A port-Hamiltonian approach to visual servo control of a pick and place system
Dirksz, Daniel A.; Scherpen, Jacquelien M.A.
2012-01-01
In this paper we take a port-Hamiltonian approach to address the problem of image-based visual servo control of a pick and place system. We realize a closed-loop system, including the nonlinear camera dynamics, which is port-Hamiltonian. Although the closed-loop system is nonlinear, the resulting
A port-Hamiltonian approach to image-based visual servo control for dynamic systems
Mahony, R.; Stramigioli, Stefano
2012-01-01
This paper introduces a port-Hamiltonian framework for the design of image-based visual servo control for dynamic mechanical systems. The approach taken introduces the concept of an image effort and provides an interpretation of energy exchange between the dynamics of the physical system and virtual
A Port-Hamiltonian Approach to Visual Servo Control of a Pick and Place System
Dirksz, Daniel A.; Scherpen, Jacquelien M. A.; Steinbuch, Maarten
In this paper, we take a port-Hamiltonian approach to address the problem of image-based visual servo control of a pick and place system. Through a coordinate transformation and a passive interconnection between mechanical system and camera dynamics we realize a closed-loop system that is
A partial Hamiltonian approach for current value Hamiltonian systems
Naz, R.; Mahomed, F. M.; Chaudhry, Azam
2014-10-01
We develop a partial Hamiltonian framework to obtain reductions and closed-form solutions via first integrals of current value Hamiltonian systems of ordinary differential equations (ODEs). The approach is algorithmic and applies to many state and costate variables of the current value Hamiltonian. However, we apply the method to models with one control, one state and one costate variable to illustrate its effectiveness. The current value Hamiltonian systems arise in economic growth theory and other economic models. We explain our approach with the help of a simple illustrative example and then apply it to two widely used economic growth models: the Ramsey model with a constant relative risk aversion (CRRA) utility function and Cobb Douglas technology and a one-sector AK model of endogenous growth are considered. We show that our newly developed systematic approach can be used to deduce results given in the literature and also to find new solutions.
Image-based visual servo control using the port-Hamiltonian Approach
Muñoz Arias, Mauricio; El Hawwary, Mohamed; Scherpen, Jacquelien M.A.
2015-01-01
This work is devoted to an image-based visual servo control strategy for standard mechanical systems in the port-Hamiltonian framework. We utilize a change of variables that transforms the port-Hamiltonian system into one with constant mass-inertia matrix, and we use an interaction matrix that
International Nuclear Information System (INIS)
Asplund, Erik; Kluener, Thorsten
2012-01-01
In this paper, control of open quantum systems with emphasis on the control of surface photochemical reactions is presented. A quantum system in a condensed phase undergoes strong dissipative processes. From a theoretical viewpoint, it is important to model such processes in a rigorous way. In this work, the description of open quantum systems is realized within the surrogate Hamiltonian approach [R. Baer and R. Kosloff, J. Chem. Phys. 106, 8862 (1997)]. An efficient and accurate method to find control fields is optimal control theory (OCT) [W. Zhu, J. Botina, and H. Rabitz, J. Chem. Phys. 108, 1953 (1998); Y. Ohtsuki, G. Turinici, and H. Rabitz, J. Chem. Phys. 120, 5509 (2004)]. To gain control of open quantum systems, the surrogate Hamiltonian approach and OCT, with time-dependent targets, are combined. Three open quantum systems are investigated by the combined method, a harmonic oscillator immersed in an ohmic bath, CO adsorbed on a platinum surface, and NO adsorbed on a nickel oxide surface. Throughout this paper, atomic units, i.e., (ℎ/2π)=m e =e=a 0 = 1, have been used unless otherwise stated.
Asplund, Erik; Klüner, Thorsten
2012-03-28
In this paper, control of open quantum systems with emphasis on the control of surface photochemical reactions is presented. A quantum system in a condensed phase undergoes strong dissipative processes. From a theoretical viewpoint, it is important to model such processes in a rigorous way. In this work, the description of open quantum systems is realized within the surrogate hamiltonian approach [R. Baer and R. Kosloff, J. Chem. Phys. 106, 8862 (1997)]. An efficient and accurate method to find control fields is optimal control theory (OCT) [W. Zhu, J. Botina, and H. Rabitz, J. Chem. Phys. 108, 1953 (1998); Y. Ohtsuki, G. Turinici, and H. Rabitz, J. Chem. Phys. 120, 5509 (2004)]. To gain control of open quantum systems, the surrogate hamiltonian approach and OCT, with time-dependent targets, are combined. Three open quantum systems are investigated by the combined method, a harmonic oscillator immersed in an ohmic bath, CO adsorbed on a platinum surface, and NO adsorbed on a nickel oxide surface. Throughout this paper, atomic units, i.e., ℏ = m(e) = e = a(0) = 1, have been used unless otherwise stated.
Naz, Rehana
2018-01-01
Pontrygin-type maximum principle is extended for the present value Hamiltonian systems and current value Hamiltonian systems of nonlinear difference equations for uniform time step $h$. A new method termed as a discrete time current value Hamiltonian method is established for the construction of first integrals for current value Hamiltonian systems of ordinary difference equations arising in Economic growth theory.
A Hamiltonian approach to Thermodynamics
Energy Technology Data Exchange (ETDEWEB)
Baldiotti, M.C., E-mail: baldiotti@uel.br [Departamento de Física, Universidade Estadual de Londrina, 86051-990, Londrina-PR (Brazil); Fresneda, R., E-mail: rodrigo.fresneda@ufabc.edu.br [Universidade Federal do ABC, Av. dos Estados 5001, 09210-580, Santo André-SP (Brazil); Molina, C., E-mail: cmolina@usp.br [Escola de Artes, Ciências e Humanidades, Universidade de São Paulo, Av. Arlindo Bettio 1000, CEP 03828-000, São Paulo-SP (Brazil)
2016-10-15
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 extensively 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.
A Hamiltonian approach to Thermodynamics
International Nuclear Information System (INIS)
Baldiotti, M.C.; Fresneda, R.; Molina, C.
2016-01-01
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 extensively 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.
A Symbolic Computation Approach to Parameterizing Controller for Polynomial Hamiltonian Systems
Directory of Open Access Journals (Sweden)
Zhong Cao
2014-01-01
Full Text Available This paper considers controller parameterization method of H∞ control for polynomial Hamiltonian systems (PHSs, which involves internal stability and external disturbance attenuation. The aims of this paper are to design a controller with parameters to insure that the systems are H∞ stable and propose an algorithm for solving parameters of the controller with symbolic computation. The proposed parameterization method avoids solving Hamilton-Jacobi-Isaacs equations, and thus the obtained controllers with parameters are relatively simple in form and easy in operation. Simulation with a numerical example shows that the controller is effective as it can optimize H∞ control by adjusting parameters. All these results are expected to be of use in the study of H∞ control for nonlinear systems with perturbations.
Ostrogradski Hamiltonian approach for geodetic brane gravity
International Nuclear Information System (INIS)
Cordero, Ruben; Molgado, Alberto; Rojas, Efrain
2010-01-01
We present an alternative Hamiltonian description of a branelike universe immersed in a flat background spacetime. This model is named geodetic brane gravity. We set up the Regge-Teitelboim model to describe our Universe where such field theory is originally thought as a second order derivative theory. We refer to an Ostrogradski Hamiltonian formalism to prepare the system to its quantization. This approach comprize the manage of both first- and second-class constraints and the counting of degrees of freedom follows accordingly.
Adaptive control of port-Hamiltonian systems
Dirksz, D.A.; Scherpen, J.M.A.; Edelmayer, András
2010-01-01
In this paper an adaptive control scheme is presented for general port-Hamiltonian systems. Adaptive control is used to compensate for control errors that are caused by unknown or uncertain parameter values of a system. The adaptive control is also combined with canonical transformation theory for
Hamiltonian quantum simulation with bounded-strength controls
International Nuclear Information System (INIS)
Bookatz, Adam D; Wocjan, Pawel; Viola, Lorenza
2014-01-01
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. (papers)
Betatron coupling: Merging Hamiltonian and matrix approaches
Directory of Open Access Journals (Sweden)
R. Calaga
2005-03-01
Full Text Available Betatron coupling is usually analyzed using either matrix formalism or Hamiltonian perturbation theory. The latter is less exact but provides a better physical insight. In this paper direct relations are derived between the two formalisms. This makes it possible to interpret the matrix approach in terms of resonances, as well as use results of both formalisms indistinctly. An approach to measure the complete coupling matrix and its determinant from turn-by-turn data is presented. Simulations using methodical accelerator design MAD-X, an accelerator design and tracking program, were performed to validate the relations and understand the scope of their application to real accelerators such as the Relativistic Heavy Ion Collider.
Almost periodic Hamiltonians: an algebraic approach
International Nuclear Information System (INIS)
Bellissard, J.
1981-07-01
We develop, by analogy with the study of periodic potential, an algebraic theory for almost periodic hamiltonians, leading to a generalized Bloch theorem. This gives rise to results concerning the spectral measures of these operators in terms of those of the corresponding Bloch hamiltonians
Generalized Hubbard Hamiltonian: renormalization group approach
International Nuclear Information System (INIS)
Cannas, S.A.; Tamarit, F.A.; Tsallis, C.
1991-01-01
We study a generalized Hubbard Hamiltonian which is closed within the framework of a Quantum Real Space Renormalization Group, which replaces the d-dimensional hypercubic lattice by a diamond-like lattice. The phase diagram of the generalized Hubbard Hamiltonian is analyzed for the half-filled band case in d = 2 and d = 3. Some evidence for superconductivity is presented. (author). 44 refs., 12 figs., 2 tabs
An effective Hamiltonian approach to quantum random walk
Indian Academy of Sciences (India)
2017-02-09
Feb 9, 2017 ... Abstract. In this article we present an effective Hamiltonian approach for discrete time quantum random walk. A form of the Hamiltonian for one-dimensional quantum walk has been prescribed, utilizing the fact that Hamil- tonians are generators of time translations. Then an attempt has been made to ...
