linearly scaling and almost Hamiltonian dielectric continuum molecular dynamics simulations through fast multipole expansions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lorenzen, Konstantin; Mathias, Gerald; Tavan, Paul, E-mail: tavan@physik.uni-muenchen.de

2015-11-14

Hamiltonian Dielectric Solvent (HADES) is a recent method [S. Bauer et al., J. Chem. Phys. 140, 104103 (2014)] which enables atomistic Hamiltonian molecular dynamics (MD) simulations of peptides and proteins in dielectric solvent continua. Such simulations become rapidly impractical for large proteins, because the computational effort of HADES scales quadratically with the number N of atoms. If one tries to achieve linear scaling by applying a fast multipole method (FMM) to the computation of the HADES electrostatics, the Hamiltonian character (conservation of total energy, linear, and angular momenta) may get lost. Here, we show that the Hamiltonian character of HADESmore » can be almost completely preserved, if the structure-adapted fast multipole method (SAMM) as recently redesigned by Lorenzen et al. [J. Chem. Theory Comput. 10, 3244-3259 (2014)] is suitably extended and is chosen as the FMM module. By this extension, the HADES/SAMM forces become exact gradients of the HADES/SAMM energy. Their translational and rotational invariance then guarantees (within the limits of numerical accuracy) the exact conservation of the linear and angular momenta. Also, the total energy is essentially conserved—up to residual algorithmic noise, which is caused by the periodically repeated SAMM interaction list updates. These updates entail very small temporal discontinuities of the force description, because the employed SAMM approximations represent deliberately balanced compromises between accuracy and efficiency. The energy-gradient corrected version of SAMM can also be applied, of course, to MD simulations of all-atom solvent-solute systems enclosed by periodic boundary conditions. However, as we demonstrate in passing, this choice does not offer any serious advantages.« less

Staff Manual for Instructional Material Centers. Fourth Revised Edition.

ERIC Educational Resources Information Center

Petrucci, Martha

For media center volunteers or inexperienced technicians, a workshop training guide provides reference and assistance in everyday problems and situations that arise in an instructional material center (IMC). Two five-hour days of instruction and participation, using the guide, are suggested for workshops. Step-by-step processing of book materials,…

Effective Hamiltonians for correlated narrow energy band systems and magnetic insulators: Role of spin-orbit interactions in metal-insulator transitions and magnetic phase transitions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chakraborty, Subrata; Vijay, Amrendra, E-mail: avijay@iitm.ac.in

Using a second-quantized many-electron Hamiltonian, we obtain (a) an effective Hamiltonian suitable for materials whose electronic properties are governed by a set of strongly correlated bands in a narrow energy range and (b) an effective spin-only Hamiltonian for magnetic materials. The present Hamiltonians faithfully include phonon and spin-related interactions as well as the external fields to study the electromagnetic response properties of complex materials and they, in appropriate limits, reduce to the model Hamiltonians due to Hubbard and Heisenberg. With the Hamiltonian for narrow-band strongly correlated materials, we show that the spin-orbit interaction provides a mechanism for metal-insulator transition, whichmore » is distinct from the Mott-Hubbard (driven by the electron correlation) and the Anderson mechanism (driven by the disorder). Next, with the spin-only Hamiltonian, we demonstrate the spin-orbit interaction to be a reason for the existence of antiferromagnetic phase in materials which are characterized by a positive isotropic spin-exchange energy. This is distinct from the Néel-VanVleck-Anderson paradigm which posits a negative spin-exchange for the existence of antiferromagnetism. We also find that the Néel temperature increases as the absolute value of the spin-orbit coupling increases.« less

Sequential Feedback Scheme Outperforms the Parallel Scheme for Hamiltonian Parameter Estimation.

PubMed

Yuan, Haidong

2016-10-14

Measurement and estimation of parameters are essential for science and engineering, where the main quest is to find the highest achievable precision with the given resources and design schemes to attain it. Two schemes, the sequential feedback scheme and the parallel scheme, are usually studied in the quantum parameter estimation. While the sequential feedback scheme represents the most general scheme, it remains unknown whether it can outperform the parallel scheme for any quantum estimation tasks. In this Letter, we show that the sequential feedback scheme has a threefold improvement over the parallel scheme for Hamiltonian parameter estimations on two-dimensional systems, and an order of O(d+1) improvement for Hamiltonian parameter estimation on d-dimensional systems. We also show that, contrary to the conventional belief, it is possible to simultaneously achieve the highest precision for estimating all three components of a magnetic field, which sets a benchmark on the local precision limit for the estimation of a magnetic field.

Classical Affine W-Algebras and the Associated Integrable Hamiltonian Hierarchies for Classical Lie Algebras

NASA Astrophysics Data System (ADS)

De Sole, Alberto; Kac, Victor G.; Valeri, Daniele

2018-06-01

We prove that any classical affine W-algebra W (g, f), where g is a classical Lie algebra and f is an arbitrary nilpotent element of g, carries an integrable Hamiltonian hierarchy of Lax type equations. This is based on the theories of generalized Adler type operators and of generalized quasideterminants, which we develop in the paper. Moreover, we show that under certain conditions, the product of two generalized Adler type operators is a Lax type operator. We use this fact to construct a large number of integrable Hamiltonian systems, recovering, as a special case, all KdV type hierarchies constructed by Drinfeld and Sokolov.

Optimizing the patient-centered environment: results of guided tours with health care providers and employees.

PubMed

Locatelli, Sara M; Turcios, Stephanie; LaVela, Sherri L

2015-01-01

To examine providers' perspectives on the care environment and patient-centered care (PCC) through the eyes of the veteran patient, using guided tours qualitative methodology. Environmental factors, such as attractiveness and function, have the potential to improve patients' experiences. Participatory qualitative methods allow researchers to explore the environment and facilitate discussion. Guided tours were conducted with 25 health care providers/employees at two Veterans Affairs (VA) health care facilities. In guided tours, participants lead the researcher through an environment, commenting on their surroundings, thoughts, and feelings. The researcher walks along with the participant, asking open-ended questions as needed to foster discussion and gain an understanding of the participant's view. Participants were asked to walk through the facility as though they were a veteran. Tours were audio recorded, with participant permission, and transcribed verbatim by research assistants. Three qualitative researchers were responsible for codebook development and coding transcripts and used data-driven coding approaches. Participants discussed physical appearance of the environment and how that influences perceptions about care. Overall, participants highlighted the need to shed the "institutional" appearance. Differences between VA and non-VA health care facilities were discussed, including availability of private rooms and staff to assist with navigating the facility. They reviewed resources in the facility, such as the information desk to assist patients and families. Finally, they offered suggestions for future improvements, including improvements to waiting areas and quiet areas for patients to relax and "get away" from their rooms. Participants highlighted many small changes to the care environment that could enhance the patient experience. Additionally, they examined the environment from the patient's perspective, to identify elements that enhance, or detract from

A Hamiltonian driven quantum-like model for overdistribution in episodic memory recollection.

NASA Astrophysics Data System (ADS)

Broekaert, Jan B.; Busemeyer, Jerome R.

2017-06-01

While people famously forget genuine memories over time, they also tend to mistakenly over-recall equivalent memories concerning a given event. The memory phenomenon is known by the name of episodic overdistribution and occurs both in memories of disjunctions and partitions of mutually exclusive events and has been tested, modeled and documented in the literature. The total classical probability of recalling exclusive sub-events most often exceeds the probability of recalling the composed event, i.e. a subadditive total. We present a Hamiltonian driven propagation for the Quantum Episodic Memory model developed by Brainerd (et al., 2015) for the episodic memory overdistribution in the experimental immediate item false memory paradigm (Brainerd and Reyna, 2008, 2010, 2015). Following the Hamiltonian method of Busemeyer and Bruza (2012) our model adds time-evolution of the perceived memory state through the stages of the experimental process based on psychologically interpretable parameters - γ_c for recollection capability of cues, κ_p for bias or description-dependence by probes and β for the average gist component in the memory state at start. With seven parameters the Hamiltonian model shows good accuracy of predictions both in the EOD-disjunction and in the EOD-subadditivity paradigm. We noticed either an outspoken preponderance of the gist over verbatim trace, or the opposite, in the initial memory state when β is real. Only for complex β a mix of both traces is present in the initial state for the EOD-subadditivity paradigm.

Passive simulation of the nonlinear port-Hamiltonian modeling of a Rhodes Piano

NASA Astrophysics Data System (ADS)

Falaize, Antoine; Hélie, Thomas

2017-03-01

This paper deals with the time-domain simulation of an electro-mechanical piano: the Fender Rhodes. A simplified description of this multi-physical system is considered. It is composed of a hammer (nonlinear mechanical component), a cantilever beam (linear damped vibrating component) and a pickup (nonlinear magneto-electronic transducer). The approach is to propose a power-balanced formulation of the complete system, from which a guaranteed-passive simulation is derived to generate physically-based realistic sound synthesis. Theses issues are addressed in four steps. First, a class of Port-Hamiltonian Systems is introduced: these input-to-output systems fulfill a power balance that can be decomposed into conservative, dissipative and source parts. Second, physical models are proposed for each component and are recast in the port-Hamiltonian formulation. In particular, a finite-dimensional model of the cantilever beam is derived, based on a standard modal decomposition applied to the Euler-Bernoulli model. Third, these systems are interconnected, providing a nonlinear finite-dimensional Port-Hamiltonian System of the piano. Fourth, a passive-guaranteed numerical method is proposed. This method is built to preserve the power balance in the discrete-time domain, and more precisely, its decomposition structured into conservative, dissipative and source parts. Finally, simulations are performed for a set of physical parameters, based on empirical but realistic values. They provide a variety of audio signals which are perceptively relevant and qualitatively similar to some signals measured on a real instrument.

Incidence of sepsis following transrectal ultrasound guided prostate biopsy at a tertiary-care medical center in Lebanon

PubMed Central

Shahait, Mohammed; Degheili, Jad; El-Merhi, Fadi; Tamim, Hani; Nasr, Rami

2016-01-01

ABSTRACT Background Urosepsis is a rare but life-threatening complication following transrectal ultrasound (TRUS) guided needle prostate biopsy. Despite the technological and pharmacological improvements, the problem of bacterial urosepsis after prostate biopsy remains. A strategy for preventing urosepsis following TRUS prostate biopsy in areas with high prevalence of resistant strains or patients presenting risk factors is lacking. Objectives The aim of this study was to assess the prevalence of urosepsis, as well its predictors, following TRUS guided needle biopsy of the prostate in a tertiary care medical center in Lebanon. Materials and Methods We carried out a retrospective study on all patients who underwent TRUS prostate biopsy at the American University of Beirut Medical Center between January 1, 2011 and June 31, 2013. Patients’ hospital charts were reviewed. Data collected included demographic information, pre-procedure disease specific information, as well as post-procedure information. Predictors of urosepsis following TRUS were assessed. Results In total, 265 patients were included in this study, where the prevalence of urosepsis following TRUS prostate biopsy was found to be 9.4%. The significant independent predictors of urosepsis were found to be: age with an OR=0.93 (95% CI: 0.88–1.00, p-value=0.03), and hypertension comorbidity with an OR=3.25 (95% CI: 1.19–8.85, p-value=0.02). Conclusion We found a high prevalence of urosepsis among patients who have undergone TRUS prostate biopsy, and identified two significant risk factors. The results of this study highlight the importance of implementing strategies for prevention of urosepsis following TRUS prostate biopsy. PMID:27136468

Multicast backup reprovisioning problem for Hamiltonian cycle-based protection on WDM networks

NASA Astrophysics Data System (ADS)

Din, Der-Rong; Huang, Jen-Shen

2014-03-01

As networks grow in size and complexity, the chance and the impact of failures increase dramatically. The pre-allocated backup resources cannot provide 100% protection guarantee when continuous failures occur in a network. In this paper, the multicast backup re-provisioning problem (MBRP) for Hamiltonian cycle (HC)-based protection on WDM networks for the link-failure case is studied. We focus on how to recover the protecting capabilities of Hamiltonian cycle against the subsequent link-failures on WDM networks for multicast transmissions, after recovering the multicast trees affected by the previous link-failure. Since this problem is a hard problem, an algorithm, which consists of several heuristics and a genetic algorithm (GA), is proposed to solve it. The simulation results of the proposed method are also given. Experimental results indicate that the proposed algorithm can solve this problem efficiently.

Simulating Open Quantum Systems with Hamiltonian Ensembles and the Nonclassicality of the Dynamics

NASA Astrophysics Data System (ADS)

Chen, Hong-Bin; Gneiting, Clemens; Lo, Ping-Yuan; Chen, Yueh-Nan; Nori, Franco

2018-01-01

The incoherent dynamical properties of open quantum systems are generically attributed to an ongoing correlation between the system and its environment. Here, we propose a novel way to assess the nature of these system-environment correlations by examining the system dynamics alone. Our approach is based on the possibility or impossibility to simulate open-system dynamics with Hamiltonian ensembles. As we show, such (im)possibility to simulate is closely linked to the system-environment correlations. We thus define the nonclassicality of open-system dynamics in terms of the nonexistence of a Hamiltonian-ensemble simulation. This classifies any nonunital open-system dynamics as nonclassical. We give examples for open-system dynamics that are unital and classical, as well as unital and nonclassical.

Analytical spectrum for a Hamiltonian of quantum dots with Rashba spin-orbit coupling

NASA Astrophysics Data System (ADS)

Dossa, Anselme F.; Avossevou, Gabriel Y. H.

2014-12-01

We determine the analytical solution for a Hamiltonian describing a confined charged particle in a quantum dot, including Rashba spin-orbit coupling and Zeeman splitting terms. The approach followed in this paper is straightforward and uses the symmetrization of the wave function's components. The eigenvalue problem for the Hamiltonian in Bargmann's Hilbert space reduces to a system of coupled first-order differential equations. Then we exploit the symmetry in the system to obtain uncoupled second-order differential equations, which are found to be the Whittaker-Ince limit of the confluent Heun equations. Analytical expressions as well as numerical results are obtained for the spectrum. One of the main features of such models, namely, the level splitting, is present through the spectrum obtained in this paper.