Quantum control mechanism analysis through field based Hamiltonian encoding
International Nuclear Information System (INIS)
Mitra, Abhra; Rabitz, Herschel
2006-01-01
Optimal control of quantum dynamics in the laboratory is proving to be increasingly successful. The control fields can be complex, and the mechanisms by which they operate have often remained obscure. Hamiltonian encoding (HE) has been proposed as a method for understanding mechanisms in quantum dynamics. In this context mechanism is defined in terms of the dominant quantum pathways leading to the final state of the controlled system. HE operates by encoding a special modulation into the Hamiltonian and decoding its signature in the dynamics to determine the dominant pathway amplitudes. Earlier work encoded the modulation directly into the Hamiltonian operators. This present work introduces the alternative scheme of field based HE, where the modulation is encoded into the control field and not directly into the Hamiltonian operators. This distinct form of modulation yields a new perspective on mechanism and is computationally faster than the earlier approach. Field based encoding is also an important step towards a laboratory based algorithm for HE as it is the only form of encoding that may be experimentally executed. HE is also extended to cover systems with noise and uncertainty and finally, a hierarchical algorithm is introduced to reveal mechanism in a stepwise fashion of ever increasing detail as desired. This new hierarchical algorithm is an improvement over earlier approaches to HE where the entire mechanism was determined in one stroke. The improvement comes from the use of less complex modulation schemes, which leads to fewer evaluations of Schroedinger's equation. A number of simulations are presented on simple systems to illustrate the new field based encoding technique for mechanism assessment
Experimental Hamiltonian identification for controlled two-level systems
International Nuclear Information System (INIS)
Schirmer, S.G.; Kolli, A.; Oi, D.K.L.
2004-01-01
We present a strategy to empirically determine the internal and control Hamiltonians for an unknown two-level system (black box) subject to various (piecewise constant) control fields when direct readout by measurement is limited to a single, fixed observable
The Electromagnetic Dipole Radiation Field through the Hamiltonian Approach
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…
Divide and conquer approach to quantum Hamiltonian simulation
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.
Hamiltonian approach to second order gauge invariant cosmological perturbations
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.
From Hamiltonian chaos to complex systems a nonlinear physics approach
Leonetti, Marc
2013-01-01
From Hamiltonian Chaos to Complex Systems: A Nonlinear Physics Approach collects contributions on recent developments in non-linear dynamics and statistical physics with an emphasis on complex systems. This book provides a wide range of state-of-the-art research in these fields. The unifying aspect of this book is a demonstration of how similar tools coming from dynamical systems, nonlinear physics, and statistical dynamics can lead to a large panorama of research in various fields of physics and beyond, most notably with the perspective of application in complex systems. This book also: Illustrates the broad research influence of tools coming from dynamical systems, nonlinear physics, and statistical dynamics Adopts a pedagogic approach to facilitate understanding by non-specialists and students Presents applications in complex systems Includes 150 illustrations From Hamiltonian Chaos to Complex Systems: A Nonlinear Physics Approach is an ideal book for graduate students and researchers working in applied...
Tsallis thermostatistics for finite systems: a Hamiltonian approach
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.
Relativistic Many-Body Hamiltonian Approach to Mesons
Llanes-Estrada, Felipe J.; Cotanch, Stephen R.
2001-01-01
We represent QCD at the hadronic scale by means of an effective Hamiltonian, $H$, formulated in the Coulomb gauge. As in the Nambu-Jona-Lasinio model, chiral symmetry is explicity broken, however our approach is renormalizable and also includes confinement through a linear potential with slope specified by lattice gauge theory. This interaction generates an infrared integrable singularity and we detail the computationally intensive procedure necessary for numerical solution. We focus upon app...
Spacecraft Attitude Control in Hamiltonian Framework
DEFF Research Database (Denmark)
Wisniewski, Rafal
2000-01-01
The objective of this paper is to give a design scheme for attitude control algorithms of a generic spacecraft. Along with the system model formulated in the Hamilton's canonical form the algorithm uses information about a required potential energy and a dissipative term. The control action...
Optimal control methods for rapidly time-varying Hamiltonians
International Nuclear Information System (INIS)
Motzoi, F.; Merkel, S. T.; Wilhelm, F. K.; Gambetta, J. M.
2011-01-01
In this article, we develop a numerical method to find optimal control pulses that accounts for the separation of timescales between the variation of the input control fields and the applied Hamiltonian. In traditional numerical optimization methods, these timescales are treated as being the same. While this approximation has had much success, in applications where the input controls are filtered substantially or mixed with a fast carrier, the resulting optimized pulses have little relation to the applied physical fields. Our technique remains numerically efficient in that the dimension of our search space is only dependent on the variation of the input control fields, while our simulation of the quantum evolution is accurate on the timescale of the fast variation in the applied Hamiltonian.
Tunneling in expanding Universe: Euclidean and Hamiltonian approaches
International Nuclear Information System (INIS)
Goncharov, A.S.; Linde, A.D.
1986-01-01
The theory of the false vacuum decay in de Sitter space and in the inflationary Universe, and also the theory of the Universe creation ''from nothing'' are discussed. This explained why tunneling in the inflationary Universe differs from that in de Sitter space and cannot be exactly homogeneous. It is shown that in several important cases the Euclidean approach should be considerably modified or is absolutely inapplicable for the description of tunneling in the expanding Universe and of the process of the quantum creation of the Universe. The Hamiltonian approach to the theory of tunneling in expanding Universe is developed. The results obtained by this method are compared with the results obtained by the Euclidean approach
A Hamiltonian approach to model and analyse networks of ...
Indian Academy of Sciences (India)
2015-09-24
Sep 24, 2015 ... Gyroscopes; energy harvesters; synchronization; Hamiltonian mechanics. ... ideas and methods from nonlinear dynamics system theory, in particular, ... deploy highly sensitive, lowpower, magnetic and electric field sensors.
Port-Hamiltonian approaches to motion generation for mechanical systems
Sakai, Satoru; Stramigioli, Stefano
This paper gives new motion generation methods for mechanical port-Hamiltonian systems. First, we propose a generation method based on an asymptotic stabilization method without damping assignment. This asymptotic stabilization method preserves the Hamiltonian structure in the closed-loop system
Hamiltonian Approach to 2+1 Dimensional Gravity
Cantini, L.; Menotti, P.; Seminara, D.
2002-12-01
It is shown that the reduced particle dynamics of 2+1 dimensional gravity in the maximally slicing gauge has hamiltonian form. We give the exact diffeomorphism which transforms the spinning cone metric in the Deser, Jackiw, 't Hooft gauge to the maximally slicing gauge. It is explicitly shown that the boundary term in the action, written in hamiltonian form gives the hamiltonian for the reduced particle dynamics. The quantum mechanical translation of the two particle hamiltonian gives rise to the logarithm of the Laplace-Beltrami operator on a cone whose angular deficit is given by the total energy of the system irrespective of the masses of the particles thus proving at the quantum level a conjecture by 't Hooft on the two particle dynamics.
Diffusion Monte Carlo approach versus adiabatic computation for local Hamiltonians
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.
Hamiltonian truncation approach to quenches in the Ising field theory
Directory of Open Access Journals (Sweden)
T. Rakovszky
2016-10-01
Full Text Available In contrast to lattice systems where powerful numerical techniques such as matrix product state based methods are available to study the non-equilibrium dynamics, the non-equilibrium behaviour of continuum systems is much harder to simulate. We demonstrate here that Hamiltonian truncation methods can be efficiently applied to this problem, by studying the quantum quench dynamics of the 1+1 dimensional Ising field theory using a truncated free fermionic space approach. After benchmarking the method with integrable quenches corresponding to changing the mass in a free Majorana fermion field theory, we study the effect of an integrability breaking perturbation by the longitudinal magnetic field. In both the ferromagnetic and paramagnetic phases of the model we find persistent oscillations with frequencies set by the low-lying particle excitations not only for small, but even for moderate size quenches. In the ferromagnetic phase these particles are the various non-perturbative confined bound states of the domain wall excitations, while in the paramagnetic phase the single magnon excitation governs the dynamics, allowing us to capture the time evolution of the magnetisation using a combination of known results from perturbation theory and form factor based methods. We point out that the dominance of low lying excitations allows for the numerical or experimental determination of the mass spectra through the study of the quench dynamics.
An approach for obtaining integrable Hamiltonians from Poisson-commuting polynomial families
Leyvraz, F.
2017-07-01
We discuss a general approach permitting the identification of a broad class of sets of Poisson-commuting Hamiltonians, which are integrable in the sense of Liouville. It is shown that all such Hamiltonians can be solved explicitly by a separation of variables ansatz. The method leads in particular to a proof that the so-called "goldfish" Hamiltonian is maximally superintegrable and leads to an elementary identification of a full set of integrals of motion. The Hamiltonians in involution with the "goldfish" Hamiltonian are also explicitly integrated. New integrable Hamiltonians are identified, among which some have the property of being isochronous, that is, all their orbits have the same period. Finally, a peculiar structure is identified in the Poisson brackets between the elementary symmetric functions and the set of Hamiltonians commuting with the "goldfish" Hamiltonian: these can be expressed as products between elementary symmetric functions and Hamiltonians. The structure displays an invariance property with respect to one element and has both a symmetry and a closure property. The meaning of this structure is not altogether clear to the author, but it turns out to be a powerful tool.
Feedback Control of a Class of Nonholonomic Hamiltonian Systems
DEFF Research Database (Denmark)
Sørensen, Mathias Jesper
Feedback control of nonholonomic systems has always been problematic due to the nonholonomic constraints that limit the space of possible system velocities. This property is very basic, and Brockett proved that a nonholonomic system cannot be asymptotically stabilized by a time-invariant smooth...... turns out to be useful when stabilizing the nonholonomic system. If the system is properly actuated it is possible to asymptotically stabilize the primary part of the configuration coordinates via a passive energy shaping and damping injecting feedback. The feedback is smooth and time......-invariant, but since it does not asymptotically stabilize the secondary part of the configuration coordinates, it does not violate Brockett’s obstruction. The results fromthe general class of nonholonomicHamiltonian systems with kinematic inputs are applied to a real implementation of a four wheel steered, four wheel...
Ab-initio Hamiltonian approach to light nuclei and to quantum field ...
Indian Academy of Sciences (India)
A successful microscopic non-perturbative Hamiltonian approach to low- ... sparse matrix eigenvalue problem with the Lanczos algorithm on leadership class .... which allows for an arbitrary phase factor eiα that we have taken to be unity. The.
Fermion Bag Approach to Lattice Hamiltonian Field Theories
Huffman, Emilie
2018-03-01
Using a model in the Gross-Neveu Ising universality class, we show how the fermion bag idea can be applied to develop algorithms to Hamiltonian lattice field theories. We argue that fermion world lines suggest an alternative method to the traditional techniques for calculating ratios of determinants in a stable manner. We show the power behind these ideas by extracting the physics of the model on large lattices.
Passivation controller design for turbo-generators based on generalised Hamiltonian system theory
Cao, M.; Shen, T.L.; Song, Y.H.
2002-01-01
A method of pre-feedback to formulate the generalised forced Hamiltonian system model for speed governor control systems is proposed. Furthermore, passivation controllers are designed based on the scheme of Hamiltonian structure for single machne infinite bus and multimachine power systems. In
Hamiltonian approach to the lattice massive Schwinger model
International Nuclear Information System (INIS)
Sidorov, A.V.; Zastavenko, L.G.
1996-01-01
The authors consider the limit e 2 /m 2 much-lt 1 of the lattice massive Schwinger model, i.e., the lattice massive QED in two space-time dimensions, up to lowest order in the effective coupling constant e 2 /m 2 . Here, m is the fermion mass parameter and e is the electron charge. They compare their lattice QED model with the analogous continuous space and lattice space models, (CSM and LSM), which do not take account of the zero momentum mode, z.m.m., of the vector potential. The difference is that (due to extra z.m.m. degree of freedom) to every eigenstate of the CSM and LSM there corresponds a family of eigenstates of the authors lattice QED with the parameter λ. They restrict their consideration to small values of the parameter λ. Then, the energies of the particle states of their lattice QED and LSM do coincide (in their approximation). In the infinite periodicity length limit the Hamiltonian of the authors lattice QED (as well as the Hamiltonian of the LSM) possesses two different Hilbert spaces of eigenfunctions. Thus, in this limit the authors lattice QED model (as well as LSM) describes something like two connected, but different, worlds
Stabilization of (state, input)-disturbed CSTRs through the port-Hamiltonian systems approach
Lu, Yafei; Fang, Zhou; Gao, Chuanhou
2017-01-01
It is a universal phenomenon that the state and input of the continuous stirred tank reactor (CSTR) systems are both disturbed. This paper proposes a (state, input)-disturbed port-Hamiltonian framework that can be used to model and further designs a stochastic passivity based controller to asymptotically stabilize in probability the (state, input)-disturbed CSTR (sidCSTR) systems. The opposite entropy function and the availability function are selected as the Hamiltonian for the model and con...
Optimal adaptive control for quantum metrology with time-dependent Hamiltonians
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
Optimal adaptive control for quantum metrology with time-dependent Hamiltonians.
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.
Transverse Lattice Approach to Light-Front Hamiltonian QCD
Dalley, S
1999-01-01
We describe a non-perturbative procedure for solving from first principles the light-front Hamiltonian problem of SU(N) pure gauge theory in D spacetime dimensions (D>2), based on enforcing Lorentz covariance of observables. A transverse lattice regulator and colour-dielectric link fields are employed, together with an associated effective potential. We argue that the light-front vacuum is necessarily trivial for large enough lattice spacing, and clarify why this leads to an Eguchi-Kawai dimensional reduction of observables to 1+1-dimensions in the infinite N limit. The procedure is then tested by explicit calculations for 2+1-dimensional SU(infinity) gauge theory, within a first approximation to the lattice effective potential. We identify a scaling trajectory which produces Lorentz covariant behaviour for the lightest glueballs. The predicted masses, in units of the measured string tension, are in agreement with recent results from conventional Euclidean lattice simulations. In addition, we obtain the poten...
Hamiltonian approach to QCD in Coulomb gauge: From the vacuum to finite temperatures
Directory of Open Access Journals (Sweden)
Reinhardt H.
2016-01-01
Full Text Available The variational Hamiltonian approach to QCD in Coulomb gauge is reviewedand the essential results obtained in recent years are summarized. First the results for thevacuum sector are discussed, with a special emphasis on the mechansim of confinementand chiral symmetry breaking. Then the deconfinement phase transition is described byintroducing temperature in the Hamiltonian approach via compactification of one spatialdimension. The effective action for the Polyakov loop is calculated and the order of thephase transition as well as the critical temperatures are obtained for the color group SU(2 and SU(3. In both cases, our predictions are in good agreement with lattice calculations.
Ab initio Hamiltonian approach to light nuclei and quantum field theory
International Nuclear Information System (INIS)
Vary, James P.
2009-01-01
A basis-function approach that has proven successful for solving the nonrelativistic strongly interacting nuclear many-body problem and appears promising for solving relativistic field theory in a light-front Hamiltonian framework is presented. Both conventional nuclear manybody theory and light-front field theory face common issues within the Hamiltonian approach - i.e. how to; (1) define the Hamiltonian; (2) renormalize to a finite space; (3) solve for non-perturbative observables, preserving as many symmetries as possible; and (4) take the continuum limit. Each of these challenges requires a substantial undertaking but appears solvable. Advances in computational physics, both algorithms and parallel computers, have proven essential to the recent progress. I will present results that illustrate the recent advances and indicate the path forward to ever more realistic applications
BRST quantization of Yang-Mills theory: A purely Hamiltonian approach on Fock space
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.
Newton algorithm for Hamiltonian characterization in quantum control
International Nuclear Information System (INIS)
Ndong, M; Sugny, D; Salomon, J
2014-01-01
We propose a Newton algorithm to characterize the Hamiltonian of a quantum system interacting with a given laser field. The algorithm is based on the assumption that the evolution operator of the system is perfectly known at a fixed time. The computational scheme uses the Crank–Nicholson approximation to explicitly determine the derivatives of the propagator with respect to the Hamiltonians of the system. In order to globalize this algorithm, we use a continuation method that improves its convergence properties. This technique is applied to a two-level quantum system and to a molecular one with a double-well potential. The numerical tests show that accurate estimates of the unknown parameters are obtained in some cases. We discuss the numerical limits of the algorithm in terms of the basin of convergence and the non-uniqueness of the solution. (paper)
Towards Ocean Grazer's Modular Power Take-Off System Modeling : A Port-Hamiltonian Approach
Barradas-Berglind, J. J.; Muñoz Arias, M.; Wei, Y.; Prins, W.A.; Vakis, A.I.; Jayawardhana, B.; Dochain, Denis; Henrion, Didier; Peaucelle, Dimitri
This paper presents a modular modeling framework for the Ocean Grazer's Power Take-Off (PTO) system, which operates as an array of point-absorber type devices connected to a hydraulic system. The modeling is based on the port-Hamiltonian (PH) framework that enables energy-based analysis and control
Escobar, Gerardo; Schaft, Arjan J. van der; Ortega, Romeo
1999-01-01
In this paper we show how, using the Hamiltonian formalism, we can systematically derive mathematical models that describe the behaviour of a large class of switching power converters, including the "Boost", "Buck", "Buck-Boost", "Čuk" and "Flyback" converters. We follow the approach earlier
Lattice Hamiltonian approach to the massless Schwinger model. Precise extraction of the mass gap
International Nuclear Information System (INIS)
Cichy, Krzysztof; Poznan Univ.; Kujawa-Cichy, Agnieszka; Szyniszewski, Marcin; Manchester Univ.
2012-12-01
We present results of applying the Hamiltonian approach to the massless Schwinger model. A finite basis is constructed using the strong coupling expansion to a very high order. Using exact diagonalization, the continuum limit can be reliably approached. This allows to reproduce the analytical results for the ground state energy, as well as the vector and scalar mass gaps to an outstanding precision better than 10 -6 %.
Lattice Hamiltonian approach to the massless Schwinger model. Precise extraction of the mass gap
Energy Technology Data Exchange (ETDEWEB)
Cichy, Krzysztof [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Poznan Univ. (Poland). Faculty of Physics; Kujawa-Cichy, Agnieszka [Poznan Univ. (Poland). Faculty of Physics; Szyniszewski, Marcin [Poznan Univ. (Poland). Faculty of Physics; Manchester Univ. (United Kingdom). NOWNano DTC
2012-12-15
We present results of applying the Hamiltonian approach to the massless Schwinger model. A finite basis is constructed using the strong coupling expansion to a very high order. Using exact diagonalization, the continuum limit can be reliably approached. This allows to reproduce the analytical results for the ground state energy, as well as the vector and scalar mass gaps to an outstanding precision better than 10{sup -6} %.
Nonautonomous linear Hamiltonian systems oscillation, spectral theory and control
Johnson, Russell; Novo, Sylvia; Núñez, Carmen; Fabbri, Roberta
2016-01-01
This monograph contains an in-depth analysis of the dynamics given by a linear Hamiltonian system of general dimension with nonautonomous bounded and uniformly continuous coefficients, without other initial assumptions on time-recurrence. Particular attention is given to the oscillation properties of the solutions as well as to a spectral theory appropriate for such systems. The book contains extensions of results which are well known when the coefficients are autonomous or periodic, as well as in the nonautonomous two-dimensional case. However, a substantial part of the theory presented here is new even in those much simpler situations. The authors make systematic use of basic facts concerning Lagrange planes and symplectic matrices, and apply some fundamental methods of topological dynamics and ergodic theory. Among the tools used in the analysis, which include Lyapunov exponents, Weyl matrices, exponential dichotomy, and weak disconjugacy, a fundamental role is played by the rotation number for linear Hami...
Entanglement capacity of nonlocal Hamiltonians: A geometric approach
International Nuclear Information System (INIS)
Lari, Behzad; Hassan, Ali Saif M.; Joag, Pramod S.
2009-01-01
We develop a geometric approach to quantify the capability of creating entanglement for a general physical interaction acting on two qubits. We use the entanglement measure proposed by us for N-qubit pure states [Ali Saif M. Hassan and Pramod S. Joag, Phys. Rev. A 77, 062334 (2008)]. This geometric method has the distinct advantage that it gives the experimentally implementable criteria to ensure the optimal entanglement production rate without requiring a detailed knowledge of the state of the two qubit system. For the production of entanglement in practice, we need criteria for optimal entanglement production, which can be checked in situ without any need to know the state, as experimentally finding out the state of a quantum system is generally a formidable task. Further, we use our method to quantify the entanglement capacity in higher level and multipartite systems. We quantify the entanglement capacity for two qutrits and find the maximal entanglement generation rate and the corresponding state for the general isotropic interaction between qutrits, using the entanglement measure of N-qudit pure states proposed by us [Ali Saif M. Hassan and Pramod S. Joag, Phys. Rev. A 80, 042302 (2009)]. Next we quantify the genuine three qubit entanglement capacity for a general interaction between qubits. We obtain the maximum entanglement generation rate and the corresponding three qubit state for a general isotropic interaction between qubits. The state maximizing the entanglement generation rate is of the Greenberger-Horne-Zeilinger class. To the best of our knowledge, the entanglement capacities for two qutrit and three qubit systems have not been reported earlier.