Stroboscopic versus nonstroboscopic dynamics in the Floquet realization of the Harper-Hofstadter Hamiltonian

NASA Astrophysics Data System (ADS)

Bukov, Marin; Polkovnikov, Anatoli

2014-10-01

We study the stroboscopic and nonstroboscopic dynamics in the Floquet realization of the Harper-Hofstadter Hamiltonian. We show that the former produces the evolution expected in the high-frequency limit only for observables, which commute with the operator to which the driving protocol couples. On the contrary, nonstroboscopic dynamics is capable of capturing the evolution governed by the Floquet Hamiltonian of any observable associated with the effective high-frequency model. We provide exact numerical simulations for the dynamics of the number operator following a quantum cyclotron orbit on a 2×2 plaquette, as well as the chiral current operator flowing along the legs of a 2×20 ladder. The exact evolution is compared with its stroboscopic and nonstroboscopic counterparts, including finite-frequency corrections.

A quantum algorithm for obtaining the lowest eigenstate of a Hamiltonian assisted with an ancillary qubit system

NASA Astrophysics Data System (ADS)

Bang, Jeongho; Lee, Seung-Woo; Lee, Chang-Woo; Jeong, Hyunseok

2015-01-01

We propose a quantum algorithm to obtain the lowest eigenstate of any Hamiltonian simulated by a quantum computer. The proposed algorithm begins with an arbitrary initial state of the simulated system. A finite series of transforms is iteratively applied to the initial state assisted with an ancillary qubit. The fraction of the lowest eigenstate in the initial state is then amplified up to 1. We prove that our algorithm can faithfully work for any arbitrary Hamiltonian in the theoretical analysis. Numerical analyses are also carried out. We firstly provide a numerical proof-of-principle demonstration with a simple Hamiltonian in order to compare our scheme with the so-called "Demon-like algorithmic cooling (DLAC)", recently proposed in Xu (Nat Photonics 8:113, 2014). The result shows a good agreement with our theoretical analysis, exhibiting the comparable behavior to the best `cooling' with the DLAC method. We then consider a random Hamiltonian model for further analysis of our algorithm. By numerical simulations, we show that the total number of iterations is proportional to , where is the difference between the two lowest eigenvalues and is an error defined as the probability that the finally obtained system state is in an unexpected (i.e., not the lowest) eigenstate.

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MedlinePlus

... Community Outreach Resource Center Toy Recall Statistics CO Poster Contest Pool Safely Business & Manufacturing Business & Manufacturing Business ... other organizations. Featured Resources Bare is Best Free Poster Safer Spaces for Babies Safety Guide Inflatable Air ...

Occupational Readiness Center Curriculum Guide. 2nd Edition.

ERIC Educational Resources Information Center

Putnam and Northern Westchester Counties Board of Cooperative Educational Services, Yorktown Heights, NY.

This curriculum guide provides materials for nine courses taught in the readiness program for students 15 years of age and over who are not benefiting from education in regular educational settings. (The program is intended to identify a suitable occupational field in which students can succeed and to develop their social and emotional readiness…

Effect of an atom on a quantum guided field in a weakly driven fiber-Bragg-grating cavity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Le Kien, Fam; Hakuta, K.

2010-02-15

We study the interaction of an atom with a quantum guided field in a weakly driven fiber-Bragg-grating (FBG) cavity. We present an effective Hamiltonian and derive the density-matrix equations for the combined atom-cavity system. We calculate the mean photon number, the second-order photon correlation function, and the atomic excited-state population. We show that due to the confinement of the guided cavity field in the fiber cross-section plane and in the space between the FBG mirrors, the presence of the atom in the FBG cavity can significantly affect the mean photon number and the photon statistics even though the cavity finessemore » is moderate, the cavity is long, and the probe field is weak.« less

A new Morse-oscillator based Hamiltonian for H 3+: Calculation of line strengths

NASA Astrophysics Data System (ADS)

Jensen, Per; Špirko, V.

1986-07-01

In two recent publications [V. Špirko, P. Jensen, P. R. Bunker, and A. Čejchan, J. Mol. Spectrosc.112, 183-202 (1985); P. Jensen, V. Špirko, and P. R. Bunker, J. Mol. Spectrosc.115, 269-293 (1986)], we have described the development of Morse oscillator adapted rotation-vibration Hamiltonians for equilateral triangular X3 and Y2X molecules, and we have used these Hamiltonians to calculate the rotation-vibration energies for H 3+ and its X3+ and Y2X+ isotopes from ab initio potential energy functions. The present paper presents a method for calculating rotation-vibration line strengths of H 3+ and its isotopes using an ab initio dipole moment function [G. D. Carney and R. N. Porter, J. Chem. Phys.60, 4251-4264 (1974)] together with the energies and wave-functions obtained by diagonalization of the Morse oscillator adapted Hamiltonians. We use this method for calculating the vibrational transition moments involving the lowest vibrational states of H 3+, D 3+, H 2D +, and D 2H +. Further, we calculate the line strengths of the low- J transitions in the rotational spectra of H 3+ in the vibrational ground state and in the ν1 and ν2 states. We hope that the calculations presented will facilitate the search for further rotation-vibration transitions of H 3+ and its isotopes.

Hamiltonian flows with random-walk behaviour originating from zero-sum games and fictitious play

NASA Astrophysics Data System (ADS)

van Strien, Sebastian

2011-06-01

In this paper we introduce Hamiltonian dynamics, inspired by zero-sum games (best response and fictitious play dynamics). The Hamiltonian functions we consider are continuous and piecewise affine (and of a very simple form). It follows that the corresponding Hamiltonian vector fields are discontinuous and multi-valued. Differential equations with discontinuities along a hyperplane are often called 'Filippov systems', and there is a large literature on such systems, see for example (di Bernardo et al 2008 Theory and applications Piecewise-Smooth Dynamical Systems (Applied Mathematical Sciences vol 163) (London: Springer); Kunze 2000 Non-Smooth Dynamical Systems (Lecture Notes in Mathematics vol 1744) (Berlin: Springer); Leine and Nijmeijer 2004 Dynamics and Bifurcations of Non-smooth Mechanical Systems (Lecture Notes in Applied and Computational Mechanics vol 18) (Berlin: Springer)). The special feature of the systems we consider here is that they have discontinuities along a large number of intersecting hyperplanes. Nevertheless, somewhat surprisingly, the flow corresponding to such a vector field exists, is unique and continuous. We believe that these vector fields deserve attention, because it turns out that the resulting dynamics are rather different from those found in more classically defined Hamiltonian dynamics. The vector field is extremely simple: outside codimension-one hyperplanes it is piecewise constant and so the flow phit piecewise a translation (without stationary points). Even so, the dynamics can be rather rich and complicated as a detailed study of specific examples show (see for example theorems 7.1 and 7.2 and also (Ostrovski and van Strien 2011 Regular Chaotic Dynf. 16 129-54)). In the last two sections of the paper we give some applications to game theory, and finish with posing a version of the Palis conjecture in the context of the class of non-smooth systems studied in this paper. To Jacob Palis on his 70th birthday.

Quantum Hamiltonian identification from measurement time traces.

PubMed

Zhang, Jun; Sarovar, Mohan

2014-08-22

Precise identification of parameters governing quantum processes is a critical task for quantum information and communication technologies. In this Letter, we consider a setting where system evolution is determined by a parametrized Hamiltonian, and the task is to estimate these parameters from temporal records of a restricted set of system observables (time traces). Based on the notion of system realization from linear systems theory, we develop a constructive algorithm that provides estimates of the unknown parameters directly from these time traces. We illustrate the algorithm and its robustness to measurement noise by applying it to a one-dimensional spin chain model with variable couplings.

Guide to making time-lapse graphics using the facilities of the National Magnetic Fusion Energy Computing Center

DOE Office of Scientific and Technical Information (OSTI.GOV)

Munro, J.K. Jr.

1980-05-01

The advent of large, fast computers has opened the way to modeling more complex physical processes and to handling very large quantities of experimental data. The amount of information that can be processed in a short period of time is so great that use of graphical displays assumes greater importance as a means of displaying this information. Information from dynamical processes can be displayed conveniently by use of animated graphics. This guide presents the basic techniques for generating black and white animated graphics, with consideration of aesthetic, mechanical, and computational problems. The guide is intended for use by someone whomore » wants to make movies on the National Magnetic Fusion Energy Computing Center (NMFECC) CDC-7600. Problems encountered by a geographically remote user are given particular attention. Detailed information is given that will allow a remote user to do some file checking and diagnosis before giving graphics files to the system for processing into film in order to spot problems without having to wait for film to be delivered. Source listings of some useful software are given in appendices along with descriptions of how to use it. 3 figures, 5 tables.« less

Fluctuation theorem for Hamiltonian Systems: Le Chatelier's principle

NASA Astrophysics Data System (ADS)

Evans, Denis J.; Searles, Debra J.; Mittag, Emil

2001-05-01

For thermostated dissipative systems, the fluctuation theorem gives an analytical expression for the ratio of probabilities that the time-averaged entropy production in a finite system observed for a finite time takes on a specified value compared to the negative of that value. In the past, it has been generally thought that the presence of some thermostating mechanism was an essential component of any system that satisfies a fluctuation theorem. In the present paper, we point out that a fluctuation theorem can be derived for purely Hamiltonian systems, with or without applied dissipative fields.

Translation invariant time-dependent massive gravity: Hamiltonian analysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mourad, Jihad; Steer, Danièle A.; Noui, Karim, E-mail: mourad@apc.univ-paris7.fr, E-mail: karim.noui@lmpt.univ-tours.fr, E-mail: steer@apc.univ-paris7.fr

2014-09-01

The canonical structure of the massive gravity in the first order moving frame formalism is studied. We work in the simplified context of translation invariant fields, with mass terms given by general non-derivative interactions, invariant under the diagonal Lorentz group, depending on the moving frame as well as a fixed reference frame. We prove that the only mass terms which give 5 propagating degrees of freedom are the dRGT mass terms, namely those which are linear in the lapse. We also complete the Hamiltonian analysis with the dynamical evolution of the system.

Hamiltonian models for the propagation of irrotational surface gravity waves over a variable bottom

NASA Astrophysics Data System (ADS)

Compelli, A.; Ivanov, R.; Todorov, M.

2017-12-01

A single incompressible, inviscid, irrotational fluid medium bounded by a free surface and varying bottom is considered. The Hamiltonian of the system is expressed in terms of the so-called Dirichlet-Neumann operators. The equations for the surface waves are presented in Hamiltonian form. Specific scaling of the variables is selected which leads to approximations of Boussinesq and Korteweg-de Vries (KdV) types, taking into account the effect of the slowly varying bottom. The arising KdV equation with variable coefficients is studied numerically when the initial condition is in the form of the one-soliton solution for the initial depth. This article is part of the theme issue 'Nonlinear water waves'.

Hamiltonian models for the propagation of irrotational surface gravity waves over a variable bottom.

PubMed

Compelli, A; Ivanov, R; Todorov, M

2018-01-28

A single incompressible, inviscid, irrotational fluid medium bounded by a free surface and varying bottom is considered. The Hamiltonian of the system is expressed in terms of the so-called Dirichlet-Neumann operators. The equations for the surface waves are presented in Hamiltonian form. Specific scaling of the variables is selected which leads to approximations of Boussinesq and Korteweg-de Vries (KdV) types, taking into account the effect of the slowly varying bottom. The arising KdV equation with variable coefficients is studied numerically when the initial condition is in the form of the one-soliton solution for the initial depth.This article is part of the theme issue 'Nonlinear water waves'. © 2017 The Author(s).

Hamiltonian fluid closures of the Vlasov-Ampère equations: From water-bags to N moment models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Perin, M.; Chandre, C.; Tassi, E.

2015-09-15

Moment closures of the Vlasov-Ampère system, whereby higher moments are represented as functions of lower moments with the constraint that the resulting fluid system remains Hamiltonian, are investigated by using water-bag theory. The link between the water-bag formalism and fluid models that involve density, fluid velocity, pressure and higher moments is established by introducing suitable thermodynamic variables. The cases of one, two, and three water-bags are treated and their Hamiltonian structures are provided. In each case, we give the associated fluid closures and we discuss their Casimir invariants. We show how the method can be extended to an arbitrary numbermore » of fields, i.e., an arbitrary number of water-bags and associated moments. The thermodynamic interpretation of the resulting models is discussed. Finally, a general procedure to derive Hamiltonian N-field fluid models is proposed.« less

Chern-Simons improved Hamiltonians for strings in three space dimensions

NASA Astrophysics Data System (ADS)

Gordeli, Ivan; Melnikov, Dmitry; Niemi, Antti J.; Sedrakyan, Ara

2016-07-01

In the case of a structureless string the extrinsic curvature and torsion determine uniquely its shape in three-dimensional ambient space, by way of solution of the Frenet equation. In many physical scenarios there are in addition symmetries that constrain the functional form of the ensuing energy function. For example, the energy of a structureless string should be independent of the way the string is framed in the Frenet equation. Thus the energy should only involve the curvature and torsion as dynamical variables, in a manner that resembles the Hamiltonian of the Abelian Higgs model. Here we investigate the effect of symmetry principles in the construction of Hamiltonians for structureless strings. We deduce from the concept of frame independence that in addition to extrinsic curvature and torsion, the string can also engage a three-dimensional Abelian bulk gauge field as a dynamical variable. We find that the presence of a bulk gauge field gives rise to a long-range interaction between different strings. Moreover, when this gauge field is subject to Chern-Simons self-interaction, it becomes plausible that interacting strings are subject to fractional statistics in three space dimensions.

Low-energy effective Hamiltonians for correlated electron systems beyond density functional theory

NASA Astrophysics Data System (ADS)

Hirayama, Motoaki; Miyake, Takashi; Imada, Masatoshi; Biermann, Silke

2017-08-01

We propose a refined scheme of deriving an effective low-energy Hamiltonian for materials with strong electronic Coulomb correlations beyond density functional theory (DFT). By tracing out the electronic states away from the target degrees of freedom in a controlled way by a perturbative scheme, we construct an effective Hamiltonian for a restricted low-energy target space incorporating the effects of high-energy degrees of freedom in an effective manner. The resulting effective Hamiltonian can afterwards be solved by accurate many-body solvers. We improve this "multiscale ab initio scheme for correlated electrons" (MACE) primarily in two directions by elaborating and combining two frameworks developed by Hirayama et al. [M. Hirayama, T. Miyake, and M. Imada, Phys. Rev. B 87, 195144 (2013), 10.1103/PhysRevB.87.195144] and Casula et al. [M. Casula, P. Werner, L. Vaugier, F. Aryasetiawan, T. Miyake, A. J. Millis, and S. Biermann, Phys. Rev. Lett. 109, 126408 (2012), 10.1103/PhysRevLett.109.126408]: (1) Double counting of electronic correlations between the DFT and the low-energy solver is avoided by using the constrained G W scheme; and (2) the frequency dependent interactions emerging from the partial trace summation are successfully separated into a nonlocal part that is treated following ideas by Hirayama et al. and a local part treated nonperturbatively in the spirit of Casula et al. and are incorporated into the renormalization of the low-energy dispersion. The scheme is favorably tested on the example of SrVO3.

Towards a nonperturbative calculation of weak Hamiltonian Wilson coefficients

DOE PAGES

Bruno, Mattia; Lehner, Christoph; Soni, Amarjit

2018-04-20

Here, we propose a method to compute the Wilson coefficients of the weak effective Hamiltonian to all orders in the strong coupling constant using Lattice QCD simulations. We perform our calculations adopting an unphysically light weak boson mass of around 2 GeV. We demonstrate that systematic errors for the Wilson coefficients C 1 and C 2, related to the current-current four-quark operators, can be controlled and present a path towards precise determinations in subsequent works.

Towards a nonperturbative calculation of weak Hamiltonian Wilson coefficients

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bruno, Mattia; Lehner, Christoph; Soni, Amarjit

Here, we propose a method to compute the Wilson coefficients of the weak effective Hamiltonian to all orders in the strong coupling constant using Lattice QCD simulations. We perform our calculations adopting an unphysically light weak boson mass of around 2 GeV. We demonstrate that systematic errors for the Wilson coefficients C 1 and C 2, related to the current-current four-quark operators, can be controlled and present a path towards precise determinations in subsequent works.

Towards a nonperturbative calculation of weak Hamiltonian Wilson coefficients

NASA Astrophysics Data System (ADS)

Bruno, Mattia; Lehner, Christoph; Soni, Amarjit; Rbc; Ukqcd Collaborations

2018-04-01

We propose a method to compute the Wilson coefficients of the weak effective Hamiltonian to all orders in the strong coupling constant using Lattice QCD simulations. We perform our calculations adopting an unphysically light weak boson mass of around 2 GeV. We demonstrate that systematic errors for the Wilson coefficients C1 and C2 , related to the current-current four-quark operators, can be controlled and present a path towards precise determinations in subsequent works.

TEACHER'S GUIDE TO OUTDOOR EDUCATION.

ERIC Educational Resources Information Center

RYAN, ARTHUR J.

INCLUDED ARE (1) A DESCRIPTIVE BROCHURE, AND (2) A TEACHER'S GUIDE FOR THE UNION COUNTY OUTDOOR EDUCATION CENTER. THE PROGRAM CONSISTS OF A DAY CENTER, WHICH PROVIDES ONE- AND TWO-DAY SESSIONS OF AT LEAST FOUR HOURS DURATION FOR GRADE 5 STUDENTS FROM PUBLIC AND NON-PROFIT SCHOOLS IN UNION COUNTY. THE DESCRIPTIVE BROCHURE RELATES (1) THE LOCATION…

Hamiltonian indices and rational spectral densities

NASA Technical Reports Server (NTRS)

Byrnes, C. I.; Duncan, T. E.

1980-01-01

Several (global) topological properties of various spaces of linear systems, particularly symmetric, lossless, and Hamiltonian systems, and multivariable spectral densities of fixed McMillan degree are announced. The study is motivated by a result asserting that on a connected but not simply connected manifold, it is not possible to find a vector field having a sink as its only critical point. In the scalar case, this is illustrated by showing that only on the space of McMillan degree = /Cauchy index/ = n, scalar transfer functions can one define a globally convergent vector field. This result holds both in discrete-time and for the nonautonomous case. With these motivations in mind, theorems of Bochner and Fogarty are used in showing that spaces of transfer functions defined by symmetry conditions are, in fact, smooth algebraic manifolds.

Solar Energy Installers Curriculum Guides. Book I.

ERIC Educational Resources Information Center

Walker, Gene C.

This first volume of a comprehensive curriculum guide for the heating-ventilation-air conditioning-refrigeration-solar student is designed to assist high school area vocational centers or community college instructors in the implementation and operation of comfort training programs. Following an introductory section, the guide provides job…

The Hamiltonian and Lagrangian approaches to the dynamics of nonholonomic systems

NASA Astrophysics Data System (ADS)

Koon, Wang Sang; Marsden, Jerrold E.

1997-08-01

This paper compares the Hamiltonian approach to systems with nonholonomic constraints (see [31, 2, 4, 29] and references therein) with the Lagrangian approach (see [16, 27, 9]). There are many differences in the approaches and each has its own advantages; some structures have been discovered on one side and their analogues on the other side are interesting to clarify. For example, the momentum equation and the reconstruction equation were first found on the Lagrangian side and are useful for the control theory of these systems, while the failure of the reduced two-form to be closed (i.e., the failure of the Poisson bracket to satisfy the Jacobi identity) was first noticed on the Hamiltonian side. Clarifying the relation between these approaches is important for the future development of the control theory and stability and bifurcation theory for such systems. In addition to this work, we treat, in this unified framework, a simplified model of the bicycle (see [12, 13]), which is an important underactuated (nonminimum phase) control system.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Herbert, J.M.

1997-02-01

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 Hamiltonianmore » 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.« less

Non-perturbative RPA-method implemented in the Coulomb gauge QCD Hamiltonian: From quarks and gluons to baryons and mesons

NASA Astrophysics Data System (ADS)

Yepez-Martinez, Tochtli; Civitarese, Osvaldo; Hess, Peter O.

2018-02-01

Starting from an algebraic model based on the QCD-Hamiltonian and previously applied to study meson states, we have developed an extension of it in order to explore the structure of baryon states. In developing our approach we have adapted concepts taken from group theory and non-perturbative many-body methods to describe states built from effective quarks and anti-quarks degrees of freedom. As a Hamiltonian we have used the QCD Hamiltonian written in the Coulomb Gauge, and expressed it in terms of effective quark-antiquark, di-quarks and di-antiquark excitations. To gain some insights about the relevant interactions of quarks in hadronic states, the Hamiltonian was approximately diagonalized by mapping quark-antiquark pairs and di-quarks (di-antiquarks) onto phonon states. In dealing with the structure of the vacuum of the theory, color-scalar and color-vector states are introduced to account for ground-state correlations. While the use of a purely color-scalar ground state is an obvious choice, so that colorless hadrons contain at least three quarks, the presence of coupled color-vector pairs in the ground state allows for colorless excitations resulting from the action of color objects upon it.

Spin Hamiltonian Analysis of the SMM V15 Using High Field ESR

NASA Astrophysics Data System (ADS)

Martens, Mathew; van Tol, Hans; Bertaina, Sylvain; Barbara, Bernard; Muller, Achim; Chiorescu, Irinel

2014-03-01

We have studied molecular magnets using high field / high frequency Electron Spin Resonance. Such molecular structures contain many quantum spins linked by exchange interactions and consequently their energy structure is often complex and require a good understanding of the molecular spin Hamiltonian. In particular, we studied the V15 molecule, comprised of 15 spins 1/2 and a total spin 1/2, which is a system that recently showed quantum Rabi oscillations of its total quantum spin. This type of molecule is an essential system for advancing molecular structures into quantum computing. We used high frequency characterization techniques (of hundreds of GHz) to gain insight into the exchange anisotropy interactions, crystal field, and anti-symmetric interactions present in this system. We analyzed the data using a detailed numerical analysis of spin interactions and our findings regarding the V15 spin Hamiltonian will be discussed. Supported by the NSF Cooperative Agreement Grant No. DMR-0654118 and No. NHMFL UCGP 5059, NSF grant No. DMR-0645408.

A parallel algorithm for Hamiltonian matrix construction in electron-molecule collision calculations: MPI-SCATCI

NASA Astrophysics Data System (ADS)

Al-Refaie, Ahmed F.; Tennyson, Jonathan

2017-12-01

Construction and diagonalization of the Hamiltonian matrix is the rate-limiting step in most low-energy electron - molecule collision calculations. Tennyson (1996) implemented a novel algorithm for Hamiltonian construction which took advantage of the structure of the wavefunction in such calculations. This algorithm is re-engineered to make use of modern computer architectures and the use of appropriate diagonalizers is considered. Test calculations demonstrate that significant speed-ups can be gained using multiple CPUs. This opens the way to calculations which consider higher collision energies, larger molecules and / or more target states. The methodology, which is implemented as part of the UK molecular R-matrix codes (UKRMol and UKRMol+) can also be used for studies of bound molecular Rydberg states, photoionization and positron-molecule collisions.

Bifurcation of solutions to Hamiltonian boundary value problems

NASA Astrophysics Data System (ADS)

McLachlan, R. I.; Offen, C.

2018-06-01

A bifurcation is a qualitative change in a family of solutions to an equation produced by varying parameters. In contrast to the local bifurcations of dynamical systems that are often related to a change in the number or stability of equilibria, bifurcations of boundary value problems are global in nature and may not be related to any obvious change in dynamical behaviour. Catastrophe theory is a well-developed framework which studies the bifurcations of critical points of functions. In this paper we study the bifurcations of solutions of boundary-value problems for symplectic maps, using the language of (finite-dimensional) singularity theory. We associate certain such problems with a geometric picture involving the intersection of Lagrangian submanifolds, and hence with the critical points of a suitable generating function. Within this framework, we then study the effect of three special cases: (i) some common boundary conditions, such as Dirichlet boundary conditions for second-order systems, restrict the possible types of bifurcations (for example, in generic planar systems only the A-series beginning with folds and cusps can occur); (ii) integrable systems, such as planar Hamiltonian systems, can exhibit a novel periodic pitchfork bifurcation; and (iii) systems with Hamiltonian symmetries or reversing symmetries can exhibit restricted bifurcations associated with the symmetry. This approach offers an alternative to the analysis of critical points in function spaces, typically used in the study of bifurcation of variational problems, and opens the way to the detection of more exotic bifurcations than the simple folds and cusps that are often found in examples.

Curriculum Based Functional Vocational Assessment Guide. Correlation of the Life Centered Career Education Curriculum with Specific Occupational Programs, Standards of Work Performance, and Campus Assessment Instruments.

ERIC Educational Resources Information Center

Quinones, William A.

This document is a guide developed for the Dallas Independent School District's (DISD's) Multiple Careers Magnet Center, which provides special education students with training in standards of work performance and specific occupational skills for successful transition to community life and employment. The document also provides information for…

Ab Initio Effective Rovibrational Hamiltonians for Non-Rigid Molecules via Curvilinear VMP2

NASA Astrophysics Data System (ADS)

Changala, Bryan; Baraban, Joshua H.

2017-06-01

Accurate predictions of spectroscopic constants for non-rigid molecules are particularly challenging for ab initio theory. For all but the smallest systems, ``brute force'' diagonalization of the full rovibrational Hamiltonian is computationally prohibitive, leaving us at the mercy of perturbative approaches. However, standard perturbative techniques, such as second order vibrational perturbation theory (VPT2), are based on the approximation that a molecule makes small amplitude vibrations about a well defined equilibrium structure. Such assumptions are physically inappropriate for non-rigid systems. In this talk, we will describe extensions to curvilinear vibrational Møller-Plesset perturbation theory (VMP2) that account for rotational and rovibrational effects in the molecular Hamiltonian. Through several examples, we will show that this approach provides predictions to nearly microwave accuracy of molecular constants including rotational and centrifugal distortion parameters, Coriolis coupling constants, and anharmonic vibrational and tunneling frequencies.

Fourier series expansion for nonlinear Hamiltonian oscillators.

PubMed

Méndez, Vicenç; Sans, Cristina; Campos, Daniel; Llopis, Isaac

2010-06-01

The problem of nonlinear Hamiltonian oscillators is one of the classical questions in physics. When an analytic solution is not possible, one can resort to obtaining a numerical solution or using perturbation theory around the linear problem. We apply the Fourier series expansion to find approximate solutions to the oscillator position as a function of time as well as the period-amplitude relationship. We compare our results with other recent approaches such as variational methods or heuristic approximations, in particular the Ren-He's method. Based on its application to the Duffing oscillator, the nonlinear pendulum and the eardrum equation, it is shown that the Fourier series expansion method is the most accurate.

Classical Coset Hamiltonian for the Electronic Motion and its Application to Anderson Localization and Hammett Equation

NASA Astrophysics Data System (ADS)

Xing, Guan; Wu, Guo-Zhen

2001-02-01

A classical coset Hamiltonian is introduced for the system of one electron in multi-sites. By this Hamiltonian, the dynamical behaviour of the electronic motion can be readily simulated. The simulation reproduces the retardation of the electron density decay in a lattice with site energies randomly distributed - an analogy with Anderson localization. This algorithm is also applied to reproduce the Hammett equation which relates the reaction rate with the property of the substitutions in the organic chemical reactions. The advantages and shortcomings of this algorithm, as contrasted with traditional quantum methods such as the molecular orbital theory, are also discussed.

Polynomial approximation of Poincare maps for Hamiltonian system

NASA Technical Reports Server (NTRS)

Froeschle, Claude; Petit, Jean-Marc

1992-01-01

Different methods are proposed and tested for transforming a non-linear differential system, and more particularly a Hamiltonian one, into a map without integrating the whole orbit as in the well-known Poincare return map technique. We construct piecewise polynomial maps by coarse-graining the phase-space surface of section into parallelograms and using either only values of the Poincare maps at the vertices or also the gradient information at the nearest neighbors to define a polynomial approximation within each cell. The numerical experiments are in good agreement with both the real symplectic and Poincare maps.

Solar Energy Installers Curriculum Guides. Book II.

ERIC Educational Resources Information Center

Walker, Gene C.

This second volume of a comprehensive curriculum guide for the heating-ventilation-air conditioning-refrigeration-solar student is designed to assist high school area vocational centers or community college instructors in the implementation and operation of comfort training programs. The guide is comprised of ten units of instruction within three…

Design Guide for Interiors

DTIC Science & Technology

1997-09-01

Medical Center. Ft. Lewis, WA. 3. Auditorium, Senior NCO Academy. Gunter AFB, AL. 4. Snack Bar, Senior NCO Academy. Gunter AFB, AL. 5. Atrium, Marshall...and enable people to perform to their maximum potential. ivGuide to Excellent Interiors Clinic Waiting, Minot AFB Auditorium, Gunter AFB Snack Shop...Medical Center. Ft. Lewis, WA. 3. Auditorium, Senior NCO Academy. Gunter AFB, AL. 4. Snack Bar, Senior NCO Academy. Gunter AFB, AL. 5. Atrium, Marshall Hall

A Keplerian-based Hamiltonian splitting for gravitational N-body simulations

NASA Astrophysics Data System (ADS)

Gonçalves Ferrari, G.; Boekholt, T.; Portegies Zwart, S. F.