Interpolation approach to Hamiltonian-varying quantum systems and the adiabatic theorem
International Nuclear Information System (INIS)
Pan, Yu; James, Matthew R.; Miao, Zibo; Amini, Nina H.; Ugrinovskii, Valery
2015-01-01
Quantum control could be implemented by varying the system Hamiltonian. According to adiabatic theorem, a slowly changing Hamiltonian can approximately keep the system at the ground state during the evolution if the initial state is a ground state. In this paper we consider this process as an interpolation between the initial and final Hamiltonians. We use the mean value of a single operator to measure the distance between the final state and the ideal ground state. This measure resembles the excitation energy or excess work performed in thermodynamics, which can be taken as the error of adiabatic approximation. We prove that under certain conditions, this error can be estimated for an arbitrarily given interpolating function. This error estimation could be used as guideline to induce adiabatic evolution. According to our calculation, the adiabatic approximation error is not linearly proportional to the average speed of the variation of the system Hamiltonian and the inverse of the energy gaps in many cases. In particular, we apply this analysis to an example in which the applicability of the adiabatic theorem is questionable. (orig.)
Superconformal gravity in Hamiltonian form: another approach to the renormalization of gravitation
International Nuclear Information System (INIS)
Kaku, M.
1983-01-01
We reexpress superconformal gravity in Hamiltonian form, explicitly displaying all 24 generators of the group as Dirac constraints on the Hilbert space. From this, we can establish a firm foundation for the canonical quantization of superconformal gravity. The purpose of writing down the Hamiltonian form of the theory is to reexamine the question of renormalization and unitarity. Usually, we start with unitary theories of gravity, such as the Einstein-Hilbert action or supergravity, both of which are probably not renormalizable. In this series of papers, we take the opposite approach and start with a theory which is renormalizable but has problems with unitarity. Conformal and superconformal gravity are both plagued with dipole ghosts when we use perturbation theory to quantize the theories. It is difficult to interpret the results of perturbation theory because the asymptotic states have zero norm and the potential between particles grows linearly with the separation distance. The purpose of writing the Hamiltonian form of these theories is to approach the question of unitarity from a different point of view. For example, a strong-coupling approach to these theories may yield a totally different perturbation expansion. We speculate that canonically quantizing the theory by power expanding in the strong-coupling regime may yield a different set of asymptotic states, somewhat similar to the situation in gauge theories. In this series of papers, we wish to reopen the question of the unitarity of conformal theories. We conjecture that ghosts are ''confined.''
Resistance of a 1D random chain: Hamiltonian version of the transfer matrix approach
Dossetti-Romero, V.; Izrailev, F. M.; Krokhin, A. A.
2004-01-01
We study some mesoscopic properties of electron transport by employing one-dimensional chains and Anderson tight-binding model. Principal attention is paid to the resistance of finite-length chains with disordered white-noise potential. We develop a new version of the transfer matrix approach based on the equivalency of a discrete Schrödinger equation and a two-dimensional Hamiltonian map describing a parametric kicked oscillator. In the two limiting cases of ballistic and localized regime we demonstrate how analytical results for the mean resistance and its second moment can be derived directly from the averaging over classical trajectories of the Hamiltonian map. We also discuss the implication of the single parameter scaling hypothesis to the resistance.
Resistance of a 1D random chain: Hamiltonian version of the transfer matrix approach
International Nuclear Information System (INIS)
Dossetti-Romero, V.; Izrailev, F.M.; Krokhin, A.A.
2004-01-01
We study some mesoscopic properties of electron transport by employing one-dimensional chains and Anderson tight-binding model. Principal attention is paid to the resistance of finite-length chains with disordered white-noise potential. We develop a new version of the transfer matrix approach based on the equivalency of a discrete Schroedinger equation and a two-dimensional Hamiltonian map describing a parametric kicked oscillator. In the two limiting cases of ballistic and localized regime we demonstrate how analytical results for the mean resistance and its second moment can be derived directly from the averaging over classical trajectories of the Hamiltonian map. We also discuss the implication of the single parameter scaling hypothesis to the resistance
Quantum dynamics of a vibronically coupled linear chain using a surrogate Hamiltonian approach
Energy Technology Data Exchange (ETDEWEB)
Lee, Myeong H., E-mail: myeong.lee@warwick.ac.uk; Troisi, Alessandro [Department of Chemistry and Centre for Scientific Computing, University of Warwick, Coventry CV4 7AL (United Kingdom)
2016-06-07
Vibronic coupling between the electronic and vibrational degrees of freedom has been reported to play an important role in charge and exciton transport in organic photovoltaic materials, molecular aggregates, and light-harvesting complexes. Explicitly accounting for effective vibrational modes rather than treating them as a thermal environment has been shown to be crucial to describe the effect of vibronic coupling. We present a methodology to study dissipative quantum dynamics of vibronically coupled systems based on a surrogate Hamiltonian approach, which is in principle not limited by Markov approximation or weak system-bath interaction, using a vibronic basis. We apply vibronic surrogate Hamiltonian method to a linear chain system and discuss how different types of relaxation process, intramolecular vibrational relaxation and intermolecular vibronic relaxation, influence population dynamics of dissipative vibronic systems.
Controlling effect of geometrically defined local structural changes on chaotic Hamiltonian systems.
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.
Asymptotic Stabilization of Non-holonomic Port-controlled Hamiltonian Systems
DEFF Research Database (Denmark)
Sørensen, Mathias Jesper; Bendtsen, Jan Dimon; Andersen, Palle
2004-01-01
A novel method for asymptotic stabilization of a class of non-holonomic systems is presented. The method is based on the port-controlled Hamiltonian description of electro-mechanical systems. The general system is augmented with so-called kinematic inputs, thus representing a special class of mob...
Hamiltonian approach to QCD in Coulomb gauge at zero and finite temperature
Directory of Open Access Journals (Sweden)
Reinhardt H.
2017-01-01
Full Text Available I report on recent results obtained within the Hamiltonian approach to QCD in Coulomb gauge. By relating the Gribov confinement scenario to the center vortex picture of confinement it is shown that the Coulomb string tension is tied to the spatial string tension. For the quark sector a vacuum wave functional is used which results in variational equations which are free of ultraviolet divergences. The variational approach is extended to finite temperatures by compactifying a spatial dimension. For the chiral and deconfinement phase transition pseudo-critical temperatures of 170MeV and 198 MeV, respectively, are obtained.
A Hamiltonian Approach to Fault Isolation in a Planar Vertical Take–Off and Landing Aircraft Model
Directory of Open Access Journals (Sweden)
Rodriguez-Alfaro Luis H.
2015-03-01
Full Text Available The problem of fault detection and isolation in a class of nonlinear systems having a Hamiltonian representation is considered. In particular, a model of a planar vertical take-off and landing aircraft with sensor and actuator faults is studied. A Hamiltonian representation is derived from an Euler-Lagrange representation of the system model considered. In this form, nonlinear decoupling is applied in order to obtain subsystems with (as much as possible specific fault sensitivity properties. The resulting decoupled subsystem is represented as a Hamiltonian system and observer-based residual generators are designed. The results are presented through simulations to show the effectiveness of the proposed approach.
An inversion-relaxation approach for sampling stationary points of spin model Hamiltonians
International Nuclear Information System (INIS)
Hughes, Ciaran; Mehta, Dhagash; Wales, David J.
2014-01-01
Sampling the stationary points of a complicated potential energy landscape is a challenging problem. Here, we introduce a sampling method based on relaxation from stationary points of the highest index of the Hessian matrix. We illustrate how this approach can find all the stationary points for potentials or Hamiltonians bounded from above, which includes a large class of important spin models, and we show that it is far more efficient than previous methods. For potentials unbounded from above, the relaxation part of the method is still efficient in finding minima and transition states, which are usually the primary focus of attention for atomistic systems
Field-strength formulation of gauge theories. The Hamiltonian approach in the Abelian theory
International Nuclear Information System (INIS)
Mendel, E.; Durand, L.
1984-01-01
We develop a Hamiltonian approach to the field-strength or dual formation of the Abelian gauge theory in which the potential A/sup μ/ is eliminated as a dynamical variable. Our work is based on the covariant gauge x/sup μ/A/sub μ/(x) = 0 which allows a simple elimination of A/sup μ/ in terms of the field strengths F/sup munu/. We obtain complete results for the generating functional for the Green's functions of the theory, Z = Z[f,g], where f and g are nonlocal currents coupled to E and B, and illustrate some unfamiliar aspects of the new formalism
Hamiltonian approach to 1 + 1 dimensional Yang-Mills theory in Coulomb gauge
International Nuclear Information System (INIS)
Reinhardt, H.; Schleifenbaum, W.
2009-01-01
We study the Hamiltonian approach to 1 + 1 dimensional Yang-Mills theory in Coulomb gauge, considering both the pure Coulomb gauge and the gauge where in addition the remaining constant gauge field is restricted to the Cartan algebra. We evaluate the corresponding Faddeev-Popov determinants, resolve Gauss' law and derive the Hamiltonians, which differ in both gauges due to additional zero modes of the Faddeev-Popov kernel in the pure Coulomb gauge. By Gauss' law the zero modes of the Faddeev-Popov kernel constrain the physical wave functionals to zero colour charge states. We solve the Schroedinger equation in the pure Coulomb gauge and determine the vacuum wave functional. The gluon and ghost propagators and the static colour Coulomb potential are calculated in the first Gribov region as well as in the fundamental modular region, and Gribov copy effects are studied. We explicitly demonstrate that the Dyson-Schwinger equations do not specify the Gribov region while the propagators and vertices do depend on the Gribov region chosen. In this sense, the Dyson-Schwinger equations alone do not provide the full non-abelian quantum gauge theory, but subsidiary conditions must be required. Implications of Gribov copy effects for lattice calculations of the infrared behaviour of gauge-fixed propagators are discussed. We compute the ghost-gluon vertex and provide a sensible truncation of Dyson-Schwinger equations. Approximations of the variational approach to the 3 + 1 dimensional theory are checked by comparison to the 1 + 1 dimensional case
On the nesting of Painlevé hierarchies: A Hamiltonian approach
International Nuclear Information System (INIS)
Pickering, A.
2012-01-01
Highlights: ► Explanation of nesting of Painlevé hierarchies in terms of Hamiltonian structures. ► Approach generally phrased and applicable to continuous and discrete systems. ► Importance of related integrable hierarchies in understanding Painlevé hierarchies. - Abstract: We consider the phenomenon whereby two different Painlevé hierarchies, related to the same hierarchy of completely integrable equations, are such that solutions of one member of one of the Painlevé hierarchies are also solutions of a higher-order member of the other Painlevé hierarchy. An explanation is given in terms of the Hamiltonian structures of the related underlying completely integrable hierarchies, and is sufficiently generally formulated so as to be applicable equally to both continuous and discrete Painlevé hierarchies. Special integrals of a further Painlevé hierarchy related by Bäcklund transformation to the other Painlevé hierarchy mentioned above can also be constructed. Examples of the application of this approach to Painlevé hierarchies related to the Korteweg–de Vries, dispersive water wave, Toda and Volterra integrable hierarchies are considered. Our results provide further evidence of the importance of the underlying structures of related completely integrable hierarchies in understanding the properties of Painlevé hierarchies.
Deconfinement phase transition in the Hamiltonian approach to Yang–Mills theory in Coulomb gauge
Directory of Open Access Journals (Sweden)
Reinhardt H.
2014-04-01
Full Text Available Recent results obtained for the deconfinement phase transition within the Hamiltonian approach to Yang–Mills theory are reviewed. Assuming a quasiparticle picture for the grand canonical gluon ensemble the thermal equilibrium state is found by minimizing the free energy with respect to the quasi-gluon energy. The deconfinement phase transition is accompanied by a drastic change of the infrared exponents of the ghost and gluon propagators. Above the phase transition the ghost form factor remains infrared divergent but its infrared exponent is approximately halved. The gluon energy being infrared divergent in the confined phase becomes infrared finite in the deconfined phase. Furthermore, the effective potential of the order parameter for confinement is calculated for SU(N Yang–Mills theory in the Hamiltonian approach by compactifying one spatial dimension and using a background gauge fixing. In the simplest truncation, neglecting the ghost and using the ultraviolet form of the gluon energy, we recover the Weiss potential. From the full non-perturbative potential (with the ghost included we extract a critical temperature of the deconfinement phase transition of 269 MeV for the gauge group SU(2 and 283 MeV for SU(3.
Computing pKa Values with a Mixing Hamiltonian Quantum Mechanical/Molecular Mechanical Approach.
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.
Nonlinear H-infinity control, Hamiltonian systems and Hamilton-Jacobi equations
Aliyu, MDS
2011-01-01
A comprehensive overview of nonlinear Haeu control theory for both continuous-time and discrete-time systems, Nonlinear Haeu-Control, Hamiltonian Systems and Hamilton-Jacobi Equations covers topics as diverse as singular nonlinear Haeu-control, nonlinear Haeu -filtering, mixed H2/ Haeu-nonlinear control and filtering, nonlinear Haeu-almost-disturbance-decoupling, and algorithms for solving the ubiquitous Hamilton-Jacobi-Isaacs equations. The link between the subject and analytical mechanics as well as the theory of partial differential equations is also elegantly summarized in a single chapter
Synchronisation in coupled quantum Hamiltonian superconducting oscillator via a control potential
International Nuclear Information System (INIS)
Al-Khawaja, Sameer
2009-01-01
This paper presents chaos synchronisation in a SQUID device mutually coupled to a resonant LC classical circuit. Via the Hamiltonian of the coupled quantum-classical system and by means of a 'control potential' in the form of a double-well, measure synchronisation has been found to exist. A transition from quasi-periodic to chaotically synchronised orbits in the phase space has been observed, as the strength of coupling is increased between both oscillators. The system reaches a non-synchronised state if the choice of the control potential were to render both oscillators non-identical.
International Nuclear Information System (INIS)
Kupka, M.; Farkasovsky, P.C.
1992-01-01
Point-contact spectra have been calculated for normal metal -heavy-fermion metal system (described by means of a simplified model Hamiltonian). Two approaches are used: one of them states that the differential conductance reflects an energy-dependent quasi-particle density of states, and 2. one drives the differential conductance are compared
International Nuclear Information System (INIS)
Rey-de-Castro, R.; Rabitz, H.
2010-01-01
We report on the laboratory implementation of quantum-control-mechanism identification through Hamiltonian encoding and observable decoding (HE-OD). Over a sequence of experiments, HE-OD introduces a special encoded signature into the components of a previously determined control field expressed in a chosen representation. The outcome appears as a modulated signal in the controlled system observable. Decoding the modulated signal identifies the hierarchy of correlations between components of the control field in a particular representation. In cases where the initial quantum state and observable operator are fully known, then HE-OD can also identify the transition amplitudes of the various Dyson expansion orders contributing to the controlled dynamics. The basic principles of HE-OD are illustrated for second harmonic generation when the components of the field representation are simply taken as the pixels in the pulse shaper. The outcome of HE-OD agrees well with simulations, verifying the concept.
The lattice spinor QED Hamiltonian critique of the continuous space approach
International Nuclear Information System (INIS)
Sidorov, A.V.; Zastavenko, L.G.
1993-01-01
We give the irreproachable, from the point of view of gauge invariance, derivation of the lattice spinor QED Hamiltonian. Our QED Hamiltonian is manifestly gauge invariant. We point out important defects of the continuous space formulation of the QED that make, in our opinion, the lattice QED obviously preferable to the continuous space QED. We state that it is impossible to give a continuous space QED formulation which is compatible with the condition of gauge invariance. 17 refs
A new approach in the design of an interactive environment for teaching Hamiltonian digraphs
International Nuclear Information System (INIS)
Iordan, A E; Panoiu, M
2014-01-01
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
Hamroun , Boussad; Dimofte , Alexandru; Lefevre , Laurent; Mendes , Eduardo
2010-01-01
International audience; — In this paper a control algorithm for the reduced port-Controlled Hamiltonian model (PCH) of the shallow water equations (PDEs) is developed. This control is developed using the Interconnection and Damping Assignment Passivity Based Control (IDA-PBC) method on the reduced PCH model without the natural dissipation. It allows to assign desired structure and energy function to the closed loop system. The same control law is then derived using an energy shaping method ba...
A port-Hamiltonian approach to power network modeling and analysis
Fiaz, S.; Zonetti, D.; Ortega, R.; Scherpen, J.M.A.; van der Schaft, A.J.
2013-01-01
In this paper we present a systematic framework for modeling of power networks. The basic idea is to view the complete power network as a port-Hamiltonian system on a graph where edges correspond to components of the power network and nodes are buses. The interconnection constraints are given by the
Optimal Power Flow for resistive DC Network : A Port-Hamiltonian approach
Benedito, Ernest; del Puerto-Flores, D.; Doria-Cerezo, A.; Scherpen, Jacquelien M.A.; Dochain, Denis; Henrion, Didier; Peaucelle, Dimitri
This paper studies the optimal power flow problem for resistive DC networks. The gradient method algorithm is written in a port-Hamiltonian form and the stability of the resulting dynamics is studied. Stability conditions are provided for general cyclic networks and a solution, when these conditions
Hamiltonian approach to GR. Pt. 2. Covariant theory of quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Cremaschini, Claudio [Faculty of Philosophy and Science, Silesian University in Opava, Institute of Physics and Research Center for Theoretical Physics and Astrophysics, Opava (Czech Republic); Tessarotto, Massimo [University of Trieste, Department of Mathematics and Geosciences, Trieste (Italy); Faculty of Philosophy and Science, Silesian University in Opava, Institute of Physics, Opava (Czech Republic)
2017-05-15
A non-perturbative quantum field theory of General Relativity is presented which leads to a new realization of the theory of covariant quantum gravity (CQG-theory). The treatment is founded on the recently identified Hamiltonian structure associated with the classical space-time, i.e., the corresponding manifestly covariant Hamilton equations and the related Hamilton-Jacobi theory. The quantum Hamiltonian operator and the CQG-wave equation for the corresponding CQG-state and wave function are realized in 4-scalar form. The new quantum wave equation is shown to be equivalent to a set of quantum hydrodynamic equations which warrant the consistency with the classical GR Hamilton-Jacobi equation in the semiclassical limit. A perturbative approximation scheme is developed, which permits the adoption of the harmonic oscillator approximation for the treatment of the Hamiltonian potential. As an application of the theory, the stationary vacuum CQG-wave equation is studied, yielding a stationary equation for the CQG-state in terms of the 4-scalar invariant-energy eigenvalue associated with the corresponding approximate quantum Hamiltonian operator. The conditions for the existence of a discrete invariant-energy spectrum are pointed out. This yields a possible estimate for the graviton mass together with a new interpretation about the quantum origin of the cosmological constant. (orig.)
Dirksz, D. A.; Scherpen, J. M. A.; Ortega, R.
2008-01-01
A dynamic extension for position feedback of port-Hamiltonian mechanical systems is studied. First we look at the consequences for the matching equations when applying Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC). Then we look at the possibilities of asymptotically
Identifying mechanisms in the control of quantum dynamics through Hamiltonian encoding
International Nuclear Information System (INIS)
Mitra, Abhra; Rabitz, Herschel
2003-01-01
A variety of means are now available to design control fields for manipulating the evolution of quantum systems. However, the underlying physical mechanisms often remain obscure, especially in the cases of strong fields and high quantum state congestion. This paper proposes a method to quantitatively determine the various pathways taken by a quantum system in going from the initial state to the final target. The mechanism is revealed by encoding a signal in the system Hamiltonian and decoding the resultant nonlinear distortion of the signal in the system time-evolution operator. The relevant interfering pathways determined by this analysis give insight into the physical mechanisms operative during the evolution of the quantum system. A hierarchy of mechanism identification algorithms with increasing ability to extract more detailed pathway information is presented. The mechanism identification concept is presented in the context of analyzing computer simulations of controlled dynamics. As illustrations of the concept, mechanisms are identified in the control of several simple, discrete-state quantum systems. The mechanism analysis tools reveal the roles of multiple interacting quantum pathways to maximally take advantage of constructive and destructive interference. Similar procedures may be applied directly in the laboratory to identify control mechanisms without resort to computer modeling, although this extension is not addressed in this paper
Fermion bag approach to Hamiltonian lattice field theories in continuous time
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.