2014-05-01

We developed a Keplerian-based Hamiltonian splitting for solving the gravitational N-body problem. This splitting allows us to approximate the solution of a general N-body problem by a composition of multiple, independently evolved two-body problems. While the Hamiltonian splitting is exact, we show that the composition of independent two-body problems results in a non-symplectic non-time-symmetric first-order map. A time-symmetric second-order map is then constructed by composing this basic first-order map with its self-adjoint. The resulting method is precise for each individual two-body solution and produces quick and accurate results for near-Keplerian N-body systems, like planetary systems or a cluster of stars that orbit a supermassive black hole. The method is also suitable for integration of N-body systems with intrinsic hierarchies, like a star cluster with primordial binaries. The superposition of Kepler solutions for each pair of particles makes the method excellently suited for parallel computing; we achieve ≳64 per cent efficiency for only eight particles per core, but close to perfect scaling for 16 384 particles on a 128 core distributed-memory computer. We present several implementations in SAKURA, one of which is publicly available via the AMUSE framework.

A systematic study of finite BRST-BFV transformations in generalized Hamiltonian formalism

NASA Astrophysics Data System (ADS)

Batalin, Igor A.; Lavrov, Peter M.; Tyutin, Igor V.

2014-09-01

We study systematically finite BRST-BFV transformations in the generalized Hamiltonian formalism. We present explicitly their Jacobians and the form of a solution to the compensation equation determining the functional field dependence of finite Fermionic parameters, necessary to generate an arbitrary finite change of gauge-fixing functions in the path integral.

Intravascular ultrasound guided directional atherectomy versus directional atherectomy guided by angiography for the treatment of femoropopliteal in-stent restenosis.

PubMed

Krishnan, Prakash; Tarricone, Arthur; K-Raman, Purushothaman; Majeed, Farhan; Kapur, Vishal; Gujja, Karthik; Wiley, Jose; Vasquez, Miguel; Lascano, Rheoneil A; Quiles, Katherine G; Distin, Tashanne; Fontenelle, Ran; Atallah-Lajam, Farah; Kini, Annapoorna; Sharma, Samin

2018-01-01

The aim of this study was to compare 1-year outcomes for patients with femoropopliteal in-stent restenosis using directional atherectomy guided by intravascular ultrasound (IVUS) versus directional atherectomy guided by angiography. This was a retrospective analysis for patients with femoropopliteal in-stent restenosis treated with IVUS-guided directional atherectomy versus directional atherectomy guided by angiography from a single center between March 2012 and February 2016. Clinically driven target lesion revascularization was the primary endpoint and was evaluated through medical chart review as well as phone call follow up. Directional atherectomy guided by IVUS reduces clinically driven target lesion revascularization for patients with femoropopliteal in-stent restenosis.

Phenomenological implications of an alternative Hamiltonian constraint for quantum cosmology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kagan, Mikhail

2005-11-15

In this paper we review a model based on loop quantum cosmology that arises from a symmetry reduction of the self-dual Plebanski action. In this formulation the symmetry reduction leads to a very simple Hamiltonian constraint that can be quantized explicitly in the framework of loop quantum cosmology. We investigate the phenomenological implications of this model in the semiclassical regime and compare those with the known results of the standard Loop Quantum Cosmology.

Child Development Associate. Learning Centers.

ERIC Educational Resources Information Center

Oscar Rose Junior Coll., Midwest City, OK.

One of a series of 18, this Child Development Associate (CDA) training module provides a guide to the construction of learning centers in preschool settings. Upon completion of the module the CDA trainee is expected to be able to analyze and improve the arrangement of space, materials and equipment; specify and rotate learning centers in the…

Studies of the spin Hamiltonian parameters and local structure for ZnO:Cu2+.

PubMed

Wu, Shao-Yi; Wei, Li-Hua; Zhang, Zhi-Hong; Wang, Xue-Feng; Hu, Yue-Xia

2008-12-15

The spin Hamiltonian parameters (the g factors and the hyperfine structure constants) and local structure for ZnO:Cu2+ are theoretically studied from the perturbation formulas of these parameters for a 3d9 ion under trigonally distorted tetrahedra. The ligand orbital and spin-orbit coupling contributions are taken into account from the cluster approach due to the significant covalency of the [CuO4](6-) cluster. According to the investigations, the impurity Cu2+ is suggested not to locate on the ideal Zn2+ site in ZnO but to undergo a slight outward displacement (approximately 0.01 angstroms) away from the ligand triangle along C3 axis. The calculated spin Hamiltonian parameters are in good agreement with the observed values. The validity of the above impurity displacement is also discussed.

The Effect of Student-Centered Approaches on Students' Interest and Achievement in Science: Relevant Topic-Based, Open and Guided Inquiry-Based, and Discussion-Based Approaches

NASA Astrophysics Data System (ADS)

Kang, Jingoo; Keinonen, Tuula

2017-04-01

Since students have lost their interest in school science, several student-centered approaches, such as using topics that are relevant for students, inquiry-based learning, and discussion-based learning have been implemented to attract pupils into science. However, the effect of these approaches was usually measured in small-scale research, and thus, the large-scale evidence supporting student-centered approaches in general use is insufficient. Accordingly, this study aimed to investigate the effect of student-centered approaches on students' interest and achievement by analyzing a large-scale data set derived from Program for International Student Assessment (PISA) 2006, to add evidence for advocating these approaches in school science, and to generalize the effects on a large population. We used Finnish PISA 2006 data, which is the most recent data that measures science literacy and that contains relevant variables for the constructs of this study. As a consequence of the factor analyses, four teaching methods were grouped as student-centered approaches (relevant topic-based, open and guided inquiry-based, and discussion-based approaches in school science) from the Finnish PISA 2006 sample. The structural equation modeling result indicated that using topics relevant for students positively affected students' interest and achievement in science. Guided inquiry-based learning was also indicated as a strong positive predictor for students' achievement, and its effect was also positively associated with students' interest. On the other hand, open inquiry-based learning was indicated as a strong negative predictor for students' achievement, as was using discussion in school science. Implications and limitations of the study were discussed.

Stability of equilibrium solutions of Hamiltonian systems with n-degrees of freedom and single resonance in the critical case

NASA Astrophysics Data System (ADS)

dos Santos, Fabio; Vidal, Claudio

2018-04-01

In this paper we give new results for the stability of one equilibrium solution of an autonomous analytic Hamiltonian system in a neighborhood of the equilibrium point with n-degrees of freedom. Our Main Theorem generalizes several results existing in the literature and mainly we give information in the critical cases (i.e., the condition of stability and instability is not fulfilled). In particular, our Main Theorem provides necessary and sufficient conditions for stability of the equilibrium solutions under the existence of a single resonance. Using analogous tools used in the Main Theorem for the critical case, we study the stability or instability of degenerate equilibrium points in Hamiltonian systems with one degree of freedom. We apply our results to the stability of Hamiltonians of the type of cosmological models as in planar as in the spatial case.

Implementation of rigorous renormalization group method for ground space and low-energy states of local Hamiltonians

NASA Astrophysics Data System (ADS)

Roberts, Brenden; Vidick, Thomas; Motrunich, Olexei I.

2017-12-01

The success of polynomial-time tensor network methods for computing ground states of certain quantum local Hamiltonians has recently been given a sound theoretical basis by Arad et al. [Math. Phys. 356, 65 (2017), 10.1007/s00220-017-2973-z]. The convergence proof, however, relies on "rigorous renormalization group" (RRG) techniques which differ fundamentally from existing algorithms. We introduce a practical adaptation of the RRG procedure which, while no longer theoretically guaranteed to converge, finds matrix product state ansatz approximations to the ground spaces and low-lying excited spectra of local Hamiltonians in realistic situations. In contrast to other schemes, RRG does not utilize variational methods on tensor networks. Rather, it operates on subsets of the system Hilbert space by constructing approximations to the global ground space in a treelike manner. We evaluate the algorithm numerically, finding similar performance to density matrix renormalization group (DMRG) in the case of a gapped nondegenerate Hamiltonian. Even in challenging situations of criticality, large ground-state degeneracy, or long-range entanglement, RRG remains able to identify candidate states having large overlap with ground and low-energy eigenstates, outperforming DMRG in some cases.

Higher Order First Integrals of Motion in a Gauge Covariant Hamiltonian Framework

NASA Astrophysics Data System (ADS)

Visinescu, Mihai

The higher order symmetries are investigated in a covariant Hamiltonian formulation. The covariant phase-space approach is extended to include the presence of external gauge fields and scalar potentials. The special role of the Killing-Yano tensors is pointed out. Some nontrivial examples involving Runge-Lenz type conserved quantities are explicitly worked out.

Internet Protocol Implementation Guide.

DTIC Science & Technology

1982-08-01

RD-R153 624 INTERNET PROTOCOL IMPLEMENTATION GIDE(U) SRI 1/2 INTERNATIONAL MENLO PARK CA NETWORK INFORMATION CENTER AUG 82 DCA2e-83-C-8e25 N... INTERNET PROTOCOL S IMPLEMENTATION GUIDE August 1982 DTICFL. !.ECTE .-" MAY 1 31985 ;z B Q.. Network Information Center SRI International Menlo Park...this is more information than the receiving Internet * module needs. The specified procedure is to take the return route recorded in the first

Universal formulation of second-order generalized Møller-Plesset perturbation theory for a spin-dependent two-component relativistic many-electron Hamiltonian

NASA Astrophysics Data System (ADS)

Nakano, Masahiko; Seino, Junji; Nakai, Hiromi

2017-05-01

We have derived and implemented a universal formulation of the second-order generalized Møller-Plesset perturbation theory (GMP2) for spin-dependent (SD) two-component relativistic many-electron Hamiltonians, such as the infinite-order Douglas-Kroll-Hess Hamiltonian for many-electron systems, which is denoted as IODKH/IODKH. Numerical assessments for He- and Ne-like atoms and 16 diatomic molecules show that the MP2 correlation energies with IODKH/IODKH agree well with those calculated with the four-component Dirac-Coulomb (DC) Hamiltonian, indicating a systematic improvement on the inclusion of relativistic two-electron terms. The present MP2 scheme for IODKH/IODKH is demonstrated to be computationally more efficient than that for DC.

Stability of Poisson Equilibria and Hamiltonian Relative Equilibria by Energy Methods

NASA Astrophysics Data System (ADS)

Patrick, George W.; Roberts, Mark; Wulff, Claudia

2004-12-01

We develop a general stability theory for equilibrium points of Poisson dynamical systems and relative equilibria of Hamiltonian systems with symmetries, including several generalisations of the Energy-Casimir and Energy-Momentum Methods. Using a topological generalisation of Lyapunov’s result that an extremal critical point of a conserved quantity is stable, we show that a Poisson equilibrium is stable if it is an isolated point in the intersection of a level set of a conserved function with a subset of the phase space that is related to the topology of the symplectic leaf space at that point. This criterion is applied to generalise the energy-momentum method to Hamiltonian systems which are invariant under non-compact symmetry groups for which the coadjoint orbit space is not Hausdorff. We also show that a G-stable relative equilibrium satisfies the stronger condition of being A-stable, where A is a specific group-theoretically defined subset of G which contains the momentum isotropy subgroup of the relative equilibrium. The results are illustrated by an application to the stability of a rigid body in an ideal irrotational fluid.

Topological Band Theory for Non-Hermitian Hamiltonians

NASA Astrophysics Data System (ADS)

Shen, Huitao; Zhen, Bo; Fu, Liang

2018-04-01

We develop the topological band theory for systems described by non-Hermitian Hamiltonians, whose energy spectra are generally complex. After generalizing the notion of gapped band structures to the non-Hermitian case, we classify "gapped" bands in one and two dimensions by explicitly finding their topological invariants. We find nontrivial generalizations of the Chern number in two dimensions, and a new classification in one dimension, whose topology is determined by the energy dispersion rather than the energy eigenstates. We then study the bulk-edge correspondence and the topological phase transition in two dimensions. Different from the Hermitian case, the transition generically involves an extended intermediate phase with complex-energy band degeneracies at isolated "exceptional points" in momentum space. We also systematically classify all types of band degeneracies.

Investigation of timing effects in modified composite quadrupolar echo pulse sequences by mean of average Hamiltonian theory

NASA Astrophysics Data System (ADS)

Mananga, Eugene Stephane

2018-01-01

The utility of the average Hamiltonian theory and its antecedent the Magnus expansion is presented. We assessed the concept of convergence of the Magnus expansion in quadrupolar spectroscopy of spin-1 via the square of the magnitude of the average Hamiltonian. We investigated this approach for two specific modified composite pulse sequences: COM-Im and COM-IVm. It is demonstrated that the size of the square of the magnitude of zero order average Hamiltonian obtained on the appropriated basis is a viable approach to study the convergence of the Magnus expansion. The approach turns to be efficient in studying pulse sequences in general and can be very useful to investigate coherent averaging in the development of high resolution NMR technique in solids. This approach allows comparing theoretically the two modified composite pulse sequences COM-Im and COM-IVm. We also compare theoretically the current modified composite sequences (COM-Im and COM-IVm) to the recently published modified composite pulse sequences (MCOM-I, MCOM-IV, MCOM-I_d, MCOM-IV_d).

Coupled tensorial forms of the second-order effective Hamiltonian for open-subshell atoms in jj-coupling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jursenas, Rytis, E-mail: Rytis.Jursenas@tfai.vu.l; Merkelis, Gintaras

2011-01-15

General expressions for the second-order effective atomic Hamiltonian are derived for open-subshell atoms in jj-coupling. The expansion terms are presented as N-body (N=0,1,2,3) effective operators given in the second quantization representation in coupled tensorial form. Two alternative coupled tensorial forms for each expansion term have been developed. To reduce the number of expressions of the effective Hamiltonian, the reduced matrix elements of antisymmetric two-particle wavefunctions are involved in the consideration. The general expressions presented allow the determination of the spin-angular part of expansion terms when studying correlation effects dealing with a number of problems in atomic structure calculations.