Supersymmetric Hamiltonian approach to edge excitations in ν=5/2 fractional quantum Hall effect
International Nuclear Information System (INIS)
Yu Ming; Zhang Xin
2008-01-01
A supersymmetric Hamiltonian is constructed for the edge excitations of the Moore-Read (Pfaffian) like state, which is a realization of the N=2 supersymmetric CS model. Fermionic generators and their conjugates are introduced to deal with the fermion pairing, whose condensation form a BCS like state. After Bogoliubov transformation, an N=2 supersymmetric and nonrelativistic Hamiltonian is found to take a known form, which is integrable. The main difference between the Moore-Read state and our BCS like state is that the number of fermion pairs in our formalism is not fixed. However, we have also found that the excited states in our model looks similar but not exactly the same as Moore and Read's
Directory of Open Access Journals (Sweden)
Weiwei Sun
2015-01-01
Full Text Available This paper presents H∞ excitation control design problem for power systems with input time delay and disturbances by using nonlinear Hamiltonian system theory. The impact of time delays introduced by remote signal transmission and processing in wide-area measurement system (WAMS is well considered. Meanwhile, the systems under investigation are disturbed by random fluctuation. First, under prefeedback technique, the power systems are described as a nonlinear Hamiltonian system. Then the H∞ excitation controller of generators connected to distant power systems with time delay and stochasticity is designed. Based on Lyapunov functional method, some sufficient conditions are proposed to guarantee the rationality and validity of the proposed control law. The closed-loop systems under the control law are asymptotically stable in mean square independent of the time delay. And we through a simulation of a two-machine power system prove the effectiveness of the results proposed in this paper.
Spinor matter fields in SL(2,C) gauge theories of gravity: Lagrangian and Hamiltonian approaches
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.
Spinor matter fields in SL(2,C) gauge theories of gravity: Lagrangian and Hamiltonian approaches
International Nuclear Information System (INIS)
Antonowicz, M.; Szczyrba, W.
1985-01-01
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
Directory of Open Access Journals (Sweden)
N. N. Romanova
1998-01-01
Full Text Available The dynamics of weakly nonlinear wave trains in unstable media is studied. This dynamics is investigated in the framework of a broad class of dynamical systems having a Hamiltonian structure. Two different types of instability are considered. The first one is the instability in a weakly supercritical media. The simplest example of instability of this type is the Kelvin-Helmholtz instability. The second one is the instability due to a weak linear coupling of modes of different nature. The simplest example of a geophysical system where the instability of this and only of this type takes place is the three-layer model of a stratified shear flow with a continuous velocity profile. For both types of instability we obtain nonlinear evolution equations describing the dynamics of wave trains having an unstable spectral interval of wavenumbers. The transformation to appropriate canonical variables turns out to be different for each case, and equations we obtained are different for the two types of instability we considered. Also obtained are evolution equations governing the dynamics of wave trains in weakly subcritical media and in media where modes are coupled in a stable way. Presented results do not depend on a specific physical nature of a medium and refer to a broad class of dynamical systems having the Hamiltonian structure of a special form.
State transformations and Hamiltonian structures for optimal control in discrete systems
Sieniutycz, S.
2006-04-01
Preserving usual definition of Hamiltonian H as the scalar product of rates and generalized momenta we investigate two basic classes of discrete optimal control processes governed by the difference rather than differential equations for the state transformation. The first class, linear in the time interval θ, secures the constancy of optimal H and satisfies a discrete Hamilton-Jacobi equation. The second class, nonlinear in θ, does not assure the constancy of optimal H and satisfies only a relationship that may be regarded as an equation of Hamilton-Jacobi type. The basic question asked is if and when Hamilton's canonical structures emerge in optimal discrete systems. For a constrained discrete control, general optimization algorithms are derived that constitute powerful theoretical and computational tools when evaluating extremum properties of constrained physical systems. The mathematical basis is Bellman's method of dynamic programming (DP) and its extension in the form of the so-called Carathéodory-Boltyanski (CB) stage optimality criterion which allows a variation of the terminal state that is otherwise fixed in Bellman's method. For systems with unconstrained intervals of the holdup time θ two powerful optimization algorithms are obtained: an unconventional discrete algorithm with a constant H and its counterpart for models nonlinear in θ. We also present the time-interval-constrained extension of the second algorithm. The results are general; namely, one arrives at: discrete canonical equations of Hamilton, maximum principles, and (at the continuous limit of processes with free intervals of time) the classical Hamilton-Jacobi theory, along with basic results of variational calculus. A vast spectrum of applications and an example are briefly discussed with particular attention paid to models nonlinear in the time interval θ.
Observation and Control of Hamiltonian Chaos in Wave-particle Interaction
International Nuclear Information System (INIS)
Doveil, F.; Ruzzon, A.; Elskens, Y.
2010-01-01
Wave-particle interactions are central in plasma physics. The paradigm beam-plasma system can be advantageously replaced by a traveling wave tube (TWT) to allow their study in a much less noisy environment. This led to detailed analysis of the self-consistent interaction between unstable waves and an either cold or warm electron beam. More recently a test cold beam has been used to observe its interaction with externally excited wave(s). This allowed observing the main features of Hamiltonian chaos and testing a new method to efficiently channel chaotic transport in phase space. To simulate accurately and efficiently the particle dynamics in the TWT and other 1D particle-wave systems, a new symplectic, symmetric, second order numerical algorithm is developed, using particle position as the independent variable, with a fixed spatial step.This contribution reviews: presentation of the TWT and its connection to plasma physics, resonant interaction of a charged particle in electrostatic waves, observation of particle trapping and transition to chaos, test of control of chaos, and description of the simulation algorithm.The velocity distribution function of the electron beam is recorded with a trochoidal energy analyzer at the output of the TWT. An arbitrary waveform generator is used to launch a prescribed spectrum of waves along the 4m long helix of the TWT. The nonlinear synchronization of particles by a single wave, responsible for Landau damping, is observed. We explore the resonant velocity domain associated with a single wave as well as the transition to large scale chaos when the resonant domains of two waves and their secondary resonances overlap. This transition exhibits a devil's staircase behavior when increasing the excitation level in agreement with numerical simulation.A new strategy for control of chaos by building barriers of transport in phase space as well as its robustness is successfully tested. The underlying concepts extend far beyond the field of
Meeds, E.; Leenders, R.; Welling, M.; Meila, M.; Heskes, T.
2015-01-01
Approximate Bayesian computation (ABC) is a powerful and elegant framework for performing inference in simulation-based models. However, due to the difficulty in scaling likelihood estimates, ABC remains useful for relatively lowdimensional problems. We introduce Hamiltonian ABC (HABC), a set of
The geometric approach to sets of ordinary differential equations and Hamiltonian dynamics
Estabrook, F. B.; Wahlquist, H. D.
1975-01-01
The calculus of differential forms is used to discuss the local integration theory of a general set of autonomous first order ordinary differential equations. Geometrically, such a set is a vector field V in the space of dependent variables. Integration consists of seeking associated geometric structures invariant along V: scalar fields, forms, vectors, and integrals over subspaces. It is shown that to any field V can be associated a Hamiltonian structure of forms if, when dealing with an odd number of dependent variables, an arbitrary equation of constraint is also added. Families of integral invariants are an immediate consequence. Poisson brackets are isomorphic to Lie products of associated CT-generating vector fields. Hamilton's variational principle follows from the fact that the maximal regular integral manifolds of a closed set of forms must include the characteristics of the set.
Fluctuations around classical solutions for gauge theories in Lagrangian and Hamiltonian approach
International Nuclear Information System (INIS)
Miskovic, Olivera; Pons, Josep M
2006-01-01
We analyse the dynamics of gauge theories and constrained systems in general under small perturbations around a classical solution in both Lagrangian and Hamiltonian formalisms. We prove that a fluctuations theory, described by a quadratic Lagrangian, has the same constraint structure and number of physical degrees of freedom as the original non-perturbed theory, assuming the non-degenerate solution has been chosen. We show that the number of Noether gauge symmetries is the same in both theories, but that the gauge algebra in the fluctuations theory becomes Abelianized. We also show that the fluctuations theory inherits all functionally independent rigid symmetries from the original theory and that these symmetries are generated by linear or quadratic generators according to whether the original symmetry is preserved by the background or is broken by it. We illustrate these results with examples
Light-Front Hamiltonian Approach to the Bound-State Problem in Quantum Electrodynamics
Jones, Billy D.
1997-10-01
Why is the study of the Lamb shift in hydrogen, which at the level of detail found in this paper was largely completed by Bethe in 1947, of any real interest today? While completing such a calculation using new techniques may be very interesting for formal and academic reasons, our primary motivation is to lay groundwork for precision bound-state calculations in QCD. The Lamb shift provides an excellent pedagogical tool for illustrating light-front Hamiltonian techniques, which are not widely known; but more importantly it presents three of the central dynamical and computational problems that we must face to make these techniques useful for solving QCD: How does a constituent picture emerge in a gauge field theory? How do bound-state energy scales emerge non-perturbatively? How does rotational symmetry emerge in a non-perturbative light-front calculation?
On the algebraic approach to the time-dependent quadratic Hamiltonian
Energy Technology Data Exchange (ETDEWEB)
Urdaneta, Ines; Palma, Alejandro [Instituto de Fisica, Benemerita Universidad Autonoma de Puebla, Puebla (Mexico); Sandoval, Lourdes, E-mail: urdaneta@sirio.ifuap.buap.m [Facultad de Ciencias de la Computacion, Benemerita Universidad Autonoma de Puebla, Puebla (Mexico)
2010-09-24
The unitary operator V(t) that diagonalizes the time-dependent quadratic Hamiltonian (TDQH) into a time-dependent harmonic oscillator (TDHO) is obtained using a Lie algebra. The method involves a factorization of the TDQH into a TDHO through a unitary Bogoliubov transformation in terms of creation and annihilation operators with time-dependent coefficients. It is shown that this operator can be easily achieved by means of the factorization, together with the commonly known Wei-Norman theorem. We discuss the conditions under which this unitary operator converges to the evolution operator U(t) of the Schroedinger equation for the TDQH, giving then a straightforward calculation of the evolution operator with respect to the procedures published in the literature.
Passive Guaranteed Simulation of Analog Audio Circuits: A Port-Hamiltonian Approach
Directory of Open Access Journals (Sweden)
Antoine Falaize
2016-09-01
Full Text Available We present a method that generates passive-guaranteed stable simulations of analog audio circuits from electronic schematics for real-time issues. On one hand, this method is based on a continuous-time power-balanced state-space representation structured into its energy-storing parts, dissipative parts, and external sources. On the other hand, a numerical scheme is especially designed to preserve this structure and the power balance. These state-space structures define the class of port-Hamiltonian systems. The derivation of this structured system associated with the electronic circuit is achieved by an automated analysis of the interconnection network combined with a dictionary of models for each elementary component. The numerical scheme is based on the combination of finite differences applied on the state (with respect to the time variable and on the total energy (with respect to the state. This combination provides a discrete-time version of the power balance. This set of algorithms is valid for both the linear and nonlinear case. Finally, three applications of increasing complexities are given: a diode clipper, a common-emitter bipolar-junction transistor amplifier, and a wah pedal. The results are compared to offline simulations obtained from a popular circuit simulator.
A mathematical approach to the effective Hamiltonian in perturbed periodic problems
International Nuclear Information System (INIS)
Gerard, C.; Martinez, A.; Sjoestrand, J.
1991-01-01
We describe a rigorous mathematical reduction of the spectral study for a class of periodic problems with perturbations which gives a justification of the method of effective Hamiltonians in solid state physics. We study the partial differential operators of the form P=P(hy, y, D y +A(hy)) on R n (when h>0 is small enough), where P(x, y, η) is elliptic, periodic in y with respect to some lattice Γ, and admits smooth bounded coefficients in (x, y). A(x) is a magnetic potential with bounded derivatives. We show that the spectral study of P near any fixed energy level can be reduced to the study of a finite system of h-pseudodifferential operators ε(x, hD x , h), acting on some Hilbert space depending on Γ. We then apply it to the study of the Schroedinger operator when the electric potential is periodic, and to some quasiperiodic potentials with vanishing magnetic field. (orig.)
Hamiltonian approach to GR - Part 1: covariant theory of classical gravity
Cremaschini, Claudio; Tessarotto, Massimo
2017-05-01
A challenging issue in General Relativity concerns the determination of the manifestly covariant continuum Hamiltonian structure underlying the Einstein field equations and the related formulation of the corresponding covariant Hamilton-Jacobi theory. The task is achieved by adopting a synchronous variational principle requiring distinction between the prescribed deterministic metric tensor \\widehat{g}(r)≡ { \\widehat{g}_{μ ν }(r)} solution of the Einstein field equations which determines the geometry of the background space-time and suitable variational fields x≡ { g,π } obeying an appropriate set of continuum Hamilton equations, referred to here as GR-Hamilton equations. It is shown that a prerequisite for reaching such a goal is that of casting the same equations in evolutionary form by means of a Lagrangian parametrization for a suitably reduced canonical state. As a result, the corresponding Hamilton-Jacobi theory is established in manifestly covariant form. Physical implications of the theory are discussed. These include the investigation of the structural stability of the GR-Hamilton equations with respect to vacuum solutions of the Einstein equations, assuming that wave-like perturbations are governed by the canonical evolution equations.
Hamiltonian approach to GR. Pt. 1. Covariant theory of classical gravity
Energy Technology Data Exchange (ETDEWEB)
Cremaschini, Claudio [Silesian University in Opava, Faculty of Philosophy and Science, Institute of Physics and Research Center for Theoretical Physics and Astrophysics, Opava (Czech Republic); Tessarotto, Massimo [University of Trieste, Department of Mathematics and Geosciences, Trieste (Italy); Silesian University in Opava, Faculty of Philosophy and Science, Institute of Physics, Opava (Czech Republic)
2017-05-15
A challenging issue in General Relativity concerns the determination of the manifestly covariant continuum Hamiltonian structure underlying the Einstein field equations and the related formulation of the corresponding covariant Hamilton-Jacobi theory. The task is achieved by adopting a synchronous variational principle requiring distinction between the prescribed deterministic metric tensor g(r) ≡ {g_μ_ν(r)} solution of the Einstein field equations which determines the geometry of the background space-time and suitable variational fields x ≡ {g,π} obeying an appropriate set of continuum Hamilton equations, referred to here as GR-Hamilton equations. It is shown that a prerequisite for reaching such a goal is that of casting the same equations in evolutionary form by means of a Lagrangian parametrization for a suitably reduced canonical state. As a result, the corresponding Hamilton-Jacobi theory is established in manifestly covariant form. Physical implications of the theory are discussed. These include the investigation of the structural stability of the GR-Hamilton equations with respect to vacuum solutions of the Einstein equations, assuming that wave-like perturbations are governed by the canonical evolution equations. (orig.)
Emergence of Landauer transport from quantum dynamics: A model Hamiltonian approach.
Pal, Partha Pratim; Ramakrishna, S; Seideman, Tamar
2018-04-14
The Landauer expression for computing current-voltage characteristics in nanoscale devices is efficient but not suited to transient phenomena and a time-dependent current because it is applicable only when the charge carriers transition into a steady flux after an external perturbation. In this article, we construct a very general expression for time-dependent current in an electrode-molecule-electrode arrangement. Utilizing a model Hamiltonian (consisting of the subsystem energy levels and their electronic coupling terms), we propagate the Schrödinger wave function equation to numerically compute the time-dependent population in the individual subsystems. The current in each electrode (defined in terms of the rate of change of the corresponding population) has two components, one due to the charges originating from the same electrode and the other due to the charges initially residing at the other electrode. We derive an analytical expression for the first component and illustrate that it agrees reasonably with its numerical counterpart at early times. Exploiting the unitary evolution of a wavefunction, we construct a more general Landauer style formula and illustrate the emergence of Landauer transport from our simulations without the assumption of time-independent charge flow. Our generalized Landauer formula is valid at all times for models beyond the wide-band limit, non-uniform electrode density of states and for time and energy-dependent electronic coupling between the subsystems. Subsequently, we investigate the ingredients in our model that regulate the onset time scale of this steady state. We compare the performance of our general current expression with the Landauer current for time-dependent electronic coupling. Finally, we comment on the applicability of the Landauer formula to compute hot-electron current arising upon plasmon decoherence.
Vilasi, Gaetano
2001-01-01
This is both a textbook and a monograph. It is partially based on a two-semester course, held by the author for third-year students in physics and mathematics at the University of Salerno, on analytical mechanics, differential geometry, symplectic manifolds and integrable systems. As a textbook, it provides a systematic and self-consistent formulation of Hamiltonian dynamics both in a rigorous coordinate language and in the modern language of differential geometry. It also presents powerful mathematical methods of theoretical physics, especially in gauge theories and general relativity. As a m
International Nuclear Information System (INIS)
Castro Moreira, I. de.
1983-01-01
A method introduced by Lewis and Leach for the obtention of exact invariants of the form I = Σ p sup(n) F sub(n) (q,t) for hamiltonian systems, is generalized and applied directly on the equations of motion. It gives us a general procedure to generates exact invariants also for non hamiltonian systems. (Author) [pt
International Nuclear Information System (INIS)
Peggs, S.; Talman, R.
1987-01-01
As proton accelerators get larger, and include more magnets, the conventional tracking programs which simulate them run slower. The purpose of this paper is to describe a method, still under development, in which element-by-element tracking around one turn is replaced by a single man, which can be processed far faster. It is assumed for this method that a conventional program exists which can perform faithful tracking in the lattice under study for some hundreds of turns, with all lattice parameters held constant. An empirical map is then generated by comparison with the tracking program. A procedure has been outlined for determining an empirical Hamiltonian, which can represent motion through many nonlinear kicks, by taking data from a conventional tracking program. Though derived by an approximate method this Hamiltonian is analytic in form and can be subjected to further analysis of varying degrees of mathematical rigor. Even though the empirical procedure has only been described in one transverse dimension, there is good reason to hope that it can be extended to include two transverse dimensions, so that it can become a more practical tool in realistic cases
A Port-Hamiltonian Approach to Optimal Frequency Regulation in Power Grids
Stegink, Tjerk; Persis, Claudio De; Schaft, Arjan van der
2015-01-01
This paper studies the problem of frequency regulation in power grids, while maximizing the social welfare. Two price-based controllers are proposed; the first one an internal-model-based controller and the second one based on a continuous gradient method for optimization. Both controllers can be
DEFF Research Database (Denmark)
Feng, Ju; Ying, Zu-Guang; Zhu, Wei-Qiu
2012-01-01
A minimax stochastic optimal semi-active control strategy for stochastically excited quasi-integrable Hamiltonian systems with parametric uncertainty by using magneto-rheological (MR) dampers is proposed. Firstly, the control problem is formulated as an n-degree-of-freedom (DOF) controlled, uncer...
Discrete variational Hamiltonian mechanics
International Nuclear Information System (INIS)
Lall, S; West, M
2006-01-01
The main contribution of this paper is to present a canonical choice of a Hamiltonian theory corresponding to the theory of discrete Lagrangian mechanics. We make use of Lagrange duality and follow a path parallel to that used for construction of the Pontryagin principle in optimal control theory. We use duality results regarding sensitivity and separability to show the relationship between generating functions and symplectic integrators. We also discuss connections to optimal control theory and numerical algorithms
The Hamiltonian Approach to Yang-Mills (2+1): An Update and Corrections to String Tension
International Nuclear Information System (INIS)
Nair, V P
2013-01-01
Yang-Mills theories in 2+1 (or 3) dimensions are interesting as nontrivial gauge theories in their own right and as effective theories of QCD at high temperatures. I shall review the basics of our Hamiltonian approach to this theory, emphasizing symmetries with a short update on its status. We will show that the calculation of the vacuum wave function for Yang-Mills theory in 2+1 dimensions is in the lowest order of a systematic expansion. Expectation values of observables can be calculated using an effective interacting chiral boson theory, which also leads to a natural expansion as a double series in the coupling constant (to be interpreted within a resummed perturbation series) and a particular kinematical factor. The calculation of the first set of corrections in this expansion shows that the string tension is modified by about −0.3% to −2.8% compared to the lowest order value. This is in good agreement with lattice estimates
Five-dimensional Hamiltonian-Jacobi approach to relativistic quantum mechanics
International Nuclear Information System (INIS)
Rose, Harald
2003-01-01
A novel theory is outlined for describing the dynamics of relativistic electrons and positrons. By introducing the Lorentz-invariant universal time as a fifth independent variable, the Hamilton-Jacobi formalism of classical mechanics is extended from three to four spatial dimensions. This approach allows one to incorporate gravitation and spin interactions in the extended five-dimensional Lagrangian in a covariant form. The universal time has the function of a hidden Bell parameter. By employing the method of variation with respect to the four coordinates of the particle and the components of the electromagnetic field, the path equation and the electromagnetic field produced by the charge and the spin of the moving particle are derived. In addition the covariant equations for the dynamics of the components of the spin tensor are obtained. These equations can be transformed to the familiar BMT equation in the case of homogeneous electromagnetic fields. The quantization of the five-dimensional Hamilton-Jacobi equation yields a five-dimensional spinor wave equation, which degenerates to the Dirac equation in the stationary case if we neglect gravitation. The quantity which corresponds to the probability density of standard quantum mechanics is the four-dimensional mass density which has a real physical meaning. By means of the Green method the wave equation is transformed into an integral equation enabling a covariant relativistic path integral formulation. Using this approach a very accurate approximation for the four-dimensional propagator is derived. The proposed formalism makes Dirac's hole theory obsolete and can readily be extended to many particles
Bountis, Tassos
2012-01-01
This book introduces and explores modern developments in the well established field of Hamiltonian dynamical systems. It focuses on high degree-of-freedom systems and the transitional regimes between regular and chaotic motion. The role of nonlinear normal modes is highlighted and the importance of low-dimensional tori in the resolution of the famous FPU paradox is emphasized. Novel powerful numerical methods are used to study localization phenomena and distinguish order from strongly and weakly chaotic regimes. The emerging hierarchy of complex structures in such regimes gives rise to particularly long-lived patterns and phenomena called quasi-stationary states, which are explored in particular in the concrete setting of one-dimensional Hamiltonian lattices and physical applications in condensed matter systems. The self-contained and pedagogical approach is blended with a unique balance between mathematical rigor, physics insights and concrete applications. End of chapter exercises and (more demanding) res...