Systems of conservation laws with third-order Hamiltonian structures

NASA Astrophysics Data System (ADS)

Ferapontov, Evgeny V.; Pavlov, Maxim V.; Vitolo, Raffaele F.

2018-06-01

We investigate n-component systems of conservation laws that possess third-order Hamiltonian structures of differential-geometric type. The classification of such systems is reduced to the projective classification of linear congruences of lines in P^{n+2} satisfying additional geometric constraints. Algebraically, the problem can be reformulated as follows: for a vector space W of dimension n+2, classify n-tuples of skew-symmetric 2-forms A^{α } \\in Λ^2(W) such that φ _{β γ }A^{β }\\wedge A^{γ }=0, for some non-degenerate symmetric φ.

Hamiltonian of Mean Force and Dissipative Scalar Field Theory

NASA Astrophysics Data System (ADS)

Jafari, Marjan; Kheirandish, Fardin

2018-04-01

Quantum dynamics of a dissipative scalar field is investigated. Using the Hamiltonian of mean force, internal energy, free energy and entropy of a dissipative scalar field are obtained. It is shown that a dissipative massive scalar field can be considered as a free massive scalar field described by an effective mass and dispersion relation. Internal energy of the scalar field, as the subsystem, is found in the limit of low temperature and weak and strong couplings to an Ohimc heat bath. Correlation functions for thermal and coherent states are derived.

Outcomes of microscope-integrated intraoperative optical coherence tomography-guided center-sparing internal limiting membrane peeling for myopic traction maculopathy: a novel technique.

PubMed

Kumar, Atul; Ravani, Raghav; Mehta, Aditi; Simakurthy, Sriram; Dhull, Chirakshi

2017-07-04

To evaluate the outcomes of pars plana vitrectomy (PPV) with microscope-integrated intraoperative optical coherence tomography (I-OCT)-guided traction removal and center-sparing internal limiting membrane (cs-ILM) peeling. Nine eyes with myopic traction maculopathy as diagnosed on SD-OCT underwent PPV with I-OCT-guided cs-ILM peeling and were evaluated prospectively for resolution of central macular thickness (CMT) and improvement in best-corrected visual acuity (BCVA), and complications, if any, were noted. All patients were followed up for more than 9 months. Resolution of the macular retinoschisis was seen in all nine eyes on SD-OCT. At 36 weeks, there was a significant improvement in mean BCVA from the preoperative BCVA (P = 0.0089) along with a reduction in the CMT from 569.77 ± 263.19 to 166.0 ± 43.91 um (P = 0.0039). None of the eyes showed worsening of BCVA or development of full-thickness macular hole in the intraoperative or follow-up period. PPV with I-OCT-guided cs-ILM peeling helps in complete removal of traction, resolution of retinoschisis and good functional recovery with low intraoperative and postoperative complications.

Higher-Order Hamiltonian Model for Unidirectional Water Waves

NASA Astrophysics Data System (ADS)

Bona, J. L.; Carvajal, X.; Panthee, M.; Scialom, M.

2018-04-01

Formally second-order correct, mathematical descriptions of long-crested water waves propagating mainly in one direction are derived. These equations are analogous to the first-order approximations of KdV- or BBM-type. The advantage of these more complex equations is that their solutions corresponding to physically relevant initial perturbations of the rest state may be accurate on a much longer timescale. The initial value problem for the class of equations that emerges from our derivation is then considered. A local well-posedness theory is straightforwardly established by a contraction mapping argument. A subclass of these equations possess a special Hamiltonian structure that implies the local theory can be continued indefinitely.

Environmental Studies. Plano Outdoor Learning Center.

ERIC Educational Resources Information Center

Plano Independent School District, TX.

This curriculum guide for the Plano Intermediate School District (Texas) Outdoor Learning Center is divided into three major sections. Section I provides information on the numbered stations/posts found along the perimeter and inner trails of the center and includes brief comments on the philosophy of environmental education and the history…

An Automation Survival Guide for Media Centers.

ERIC Educational Resources Information Center

Whaley, Roger E.

1989-01-01

Reviews factors that should affect the decision to automate a school media center and offers suggestions for the automation process. Topics discussed include getting the library collection ready for automation, deciding what automated functions are needed, evaluating software vendors, selecting software, and budgeting. (CLB)

Hispanic/Latino Natural Support Systems. CSAP Implementation Guide.

ERIC Educational Resources Information Center

Acosta, Annie; Hamel, Vicki

This guide is intended to share knowledge about the Hispanic/Latino community with Center for Substance Abuse Prevention (CSAP) grant recipients and to help them develop effective prevention services responsive to the communities they serve. The guide: (1) highlights specific characteristics of the Hispanic and Latino communities that affect…

Equivalent theories redefine Hamiltonian observables to exhibit change in general relativity

NASA Astrophysics Data System (ADS)

Pitts, J. Brian

2017-03-01

Change and local spatial variation are missing in canonical General Relativity’s observables as usually defined, an aspect of the problem of time. Definitions can be tested using equivalent formulations of a theory, non-gauge and gauge, because they must have equivalent observables and everything is observable in the non-gauge formulation. Taking an observable from the non-gauge formulation and finding the equivalent in the gauge formulation, one requires that the equivalent be an observable, thus constraining definitions. For massive photons, the de Broglie-Proca non-gauge formulation observable {{A}μ} is equivalent to the Stueckelberg-Utiyama gauge formulation quantity {{A}μ}+{{\\partial}μ}φ, which must therefore be an observable. To achieve that result, observables must have 0 Poisson bracket not with each first-class constraint, but with the Rosenfeld-Anderson-Bergmann-Castellani gauge generator G, a tuned sum of first-class constraints, in accord with the Pons-Salisbury-Sundermeyer definition of observables. The definition for external gauge symmetries can be tested using massive gravity, where one can install gauge freedom by parametrization with clock fields X A . The non-gauge observable {{g}μ ν} has the gauge equivalent {{X}A}{{,}μ}{{g}μ ν}{{X}B}{{,}ν}. The Poisson bracket of {{X}A}{{,}μ}{{g}μ ν}{{X}B}{{,}ν} with G turns out to be not 0 but a Lie derivative. This non-zero Poisson bracket refines and systematizes Kuchař’s proposal to relax the 0 Poisson bracket condition with the Hamiltonian constraint. Thus observables need covariance, not invariance, in relation to external gauge symmetries. The Lagrangian and Hamiltonian for massive gravity are those of General Relativity  +   Λ   +  4 scalars, so the same definition of observables applies to General Relativity. Local fields such as {{g}μ ν} are observables. Thus observables change. Requiring equivalent observables for equivalent theories also recovers Hamiltonian

Intravascular ultrasound guided directional atherectomy versus directional atherectomy guided by angiography for the treatment of femoropopliteal in-stent restenosis

PubMed Central

Krishnan, Prakash; Tarricone, Arthur; K-Raman, Purushothaman; Majeed, Farhan; Kapur, Vishal; Gujja, Karthik; Wiley, Jose; Vasquez, Miguel; Lascano, Rheoneil A.; Quiles, Katherine G.; Distin, Tashanne; Fontenelle, Ran; Atallah-Lajam, Farah; Kini, Annapoorna; Sharma, Samin

2017-01-01

Background: The aim of this study was to compare 1-year outcomes for patients with femoropopliteal in-stent restenosis using directional atherectomy guided by intravascular ultrasound (IVUS) versus directional atherectomy guided by angiography. Methods and results: This was a retrospective analysis for patients with femoropopliteal in-stent restenosis treated with IVUS-guided directional atherectomy versus directional atherectomy guided by angiography from a single center between March 2012 and February 2016. Clinically driven target lesion revascularization was the primary endpoint and was evaluated through medical chart review as well as phone call follow up. Conclusions: Directional atherectomy guided by IVUS reduces clinically driven target lesion revascularization for patients with femoropopliteal in-stent restenosis. PMID:29265002

Community Learning Centers

ERIC Educational Resources Information Center

Jennings, Wayne

2005-01-01

The Community Learning Centers plan provides a systemically changed model for the 21st century. This top-to-bottom transformation of current education addresses all aspects of schools with a detailed framework to guide serious educational reformers. This fresh approach to principles of learning, curriculum, staffing, facilities, student as…

Hamiltonian Monte Carlo Inversion of Seismic Sources in Complex Media

NASA Astrophysics Data System (ADS)

Fichtner, A.; Simutė, S.

2017-12-01

We present a probabilistic seismic source inversion method that properly accounts for 3D heterogeneous Earth structure and provides full uncertainty information on the timing, location and mechanism of the event. Our method rests on two essential elements: (1) reciprocity and spectral-element simulations in complex media, and (2) Hamiltonian Monte Carlo sampling that requires only a small amount of test models. Using spectral-element simulations of 3D, visco-elastic, anisotropic wave propagation, we precompute a data base of the strain tensor in time and space by placing sources at the positions of receivers. Exploiting reciprocity, this receiver-side strain data base can be used to promptly compute synthetic seismograms at the receiver locations for any hypothetical source within the volume of interest. The rapid solution of the forward problem enables a Bayesian solution of the inverse problem. For this, we developed a variant of Hamiltonian Monte Carlo (HMC) sampling. Taking advantage of easily computable derivatives, HMC converges to the posterior probability density with orders of magnitude less samples than derivative-free Monte Carlo methods. (Exact numbers depend on observational errors and the quality of the prior). We apply our method to the Japanese Islands region where we previously constrained 3D structure of the crust and upper mantle using full-waveform inversion with a minimum period of around 15 s.

Recommendations for Child Care Centers. Revised Edition.

ERIC Educational Resources Information Center

Moore, Gary T.; Lane, Carol G.; Hill, Ann B.; Cohen, Uriel; McGinty, Tim

Part of a seven-volume series on children's environments, this monograph is a design guide for policy, planning, programming, design, and evaluation of early childhood facilities. The design guide includes 115 patterns for large, medium, and small child care centers in neighborhood and work-place settings. Many of the patterns are appropriate also…

On the structure of the two-stream instability–complex G-Hamiltonian structure and Krein collisions between positive- and negative-action modes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Ruili; Liu, Jian; Xiao, Jianyuan

2016-07-15

The two-stream instability is probably the most important elementary example of collective instabilities in plasma physics and beam-plasma systems. For a warm plasma with two charged particle species, the instability diagram of the two-stream instability based on a 1D warm-fluid model exhibits an interesting band structure that has not been explained. We show that the band structure for this instability is the consequence of the Hamiltonian nature of the warm two-fluid system. Interestingly, the Hamiltonian nature manifests as a complex G-Hamiltonian structure in wave-number space, which directly determines the instability diagram. Specifically, it is shown that the boundaries between themore » stable and unstable regions are locations for Krein collisions between eigenmodes with different Krein signatures. In terms of physics, this rigorously implies that the system is destabilized when a positive-action mode resonates with a negative-action mode, and that this is the only mechanism by which the system can be destabilized. It is anticipated that this physical mechanism of destabilization is valid for other collective instabilities in conservative systems in plasma physics, accelerator physics, and fluid dynamics systems, which admit infinite-dimensional Hamiltonian structures.« less

Cataloging Guide for Instructional Materials Used in Livonia Public Schools Instructional Materials Centers.

ERIC Educational Resources Information Center

Livonia Public Schools, MI.

This working guide for Livonia's Public Schools provides detailed instructions in preparing and handling catalog cards, a supplemental cataloging and classification guide, and typing rules for technical processing. Standard abbreviations are given for making classification entries, and separate cataloging instructions are given for charts,…

Key Skills Portfolio Assessment: Good Practice Guide

ERIC Educational Resources Information Center

Rolfe, Martin; Wilson, Lorraine

2007-01-01

This guide offers advice and guidance to key skills managers, coordinators and other practitioners who are responsible for ensuring that the standards of portfolio assessment in their center are consistent across the center and with national standards. It describes and offers advice and guidance on the stages of assessment and internal moderation…

A Kentucky Journey--African American Heritage. Teacher's Guide.

ERIC Educational Resources Information Center

Kentucky Historical Society, Frankfort.

This guide to the core exhibit of the Kentucky History Center (Frankfort) focuses on African American history in the commonwealth of Kentucky. The guide extracts text from seven of the exhibit's chronological areas and lists environments, displays, and other exhibit features to help students understand some of the events that shaped the African…

Colorado Outdoor Education Center Teacher's Field Guide.

ERIC Educational Resources Information Center

Colorado Outdoor Education Center, Inc., Florissant.

The Colorado Outdoor Education Center aims to educate the total person by offering programs which help each individual to gain a sense of the earth, of community, and of self. At High Trails the students are brought into direct contact with nature, utilizing small groups and emphasizing direct experiences. The integrated, multi-disciplinary…

Does a Single Eigenstate Encode the Full Hamiltonian?

NASA Astrophysics Data System (ADS)

Garrison, James R.; Grover, Tarun

2018-04-01

The eigenstate thermalization hypothesis (ETH) posits that the reduced density matrix for a subsystem corresponding to an excited eigenstate is "thermal." Here we expound on this hypothesis by asking: For which class of operators, local or nonlocal, is ETH satisfied? We show that this question is directly related to a seemingly unrelated question: Is the Hamiltonian of a system encoded within a single eigenstate? We formulate a strong form of ETH where, in the thermodynamic limit, the reduced density matrix of a subsystem corresponding to a pure, finite energy density eigenstate asymptotically becomes equal to the thermal reduced density matrix, as long as the subsystem size is much less than the total system size, irrespective of how large the subsystem is compared to any intrinsic length scale of the system. This allows one to access the properties of the underlying Hamiltonian at arbitrary energy densities (or temperatures) using just a single eigenstate. We provide support for our conjecture by performing an exact diagonalization study of a nonintegrable 1D quantum lattice model with only energy conservation. In addition, we examine the case in which the subsystem size is a finite fraction of the total system size, and we find that, even in this case, many operators continue to match their canonical expectation values, at least approximately. In particular, the von Neumann entanglement entropy equals the thermal entropy as long as the subsystem is less than half the total system. Our results are consistent with the possibility that a single eigenstate correctly predicts the expectation values of all operators with support on less than half the total system, as long as one uses a microcanonical ensemble with vanishing energy width for comparison. We also study, both analytically and numerically, a particle-number conserving model at infinite temperature that substantiates our conjectures.

Open quantum systems, effective Hamiltonians, and device characterization

NASA Astrophysics Data System (ADS)

Duffus, S. N. A.; Dwyer, V. M.; Everitt, M. J.

2017-10-01

High fidelity models, which are able to both support accurate device characterization and correctly account for environmental effects, are crucial to the engineering of scalable quantum technologies. As it ensures positivity of the density matrix, one preferred model of open systems describes the dynamics with a master equation in Lindblad form. In practice, Linblad operators are rarely derived from first principles, and often a particular form of annihilator is assumed. This results in dynamical models that miss those additional terms which must generally be added for the master equation to assume the Lindblad form, together with the other concomitant terms that must be assimilated into an effective Hamiltonian to produce the correct free evolution. In first principles derivations, such additional terms are often canceled (or countered), frequently in a somewhat ad hoc manner, leading to a number of competing models. Whilst the implications of this paper are quite general, to illustrate the point we focus here on an example anharmonic system; specifically that of a superconducting quantum interference device (SQUID) coupled to an Ohmic bath. The resulting master equation implies that the environment has a significant impact on the system's energy; we discuss the prospect of keeping or canceling this impact and note that, for the SQUID, monitoring the magnetic susceptibility under control of the capacitive coupling strength and the externally applied flux results in experimentally measurable differences between a number of these models. In particular, one should be able to determine whether a squeezing term of the form X ̂P ̂+P ̂X ̂ should be present in the effective Hamiltonian or not. If model generation is not performed correctly, device characterization will be prone to systemic errors.

Enhanced conformational sampling using replica exchange with concurrent solute scaling and hamiltonian biasing realized in one dimension.

PubMed

Yang, Mingjun; Huang, Jing; MacKerell, Alexander D

2015-06-09

Replica exchange (REX) is a powerful computational tool for overcoming the quasi-ergodic sampling problem of complex molecular systems. Recently, several multidimensional extensions of this method have been developed to realize exchanges in both temperature and biasing potential space or the use of multiple biasing potentials to improve sampling efficiency. However, increased computational cost due to the multidimensionality of exchanges becomes challenging for use on complex systems under explicit solvent conditions. In this study, we develop a one-dimensional (1D) REX algorithm to concurrently combine the advantages of overall enhanced sampling from Hamiltonian solute scaling and the specific enhancement of collective variables using Hamiltonian biasing potentials. In the present Hamiltonian replica exchange method, termed HREST-BP, Hamiltonian solute scaling is applied to the solute subsystem, and its interactions with the environment to enhance overall conformational transitions and biasing potentials are added along selected collective variables associated with specific conformational transitions, thereby balancing the sampling of different hierarchical degrees of freedom. The two enhanced sampling approaches are implemented concurrently allowing for the use of a small number of replicas (e.g., 6 to 8) in 1D, thus greatly reducing the computational cost in complex system simulations. The present method is applied to conformational sampling of two nitrogen-linked glycans (N-glycans) found on the HIV gp120 envelope protein. Considering the general importance of the conformational sampling problem, HREST-BP represents an efficient procedure for the study of complex saccharides, and, more generally, the method is anticipated to be of general utility for the conformational sampling in a wide range of macromolecular systems.

Normalization of Hamiltonian and nonlinear stability of the triangular equilibrium points in non-resonance case with perturbations

NASA Astrophysics Data System (ADS)

Kishor, Ram; Kushvah, Badam Singh

2017-09-01

For the study of nonlinear stability of a dynamical system, normalized Hamiltonian of the system is very important to discuss the dynamics in the vicinity of invariant objects. In general, it represents a nonlinear approximation to the dynamics, which is very helpful to obtain the information as regards a realistic solution of the problem. In the present study, normalization of the Hamiltonian and analysis of nonlinear stability in non-resonance case, in the Chermnykh-like problem under the influence of perturbations in the form of radiation pressure, oblateness, and a disc is performed. To describe nonlinear stability, initially, quadratic part of the Hamiltonian is normalized in the neighborhood of triangular equilibrium point and then higher order normalization is performed by computing the fourth order normalized Hamiltonian with the help of Lie transforms. In non-resonance case, nonlinear stability of the system is discussed using the Arnold-Moser theorem. Again, the effects of radiation pressure, oblateness and the presence of the disc are analyzed separately and it is observed that in the absence as well as presence of perturbation parameters, triangular equilibrium point is unstable in the nonlinear sense within the stability range 0<μ<μ1=\\bar{μc} due to failure of the Arnold-Moser theorem. However, perturbation parameters affect the values of μ at which D4=0, significantly. This study may help to analyze more generalized cases of the problem in the presence of some other types of perturbations such as P-R drag and solar wind drag. The results are limited to the regular symmetric disc but it can be extended in the future.

Quasi-additive estimates on the Hamiltonian for the one-dimensional long range Ising model

NASA Astrophysics Data System (ADS)

Littin, Jorge; Picco, Pierre

2017-07-01

In this work, we study the problem of getting quasi-additive bounds for the Hamiltonian of the long range Ising model, when the two-body interaction term decays proportionally to 1/d2 -α , α ∈(0,1 ) . We revisit the paper by Cassandro et al. [J. Math. Phys. 46, 053305 (2005)] where they extend to the case α ∈[0 ,ln3/ln2 -1 ) the result of the existence of a phase transition by using a Peierls argument given by Fröhlich and Spencer [Commun. Math. Phys. 84, 87-101 (1982)] for α =0 . The main arguments of Cassandro et al. [J. Math. Phys. 46, 053305 (2005)] are based in a quasi-additive decomposition of the Hamiltonian in terms of hierarchical structures called triangles and contours, which are related to the original definition of contours introduced by Fröhlich and Spencer [Commun. Math. Phys. 84, 87-101 (1982)]. In this work, we study the existence of a quasi-additive decomposition of the Hamiltonian in terms of the contours defined in the work of Cassandro et al. [J. Math. Phys. 46, 053305 (2005)]. The most relevant result obtained is Theorem 4.3 where we show that there is a quasi-additive decomposition for the Hamiltonian in terms of contours when α ∈[0,1 ) but not in terms of triangles. The fact that it cannot be a quasi-additive bound in terms of triangles lead to a very interesting maximization problem whose maximizer is related to a discrete Cantor set. As a consequence of the quasi-additive bounds, we prove that we can generalise the [Cassandro et al., J. Math. Phys. 46, 053305 (2005)] result, that is, a Peierls argument, to the whole interval α ∈[0,1 ) . We also state here the result of Cassandro et al. [Commun. Math. Phys. 327, 951-991 (2014)] about cluster expansions which implies that Theorem 2.4 that concerns interfaces and Theorem 2.5 that concerns n point truncated correlation functions in Cassandro et al. [Commun. Math. Phys. 327, 951-991 (2014)] are valid for all α ∈[0,1 ) instead of only α ∈[0 ,ln3/ln2 -1 ) .

Modeling Optical Spectra of Large Organic Systems Using Real-Time Propagation of Semiempirical Effective Hamiltonians.

PubMed

Ghosh, Soumen; Andersen, Amity; Gagliardi, Laura; Cramer, Christopher J; Govind, Niranjan

2017-09-12

We present an implementation of a time-dependent semiempirical method (INDO/S) in NWChem using real-time (RT) propagation to address, in principle, the entire spectrum of valence electronic excitations. Adopting this model, we study the UV/vis spectra of medium-sized systems such as P3B2 and f-coronene, and in addition much larger systems such as ubiquitin in the gas phase and the betanin chromophore in the presence of two explicit solvents (water and methanol). RT-INDO/S provides qualitatively and often quantitatively accurate results when compared with RT- TDDFT or experimental spectra. Even though we only consider the INDO/S Hamiltonian in this work, our implementation provides a framework for performing electron dynamics in large systems using semiempirical Hartree-Fock Hamiltonians in general.

Unifying perspective: Solitary traveling waves as discrete breathers in Hamiltonian lattices and energy criteria for their stability

NASA Astrophysics Data System (ADS)

Cuevas-Maraver, Jesús; Kevrekidis, Panayotis G.; Vainchtein, Anna; Xu, Haitao

2017-09-01

In this work, we provide two complementary perspectives for the (spectral) stability of solitary traveling waves in Hamiltonian nonlinear dynamical lattices, of which the Fermi-Pasta-Ulam and the Toda lattice are prototypical examples. One is as an eigenvalue problem for a stationary solution in a cotraveling frame, while the other is as a periodic orbit modulo shifts. We connect the eigenvalues of the former with the Floquet multipliers of the latter and using this formulation derive an energy-based spectral stability criterion. It states that a sufficient (but not necessary) condition for a change in the wave stability occurs when the functional dependence of the energy (Hamiltonian) H of the model on the wave velocity c changes its monotonicity. Moreover, near the critical velocity where the change of stability occurs, we provide an explicit leading-order computation of the unstable eigenvalues, based on the second derivative of the Hamiltonian H''(c0) evaluated at the critical velocity c0. We corroborate this conclusion with a series of analytically and numerically tractable examples and discuss its parallels with a recent energy-based criterion for the stability of discrete breathers.

School Emergency Planning Guide.

ERIC Educational Resources Information Center

Benedetto, Harry J.

This guide was prepared to assist Pennsylvania schools and communities in the development of comprehensive emergency plans. Procedures for identifying and responding to potential community and school emergency situations are presented. A plan for developing and organizing mass care centers utilizing school and community facilities and resources is…

Economics: A Resource Guide.

ERIC Educational Resources Information Center

Texas Education Agency, Austin. Div. of Curriculum Development.

The guide, designed for teachers, supervisors, and resource center directors, identifies sources of classroom materials in economics for elementary and secondary grades. Section I lists 87 pamphlets and periodicals published by the 12 federal reserve districts in the United States. Topics include water use, small farm economics, business…

Hamiltonian analysis of curvature-squared gravity with or without conformal invariance

NASA Astrophysics Data System (ADS)

KlusoÅ, Josef; Oksanen, Markku; Tureanu, Anca

2014-03-01

We analyze gravitational theories with quadratic curvature terms, including the case of conformally invariant Weyl gravity, motivated by the intention to find a renormalizable theory of gravity in the ultraviolet region, yet yielding general relativity at long distances. In the Hamiltonian formulation of Weyl gravity, the number of local constraints is equal to the number of unstable directions in phase space, which in principle could be sufficient for eliminating the unstable degrees of freedom in the full nonlinear theory. All the other theories of quadratic type are unstable—a problem appearing as ghost modes in the linearized theory. We find that the full projection of the Weyl tensor onto a three-dimensional hypersurface contains an additional fully traceless component, given by a quadratic extrinsic curvature tensor. A certain inconsistency in the literature is found and resolved: when the conformal invariance of Weyl gravity is broken by a cosmological constant term, the theory becomes pathological, since a constraint required by the Hamiltonian analysis imposes the determinant of the metric of spacetime to be zero. In order to resolve this problem by restoring the conformal invariance, we introduce a new scalar field that couples to the curvature of spacetime, reminiscent of the introduction of vector fields for ensuring the gauge invariance.

Exponentially-Biased Ground-State Sampling of Quantum Annealing Machines with Transverse-Field Driving Hamiltonians

NASA Technical Reports Server (NTRS)

Mandra, Salvatore

2017-01-01

We study the performance of the D-Wave 2X quantum annealing machine on systems with well-controlled ground-state degeneracy. While obtaining the ground state of a spin-glass benchmark instance represents a difficult task, the gold standard for any optimization algorithm or machine is to sample all solutions that minimize the Hamiltonian with more or less equal probability. Our results show that while naive transverse-field quantum annealing on the D-Wave 2X device can find the ground-state energy of the problems, it is not well suited in identifying all degenerate ground-state configurations associated to a particular instance. Even worse, some states are exponentially suppressed, in agreement with previous studies on toy model problems [New J. Phys. 11, 073021 (2009)]. These results suggest that more complex driving Hamiltonians are needed in future quantum annealing machines to ensure a fair sampling of the ground-state manifold.

Long-time correlation for the chaotic orbit in the two-wave Hamiltonian

NASA Astrophysics Data System (ADS)

Hatori, Tadatsugu; Irie, Haruyuki

1987-03-01

The time correlation function of velocity is found to decay with the power law for the orbit governed by a Hamiltonian, H=v sup 2/2 - Mcosx - Pcos (k(x-t)). The renormalization group technique can predict the power of decay for the correlation function defined by the ensemble average. The power spectrum becomes the 1/f-type for a special case.

Family Learning Outdoors: Guided Participation on a Nature Walk

ERIC Educational Resources Information Center

Zimmerman, Heather Toomey; McClain, Lucy R.

2016-01-01

This informal learning research project examined how guided participation processes support the use of cultural tools (such as scientific equipment) during a nature walk at one nature center. This paper analyzed family interactions outdoors using microethnographic methods. An informal learning framework based on guided participation and cultural…

Semiclassics for matrix Hamiltonians: The Gutzwiller trace formula with applications to graphene-type systems

NASA Astrophysics Data System (ADS)

Vogl, M.; Pankratov, O.; Shallcross, S.

2017-07-01

We present a tractable and physically transparent semiclassical theory of matrix-valued Hamiltonians, i.e., those that describe quantum systems with internal degrees of freedoms, based on a generalization of the Gutzwiller trace formula for a n ×n dimensional Hamiltonian H (p ̂,q ̂) . The classical dynamics is governed by n Hamilton-Jacobi (HJ) equations that act in a phase space endowed with a classical Berry curvature encoding anholonomy in the parallel transport of the eigenvectors of H (p ,q ) ; these vectors describe the internal structure of the semiclassical particles. At the O (ℏ1) level and for nondegenerate HJ systems, this curvature results in an additional semiclassical phase composed of (i) a Berry phase and (ii) a dynamical phase resulting from the classical particles "moving through the Berry curvature". We show that the dynamical part of this semiclassical phase will, generally, be zero only for the case in which the Berry phase is topological (i.e., depends only on the winding number). We illustrate the method by calculating the Landau spectrum for monolayer graphene, the four-band model of AB bilayer graphene, and for a more complicated matrix Hamiltonian describing the silicene band structure. Finally, we apply our method to an inhomogeneous system consisting of a strain engineered one-dimensional moiré in bilayer graphene, finding localized states near the Dirac point that arise from electron trapping in a semiclassical moiré potential. The semiclassical density of states of these localized states we show to be in perfect agreement with an exact quantum mechanical calculation of the density of states.

Data Center Energy Efficiency Measurement Assessment Kit Guide and Specification

DOE Office of Scientific and Technical Information (OSTI.GOV)

None

2012-10-26

A portable and temporary wireless mesh assessment kit can be used to speed up and reduce the costs of a data center energy use assessment and overcome the issues with respect to shutdowns. The assessment kit is comprised of temperature, relative humidity, and pressure sensors. Also included are power meters that can be installed on computer room air conditioners (CRACs) without intrusive interruption of data center operations. The assessment kit produces data required for a detailed energy assessment of the data center.

Adiabatic particle motion in a nearly drift-free magnetic field: Application to the geomagnetic tail

NASA Technical Reports Server (NTRS)

Stern, D. P.

1977-01-01

The guiding center motion of particles in a nearly drift free magnetic field is analyzed in order to investigate the dependence of mean drift velocity on equatorial pitch angle, the variation of local drift velocity along the trajectory, and other properties. The mean drift for adiabatic particles is expressed by means of elliptic integrals. Approximations to the twice-averaged Hamiltonian W near z = O are derived, permitting simple representation of drift paths if an electric potential also exists. In addition, the use of W or of expressions for the longitudinal invariant allows the derivation of the twice averaged Liouville equation and of the corresponding Vlasov equation. Bounce times are calculated (using the drift-free approximation), as are instantaneous guiding center drift velocities, which are then used to provide a numerical check on the formulas for the mean drift.

Computing pKa Values with a Mixing Hamiltonian Quantum Mechanical/Molecular Mechanical Approach.

PubMed

Liu, Yang; Fan, Xiaoli; Jin, Yingdi; Hu, Xiangqian; Hu, Hao

2013-09-10

Accurate computation of the pKa value of a compound in solution is important but challenging. Here, a new mixing quantum mechanical/molecular mechanical (QM/MM) Hamiltonian method is developed to simulate the free-energy change associated with the protonation/deprotonation processes in solution. The mixing Hamiltonian method is designed for efficient quantum mechanical free-energy simulations by alchemically varying the nuclear potential, i.e., the nuclear charge of the transforming nucleus. In pKa calculation, the charge on the proton is varied in fraction between 0 and 1, corresponding to the fully deprotonated and protonated states, respectively. Inspired by the mixing potential QM/MM free energy simulation method developed previously [H. Hu and W. T. Yang, J. Chem. Phys. 2005, 123, 041102], this method succeeds many advantages of a large class of λ-coupled free-energy simulation methods and the linear combination of atomic potential approach. Theory and technique details of this method, along with the calculation results of the pKa of methanol and methanethiol molecules in aqueous solution, are reported. The results show satisfactory agreement with the experimental data.

Hamiltonian methods of modeling and control of AC microgrids with spinning machines and inverters

DOE Office of Scientific and Technical Information (OSTI.GOV)

Matthews, Ronald C.; Weaver, Wayne W.; Robinett, Rush D.

This study presents a novel approach to the modeling and control of AC microgrids that contain spinning machines, power electronic inverters and energy storage devices. The inverters in the system can adjust their frequencies and power angles very quickly, so the modeling focuses on establishing a common reference frequency and angle in the microgrid based on the spinning machines. From this dynamic model, nonlinear Hamiltonian surface shaping and power flow control method is applied and shown to stabilize. From this approach the energy flow in the system is used to show the energy storage device requirements and limitations for themore » system. This paper first describes the model for a single bus AC microgrid with a Hamiltonian control, then extends this model and control to a more general class of multiple bus AC microgrids. Finally, simulation results demonstrate the efficacy of the approach in stabilizing and optimization of the microgrid.« less

Hamiltonian Systems and Optimal Control in Computational Anatomy: 100 Years Since D'Arcy Thompson.

PubMed

Miller, Michael I; Trouvé, Alain; Younes, Laurent

2015-01-01

The Computational Anatomy project is the morphome-scale study of shape and form, which we model as an orbit under diffeomorphic group action. Metric comparison calculates the geodesic length of the diffeomorphic flow connecting one form to another. Geodesic connection provides a positioning system for coordinatizing the forms and positioning their associated functional information. This article reviews progress since the Euler-Lagrange characterization of the geodesics a decade ago. Geodesic positioning is posed as a series of problems in Hamiltonian control, which emphasize the key reduction from the Eulerian momentum with dimension of the flow of the group, to the parametric coordinates appropriate to the dimension of the submanifolds being positioned. The Hamiltonian viewpoint provides important extensions of the core setting to new, object-informed positioning systems. Several submanifold mapping problems are discussed as they apply to metamorphosis, multiple shape spaces, and longitudinal time series studies of growth and atrophy via shape splines.

Hamiltonian methods of modeling and control of AC microgrids with spinning machines and inverters

DOE PAGES

Matthews, Ronald C.; Weaver, Wayne W.; Robinett, Rush D.; ...

2017-12-22

This study presents a novel approach to the modeling and control of AC microgrids that contain spinning machines, power electronic inverters and energy storage devices. The inverters in the system can adjust their frequencies and power angles very quickly, so the modeling focuses on establishing a common reference frequency and angle in the microgrid based on the spinning machines. From this dynamic model, nonlinear Hamiltonian surface shaping and power flow control method is applied and shown to stabilize. From this approach the energy flow in the system is used to show the energy storage device requirements and limitations for themore » system. This paper first describes the model for a single bus AC microgrid with a Hamiltonian control, then extends this model and control to a more general class of multiple bus AC microgrids. Finally, simulation results demonstrate the efficacy of the approach in stabilizing and optimization of the microgrid.« less

Weather integration in TMC operations : a self-evaluation and planning guide.

DOT National Transportation Integrated Search

2009-04-01

This flyer describes how Traffic Management Centers (TMC) can integrate weather information into their daily operations, and is based on the Road Weather Management Program publication, Self-Evaluation and Planning Guide (FHWA-JPO-08-057). The Guide ...

Computer Bits: Child Care Center Management Software Buying Guide Update.

ERIC Educational Resources Information Center

Neugebauer, Roger

1987-01-01

Compares seven center management programs used for basic financial and data management tasks such as accounting, payroll and attendance records, and mailing lists. Describes three other specialized programs and gives guidelines for selecting the best software for a particular center. (NH)

Integrable Equations in Multi-Dimensions (2+1) are Bi-Hamiltonian Systems,

DTIC Science & Technology

1987-02-01

equation [18]. It should be noted that the 80 equation has more similarities [19] with the Kadomtsev - Petviashvili (KP...Cimento, 39B, 1 (1977). [31] P. Caudrey, Discrete and Periodic Spectral Transforms Related to the Kadomtsev - Petviashvili Equation , preprint U.M.I.S.T. (1985). II ’AI D p-I 4, - -- - -- - - -w 4 ...TOM NONLINEAR STUDIES IDTIC I IELEC )// MAR 2 51988 I / \\ / Integrable Equations in Multi- dimensions (2+1) are Bi-Hamiltonian Systems by A.S.

Special article: Creation of a guide for the transfer of care of the malignant hyperthermia patient from ambulatory surgery centers to receiving hospital facilities.

PubMed

Larach, Marilyn Green; Dirksen, Sharon J Hirshey; Belani, Kumar G; Brandom, Barbara W; Metz, Keith M; Policastro, Michael A; Rosenberg, Henry; Valedon, Arnaldo; Watson, Charles B

2012-01-01

Volatile anesthetics and/or succinylcholine may trigger a potentially lethal malignant hyperthermia (MH) event requiring critical care crisis management. If the MH triggering anesthetic is given in an ambulatory surgical center (ASC), then the patient will need to be transferred to a receiving hospital. Before May 2010, there was no clinical guide regarding the development of a specific transfer plan for MH patients in an ASC. MECHANISM BY WHICH THE STATEMENT WAS GENERATED: A consensual process lasting 18 months among 13 representatives of the Malignant Hyperthermia Association of the United States, the Ambulatory Surgery Foundation, the Society for Ambulatory Anesthesia, the Society for Academic Emergency Medicine, and the National Association of Emergency Medical Technicians led to the creation of this guide. EVIDENCE FOR THE STATEMENT: Most of the guide is based on the clinical experience and scientific expertise of the 13 representatives. The list of representatives appears in Appendix 1. The recommendation that IV dantrolene should be initiated pending transfer is also supported by clinical research demonstrating that the likelihood of significant MH complications doubles for every 30-minute delay in dantrolene administration (Anesth Analg 2010;110:498-507). This guide includes a list of potential clinical problems and therapeutic interventions to assist each ASC in the development of its own unique MH transfer plan. Points to consider include receiving health care facility capabilities, indicators of patient stability and necessary report data, transport team considerations and capabilities, implementation of transfer decisions, and coordination of communication among the ASC, the receiving hospital, and the transport team. See Appendix 2 for the guide.

Stability and Hamiltonian formulation of higher derivative theories

NASA Astrophysics Data System (ADS)

Schmidt, Hans-Jürgen

1994-06-01

We analyze the presuppositions leading to instabilities in theories of order higher than second. The type of fourth-order gravity which leads to an inflationary (quasi-de Sitter) period of cosmic evolution by inclusion of one curvature-squared term (i.e., the Starobinsky model) is used as an example. The corresponding Hamiltonian formulation (which is necessary for deducing the Wheeler-DeWitt equation) is found both in the Ostrogradski approach and in another form. As an example, a closed form solution of the Wheeler-DeWitt equation for a spatially flat Friedmann model and L=R2 is found. The method proposed by Simon to bring fourth order gravity to second order can be (if suitably generalized) applied to bring sixth-order gravity to second order.

Pennsylvania Online: A Curriculum Guide for School Library Media Centers.

ERIC Educational Resources Information Center

Pennsylvania State Library, Harrisburg.

This curriculum guide is intended for any librarian in Pennsylvania committed to teaching online searching and looking for guidelines to integrate the skill into the full academic curriculum. The publication will enable school librarians to assist students in developing the skills that will enable them to search and retrieve information from…

Many-body self-localization in a translation-invariant Hamiltonian

NASA Astrophysics Data System (ADS)

Mondaini, Rubem; Cai, Zi

2017-07-01

We study the statistical and dynamical aspects of a translation-invariant Hamiltonian, without quench disorder, as an example of the manifestation of the phenomenon of many-body localization. This is characterized by the breakdown of thermalization and by information preservation of initial preparations at long times. To realize this, we use quasiperiodic long-range interactions, which are now achievable in high-finesse cavity experiments, to find evidence suggestive of a divergent time-scale in which charge inhomogeneities in the initial state survive asymptotically. This is reminiscent of a glassy behavior, which appears in the ground state of this system, being also present at infinite temperatures.

Adiabatic dynamics of one-dimensional classical Hamiltonian dissipative systems

NASA Astrophysics Data System (ADS)

Pritula, G. M.; Petrenko, E. V.; Usatenko, O. V.

2018-02-01

A linearized plane pendulum with the slowly varying mass and length of string and the suspension point moving at a slowly varying speed is presented as an example of a simple 1D mechanical system described by the generalized harmonic oscillator equation, which is a basic model in discussion of the adiabatic dynamics and geometric phase. The expression for the pendulum geometric phase is obtained by three different methods. The pendulum is shown to be canonically equivalent to the damped harmonic oscillator. This supports the mathematical conclusion, not widely accepted in physical community, of no difference between the dissipative and Hamiltonian 1D systems.

A Teachers' Guide for the Outdoor School Program.

ERIC Educational Resources Information Center

Battle Creek Public Schools, MI.

The general aim of this guide is to aid the teachers of the fifth and sixth grade boys and girls who participate in the Outdoor School program at the Battle Creek Outdoor Center. Another major aim of this guide is to aid the outdoor school teachers who bear the major responsibility in implementing the outdoor school program. An historical overview…

Direct experimental visualization of the global Hamiltonian progression of two-dimensional Lagrangian flow topologies from integrable to chaotic state.

PubMed

Baskan, O; Speetjens, M F M; Metcalfe, G; Clercx, H J H

2015-10-01

Countless theoretical/numerical studies on transport and mixing in two-dimensional (2D) unsteady flows lean on the assumption that Hamiltonian mechanisms govern the Lagrangian dynamics of passive tracers. However, experimental studies specifically investigating said mechanisms are rare. Moreover, they typically concern local behavior in specific states (usually far away from the integrable state) and generally expose this indirectly by dye visualization. Laboratory experiments explicitly addressing the global Hamiltonian progression of the Lagrangian flow topology entirely from integrable to chaotic state, i.e., the fundamental route to efficient transport by chaotic advection, appear non-existent. This motivates our study on experimental visualization of this progression by direct measurement of Poincaré sections of passive tracer particles in a representative 2D time-periodic flow. This admits (i) accurate replication of the experimental initial conditions, facilitating true one-to-one comparison of simulated and measured behavior, and (ii) direct experimental investigation of the ensuing Lagrangian dynamics. The analysis reveals a close agreement between computations and observations and thus experimentally validates the full global Hamiltonian progression at a great level of detail.

Urban Wild: A Manual for the Development, Implementation, and Operation of Nature Centers on School Campuses.

ERIC Educational Resources Information Center

Ortiz, James L.

The purpose of this guide is to stimulate the development of nature centers. The guide offers possible solutions for common problems which many schools face when considering an on-campus nature center, for example, lack of readily available open space, minimum knowledge of how to develop and maintain an on-campus nature center, and lack of…

The wicked question answered: positive deviance delivers patient-centered care.

PubMed

Gary, Jodie C

2014-01-01

How nurses respond when faced with the dilemma of providing patient-centered care in the absence of patient-centered practice guidelines remains relatively unreported. Standards may not be available to guide nurses or may not be realistic for implementation at the point of care. Nurses may be forced to react creatively to meet the needs of their patients. The purpose was to understand nursing care when standard practice guidelines did not meet patient-specific care needs and to develop various viewpoints related to the use of positive deviance in providing patient-centered care. Complexity theory and the framework of a wicked question were used to guide a 3-round online national Delphi study from November 2011 to February 2012. The panel was accessed through the American Association of Critical Care Nurses to expose the care provided when standard practice guidelines were lacking. Findings support the presence of positive deviance and expose care provided by nurses when standard practice guidelines lacked the ability to provide patient-centered care. Dominant themes of positive deviance are recommended as priorities for future research. Better guidelines are needed that work for nurses, instead of against them, that would not force a nurse into actions that are not patient centered. Guidelines should guide practice and assist in allowing nurses to provide care that is centered on the best needs of the patient in the specific care situation.

Method for maintaining a cutting blade centered in a kerf

DOEpatents

Blaedel, Kenneth L.; Davis, Pete J.; Landram, Charles S.

2002-01-01

A saw having a self-pumped hydrodynamic blade guide or bearing for retaining the saw blade in a centered position in the saw kerf (width of cut made by the saw). The hydrodynamic blade guide or bearing utilizes pockets or grooves incorporated into the sides of the blade. The saw kerf in the workpiece provides the guide or bearing stator surface. Both sides of the blade entrain cutting fluid as the blade enters the kerf in the workpiece, and the trapped fluid provides pressure between the blade and the workpiece as an inverse function of the gap between the blade surface and the workpiece surface. If the blade wanders from the center of the kerf, then one gap will increase and one gap will decrease and the consequent pressure difference between the two sides of the blade will cause the blade to re-center itself in the kerf. Saws using the hydrodynamic blade guide or bearing have particular application in slicing slabs from boules of single crystal materials, for example, as well as for cutting other difficult to saw materials such as ceramics, glass, and brittle composite materials.

North Central Climate Science Center--science agenda 2012-2017

USGS Publications Warehouse

Morisette, Jeffrey T.

2012-01-01

The information presented here provides the five-year science agenda for the North Central Climate Science Center. It is meant to be a high-level guide that describes the spatial context of the center, the primary partners and stakeholders, and the strategic framework the center will use in applying climate science to inform management.

Hamiltonian approaches to spatial and temporal discretization of fully compressible equations

NASA Astrophysics Data System (ADS)

Dubos, Thomas; Dubey, Sarvesh

2017-04-01

The fully compressible Euler (FCE) equations are the most accurate for representing atmospheric motion, compared to approximate systems like the hydrostatic, anelastic or pseudo-incompressible systems. The price to pay for this accuracy is the presence of additional degrees of freedom and high-frequency acoustic waves that must be treated implicitly. In this work we explore a Hamiltonian approach to the issue of stable spatial and temporal discretization of the FCE using a non-Eulerian vertical coordinate. For scalability, a horizontally-explicit, vertically-implicit (HEVI) time discretization is adopted. The Hamiltonian structure of the equations is used to obtain the spatial finite-difference discretization and also in order to identify those terms of the equations of motion that need to be treated implicitly. A novel treatment of the lower boundary condition in the presence of orography is introduced: rather than enforcing a no-normal-flow boundary condition, which couples the horizontal and vertical velocity components and interferes with the HEVI structure, the ground is treated as a flexible surface with arbitrarily large stiffness, resulting in a decoupling of the horizontal and vertical dynamics and yielding a simple implicit problem which can be solved efficiently. Standard test cases performed in a vertical slice configuration suggest that an effective horizontal acoustic Courant number close to 1 can be achieved.

Pennsylvania Online: A Curriculum Guide for School Library Media Centers.

ERIC Educational Resources Information Center

Pennsylvania State Library, Harrisburg.

This curriculum guide is intended to meet the needs of librarians in all schools in Pennsylvania, including those lacking access to online technologies. It is recommended that the online curriculum be integrated with the teaching of library media skills in other discipline areas at appropriate elementary and secondary grade levels, and that…

A study of the linear free energy model for DNA structures using the generalized Hamiltonian formalism

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yavari, M., E-mail: yavari@iaukashan.ac.ir

2016-06-15

We generalize the results of Nesterenko [13, 14] and Gogilidze and Surovtsev [15] for DNA structures. Using the generalized Hamiltonian formalism, we investigate solutions of the equilibrium shape equations for the linear free energy model.

Using Hamiltonian control to desynchronize Kuramoto oscillators

NASA Astrophysics Data System (ADS)

Gjata, Oltiana; Asllani, Malbor; Barletti, Luigi; Carletti, Timoteo

2017-02-01

Many coordination phenomena are based on a synchronization process, whose global behavior emerges from the interactions among the individual parts. Often in nature, such self-organized mechanism allows the system to behave as a whole and thus grounding its very first existence, or expected functioning, on such process. There are, however, cases where synchronization acts against the stability of the system; for instance in some neurodegenerative diseases or epilepsy or the famous case of Millennium Bridge where the crowd synchronization of the pedestrians seriously endangered the stability of the structure. In this paper we propose an innovative control method to tackle the synchronization process based on the application of the Hamiltonian control theory, by adding a small control term to the system we are able to impede the onset of the synchronization. We present our results on a generalized class of the paradigmatic Kuramoto model.

Franck-Condon Factors for Diatomics: Insights and Analysis Using the Fourier Grid Hamiltonian Method

ERIC Educational Resources Information Center

Ghosh, Supriya; Dixit, Mayank Kumar; Bhattacharyya, S. P.; Tembe, B. L.

2013-01-01

Franck-Condon factors (FCFs) play a crucial role in determining the intensities of the vibrational bands in electronic transitions. In this article, a relatively simple method to calculate the FCFs is illustrated. An algorithm for the Fourier Grid Hamiltonian (FGH) method for computing the vibrational wave functions and the corresponding energy…

Effective lattice Hamiltonian for monolayer tin disulfide: Tailoring electronic structure with electric and magnetic fields

NASA Astrophysics Data System (ADS)

Yu, Jin; van Veen, Edo; Katsnelson, Mikhail I.; Yuan, Shengjun

2018-06-01

The electronic properties of monolayer tin dilsulfide (ML -Sn S2 ), a recently synthesized metal dichalcogenide, are studied by a combination of first-principles calculations and tight-binding (TB) approximation. An effective lattice Hamiltonian based on six hybrid s p -like orbitals with trigonal rotation symmetry are proposed to calculate the band structure and density of states for ML -Sn S2 , which demonstrates good quantitative agreement with relativistic density-functional-theory calculations in a wide energy range. We show that the proposed TB model can be easily applied to the case of an external electric field, yielding results consistent with those obtained from full Hamiltonian results. In the presence of a perpendicular magnetic field, highly degenerate equidistant Landau levels are obtained, showing typical two-dimensional electron gas behavior. Thus, the proposed TB model provides a simple way in describing properties in ML -Sn S2 .

Five-dimensional collective Hamiltonian with the Gogny force: An ongoing saga

NASA Astrophysics Data System (ADS)

Libert, J.; Delaroche, J.-P.; Girod, M.

2016-07-01

We provide a sample of analyses for nuclear spectroscopic properties based on the five-dimensional collective Hamiltonian (5DCH) implemented with the Gogny force. The very first illustration is dating back to the late 70's. It is next followed by others, focusing on shape coexistence, shape isomerism, superdeformation, and systematics over the periodic table. Finally, the inclusion of Thouless-Valatin dynamical contributions to vibrational mass parameters is briefly discussed as a mean of strengthening the basis of the 5DCH theory.

The effects of guided inquiry instruction on student achievement in high school biology

NASA Astrophysics Data System (ADS)

Vass, Laszlo

The purpose of this quantitative, quasi-experimental study was to measure the effect of a student-centered instructional method called guided inquiry on the achievement of students in a unit of study in high school biology. The study used a non-random sample of 109 students, the control group of 55 students enrolled in high school one, received teacher centered instruction while the experimental group of 54 students enrolled at high school two received student-centered, guided inquiry instruction. The pretest-posttest design of the study analyzed scores using an independent t-test, a dependent t-test (p = <.001), an ANCOVA (p = .007), mixed method ANOVA (p = .024) and hierarchical linear regression (p = <.001). The experimental group that received guided inquiry instruction had statistically significantly higher achievement than the control group.

Spinor matter fields in SL(2,C) gauge theories of gravity: Lagrangian and Hamiltonian approaches

NASA Astrophysics Data System (ADS)

Antonowicz, Marek; Szczyrba, Wiktor

1985-06-01

We consider the SL(2,C)-covariant Lagrangian formulation of gravitational theories with the presence of spinor matter fields. The invariance properties of such theories give rise to the conservation laws (the contracted Bianchi identities) having in the presence of matter fields a more complicated form than those known in the literature previously. A general SL(2,C) gauge theory of gravity is cast into an SL(2,C)-covariant Hamiltonian formulation. Breaking the SL(2,C) symmetry of the system to the SU(2) symmetry, by introducing a spacelike slicing of spacetime, we get an SU(2)-covariant Hamiltonian picture. The qualitative analysis of SL(2,C) gauge theories of gravity in the SU(2)-covariant formulation enables us to define the dynamical symplectic variables and the gauge variables of the theory under consideration as well as to divide the set of field equations into the dynamical equations and the constraints. In the SU(2)-covariant Hamiltonian formulation the primary constraints, which are generic for first-order matter Lagrangians (Dirac, Weyl, Fierz-Pauli), can be reduced. The effective matter symplectic variables are given by SU(2)-spinor-valued half-forms on three-dimensional slices of spacetime. The coupled Einstein-Cartan-Dirac (Weyl, Fierz-Pauli) system is analyzed from the (3+1) point of view. This analysis is complete; the field equations of the Einstein-Cartan-Dirac theory split into 18 gravitational dynamical equations, 8 dynamical Dirac equations, and 7 first-class constraints. The system has 4+8=12 independent degrees of freedom in the phase space.

The wave function and minimum uncertainty function of the bound quadratic Hamiltonian system

NASA Technical Reports Server (NTRS)

Yeon, Kyu Hwang; Um, Chung IN; George, T. F.

1994-01-01

The bound quadratic Hamiltonian system is analyzed explicitly on the basis of quantum mechanics. We have derived the invariant quantity with an auxiliary equation as the classical equation of motion. With the use of this invariant it can be determined whether or not the system is bound. In bound system we have evaluated the exact eigenfunction and minimum uncertainty function through unitary transformation.

MMS observations of large guide field symmetric reconnection between colliding reconnection jets at the center of a magnetic flux rope at the magnetopause

NASA Astrophysics Data System (ADS)

Øieroset, M.; Phan, T. D.; Haggerty, C.; Shay, M. A.; Eastwood, J. P.; Gershman, D. J.; Drake, J. F.; Fujimoto, M.; Ergun, R. E.; Mozer, F. S.; Oka, M.; Torbert, R. B.; Burch, J. L.; Wang, S.; Chen, L. J.; Swisdak, M.; Pollock, C.; Dorelli, J. C.; Fuselier, S. A.; Lavraud, B.; Giles, B. L.; Moore, T. E.; Saito, Y.; Avanov, L. A.; Paterson, W.; Strangeway, R. J.; Russell, C. T.; Khotyaintsev, Y.; Lindqvist, P. A.; Malakit, K.

2016-06-01

We report evidence for reconnection between colliding reconnection jets in a compressed current sheet at the center of a magnetic flux rope at Earth's magnetopause. The reconnection involved nearly symmetric inflow boundary conditions with a strong guide field of two. The thin (2.5 ion-skin depth (di) width) current sheet (at ~12 di downstream of the X line) was well resolved by MMS, which revealed large asymmetries in plasma and field structures in the exhaust. Ion perpendicular heating, electron parallel heating, and density compression occurred on one side of the exhaust, while ion parallel heating and density depression were shifted to the other side. The normal electric field and double out-of-plane (bifurcated) currents spanned almost the entire exhaust. These observations are in good agreement with a kinetic simulation for similar boundary conditions, demonstrating in new detail that the structure of large guide field symmetric reconnection is distinctly different from antiparallel reconnection.

MMS observations of large guide field symmetric reconnection between colliding reconnection jets at the center of a magnetic flux rope at the magnetopause

NASA Astrophysics Data System (ADS)

Oieroset, M.; Phan, T.; Haggerty, C. C.; Shay, M. A.; Eastwood, J. P.; Gershman, D. J.; Drake, J. F.; Fujimoto, M.; Ergun, R.; Mozer, F.; Oka, M.; Torbert, R. B.; Burch, J. L.; Wang, S.; Chen, L. J.; Swisdak, M.; Pollock, C.; Dorelli, J.; Fuselier, S. A.; Lavraud, B.; Giles, B. L.; Moore, T. E.; Saito, Y.; Avanov, L. A.; Paterson, W. R.; Strangeway, R. J.; Russell, C. T.; Khotyaintsev, Y. V.; Lindqvist, P. A.; Malakit, K.

2016-12-01

We report evidence for reconnection between colliding reconnection jets in a compressed current sheet at the center of a magnetic flux rope at Earth's magnetopause. The reconnection involved nearly symmetric inflow boundary conditions with a strong guide field of two. The thin (2.5 ion-skin depth (di) width) current sheet (at 12 di downstream of the X line) was well resolved by Magnetospheric Multiscale, which revealed large asymmetries in plasma and field structures in the exhaust. Ion perpendicular heating, electron parallel heating, and density compression occurred on one side of the exhaust, while ion parallel heating and density depression were shifted to the other side. The normal electric field and double out-of-plane (bifurcated) currents spanned almost the entire exhaust. These observations are in good agreement with a kinetic simulation for similar boundary conditions, demonstrating in new detail that the structure of large guide field symmetric reconnection is distinctly different from antiparallel reconnection.

MMS Observations of Large Guide Field Symmetric Reconnection Between Colliding Reconnection Jets at the Center of a Magnetic Flux Rope at the Magnetopause

NASA Technical Reports Server (NTRS)

Oieroset, M.; Phan, T. D.; Haggerty, C.; Shay, M. A.; Eastwood, J. P.; Gershman, D. J.; Drake, J. F.; Fujimoto, M.; Ergun, R. E.; Mozer, F. S.;

Minimum Hamiltonian ascent trajectory evaluation (MASTRE) program (update to automatic flight trajectory design, performance prediction, and vehicle sizing for support of shuttle and shuttle derived vehicles) users manual

NASA Technical Reports Server (NTRS)

Lyons, J. T.; Borchers, William R.

1993-01-01

Documentation for the User Interface Program for the Minimum Hamiltonian Ascent Trajectory Evaluation (MASTRE) is provided. The User Interface Program is a separate software package designed to ease the user input requirements when using the MASTRE Trajectory Program. This document supplements documentation on the MASTRE Program that consists of the MASTRE Engineering Manual and the MASTRE Programmers Guide. The User Interface Program provides a series of menus and tables using the VAX Screen Management Guideline (SMG) software. These menus and tables allow the user to modify the MASTRE Program input without the need for learning the various program dependent mnemonics. In addition, the User Interface Program allows the user to modify and/or review additional input Namelist and data files, to build and review command files, to formulate and calculate mass properties related data, and to have a plotting capability.