Noncanonical Hamiltonian mechanics
International Nuclear Information System (INIS)
Litteljohn, R.G.
1986-01-01
Noncanonical variables in Hamiltonian mechanics were first used by Lagrange in 1808. In spite of this, most work in Hamiltonian mechanics has been carried out in canonical variables, up to this day. One reason for this is that noncanonical coordinates are seldom needed for mechanical problems based on Lagrangians of the form L = T - V, where T is the kinetic energy and V is the potential energy. Of course, such Lagrangians arise naturally in celestial mechanics, and as a result they form the paradigms of nineteenth-century mechanics and have become enshrined in all the mechanics textbooks. Certain features of modern problems, however, lead to the use of noncanonical coordinates. Among these are issues of gauge invariance and singular Lagrange a Poisson structures. In addition, certain problems, like the flow of magnetic-field lines in physical space, are naturally formulated in terms of noncanonical coordinates. None of these features is present in the nineteenth-century paradigms of mechanics, but they do arise in problems involving particle motion in the presence of magnetic fields. For example, the motion of a particle in an electromagnetic wave is an important one in plasma physics, but the usual Hamiltonian formulation is gauge dependent. For this problem, noncanonical approaches based on Lagrangians in phase space lead to powerful computational techniques which are gauge invariant. In the limit of strong magnetic fields, particle motion becomes 'guiding-center motion'. Guiding-center motion is also best understood in terms of noncanonical coordinates. Finally the flow of magnetic-field lines through physical space is a Hamiltonian system which is best understood with noncanonical coordinates. No doubt many more systems will arise in the future for which these noncanonical techniques can be applied. (author)
Seslija, Marko; van der Schaft, Arjan; Scherpen, Jacquelien M.A.
This paper addresses the issue of structure-preserving discretization of open distributed-parameter systems with Hamiltonian dynamics. Employing the formalism of discrete exterior calculus, we introduce a simplicial Dirac structure as a discrete analogue of the Stokes-Dirac structure and demonstrate
Seslija, Marko; Scherpen, Jacquelien M.A.; van der Schaft, Arjan
2011-01-01
This paper addresses the issue of structure-preserving discretization of open distributed-parameter systems with Hamiltonian dynamics. Employing the formalism of discrete exterior calculus, we introduce simplicial Dirac structures as discrete analogues of the Stokes-Dirac structure and demonstrate
Energy Technology Data Exchange (ETDEWEB)
Levi, Michele [Institut d' Astrophysique de Paris, Université Pierre et Marie Curie, CNRS-UMR 7095, 98 bis Boulevard Arago, 75014 Paris (France); Steinhoff, Jan, E-mail: michele.levi@upmc.fr, E-mail: jan.steinhoff@ist.utl.pt [Centro Multidisciplinar de Astrofisica, Instituto Superior Tecnico, Universidade de Lisboa, Avenida Rovisco Pais 1, 1049-001 Lisboa (Portugal)
2014-12-01
The next-to-next-to-leading order spin1-spin2 potential for an inspiralling binary, that is essential for accuracy to fourth post-Newtonian order, if both components in the binary are spinning rapidly, has been recently derived independently via the ADM Hamiltonian and the Effective Field Theory approaches, using different gauges and variables. Here we show the complete physical equivalence of the two results, thereby we first prove the equivalence of the ADM Hamiltonian and the Effective Field Theory approaches at next-to-next-to-leading order with the inclusion of spins. The main difficulty in the spinning sectors, which also prescribes the manner in which the comparison of the two results is tackled here, is the existence of redundant unphysical spin degrees of freedom, associated with the spin gauge choice of a point within the extended spinning object for its representative worldline. After gauge fixing and eliminating the unphysical degrees of freedom of the spin and its conjugate at the level of the action, we arrive at curved spacetime generalizations of the Newton-Wigner variables in closed form, which can also be used to obtain further Hamiltonians, based on an Effective Field Theory formulation and computation. Finally, we make use of our validated result to provide gauge invariant relations among the binding energy, angular momentum, and orbital frequency of an inspiralling binary with generic compact spinning components to fourth post-Newtonian order, including all known sectors up to date.
Energy-Shaping of Port-Controlled Hamiltonian Systems by Interconnection
Ortega, Romeo; Schaft, Arjan van der; Maschke, Bernhard; Escobar, Gerardo
1999-01-01
Passivity-based control (PBC) has shown to be very powerful to design robust controllers for physical systems described by Euler-Lagrange (EL) equations of motion. The application of PBC in regulation problems of mechanical systems yields controllers that have a clear physical interpretation in
Paston, S A; Prokhvatilov, E V
2002-01-01
The Hamiltonian, reproducing the results of the two-dimensional quantum electrodynamics in the Lorentz coordinates, is constructed on the light front. The procedure of bosonization and analysis of the boson perturbation theory in all the orders by the fermions mass are applied for this purpose. Besides the common terms, originating by the naive quantization on the light front, the obtained Hamiltonian contains an additional counterterm. It is proportional to the linear combination of the fermion zero modes (multiplied by a certain factor compensating the charge and fermion number). The coefficient before this counterterm has no ultraviolet divergence, depends on the value of the fermion condensate in the theta-vacuum and by the small fermion mass is linear by it
Hamiltonian Algorithm Sound Synthesis
大矢, 健一
2013-01-01
Hamiltonian Algorithm (HA) is an algorithm for searching solutions is optimization problems. This paper introduces a sound synthesis technique using Hamiltonian Algorithm and shows a simple example. "Hamiltonian Algorithm Sound Synthesis" uses phase transition effect in HA. Because of this transition effect, totally new waveforms are produced.
Energy Technology Data Exchange (ETDEWEB)
Bravetti, Alessandro, E-mail: alessandro.bravetti@iimas.unam.mx [Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, A. P. 70543, México, DF 04510 (Mexico); Cruz, Hans, E-mail: hans@ciencias.unam.mx [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, A. P. 70543, México, DF 04510 (Mexico); Tapias, Diego, E-mail: diego.tapias@nucleares.unam.mx [Facultad de Ciencias, Universidad Nacional Autónoma de México, A.P. 70543, México, DF 04510 (Mexico)
2017-01-15
In this work we introduce contact Hamiltonian mechanics, an extension of symplectic Hamiltonian mechanics, and show that it is a natural candidate for a geometric description of non-dissipative and dissipative systems. For this purpose we review in detail the major features of standard symplectic Hamiltonian dynamics and show that all of them can be generalized to the contact case.
Noncanonical Hamiltonian methods in plasma dynamics
International Nuclear Information System (INIS)
Kaufman, A.N.
1981-11-01
A Hamiltonian approach to plasma dynamics has numerous advantages over equivalent formulations which ignore the underlying Hamiltonian structure. In addition to achieving a deeper understanding of processes, Hamiltonian methods yield concise expressions (such as the Kubo form for linear susceptibility), greatly shorten the length of calculations, expose relationships (such as between the ponderomotive Hamiltonian and the linear susceptibility), determine invariants in terms of symmetry operations, and cover situations of great generality. In addition, they yield the Poincare invariants, in particular Liouville volume and adiabatic actions
International Nuclear Information System (INIS)
Singh, K.K.; Goswami, P.
1984-08-01
Thermodynamics of a weakly interacting fermion-boson mixture has been worked out on the basis of the effective Hamiltonian derived in an earlier paper. Tricritical point behaviour is discussed in terms of the fields (T,μ 3 ,μ 4 ). For the degenerate phase of the mixture, the theory reproduces the classical Landau expansion near a tricritical point. For the non-degenerate phase, the theory differs materially from the Landau theory; it predicts tricritical exponents in agreement with those calculated by applying renormalization group theory to phenomenological models, and a slope for the upper line larger than that of the lambda-line in the chi-T plane. (author)
Observation of Hamiltonian chaos and its control in wave-particle interaction
International Nuclear Information System (INIS)
Doveil, F; Macor, A; Aissi, A
2007-01-01
Wave-particle interactions are central in plasma physics. They can be studied in a traveling wave tube (TWT) to avoid intrinsic plasma noise. This led to detailed experimental analysis of the self-consistent interaction between unstable waves and an either cold or warm beam. More recently a test cold electron beam has been used to observe its non-self-consistent interaction with externally excited wave(s). The velocity distribution function of the electron beam is recorded with a trochoidal energy analyzer at the output of the TWT. An arbitrary waveform generator is used to launch a prescribed spectrum of waves along the slow wave structure (a 4 m long helix) of the TWT. The nonlinear synchronization of particles by a single wave responsible for Landau damping is observed. The resonant velocity domain associated with a single wave is also observed, as well as the transition to large scale chaos when the resonant domains of two waves and their secondary resonances overlap. This transition exhibits a 'devil's staircase' behavior when increasing the excitation amplitude in agreement with numerical simulation. A new strategy for control of chaos by building barriers of transport which prevent electrons from escaping from a given velocity region as well as its robustness are successfully tested. The underlying concepts extend far beyond the field of electron devices and plasma physics
Port Hamiltonian modeling of Power Networks
van Schaik, F.; van der Schaft, Abraham; Scherpen, Jacquelien M.A.; Zonetti, Daniele; Ortega, R
2012-01-01
In this talk a full nonlinear model for the power network in port–Hamiltonian framework is derived to study its stability properties. For this we use the modularity approach i.e., we first derive the models of individual components in power network as port-Hamiltonian systems and then we combine all
Nested Sampling with Constrained Hamiltonian Monte Carlo
Betancourt, M. J.
2010-01-01
Nested sampling is a powerful approach to Bayesian inference ultimately limited by the computationally demanding task of sampling from a heavily constrained probability distribution. An effective algorithm in its own right, Hamiltonian Monte Carlo is readily adapted to efficiently sample from any smooth, constrained distribution. Utilizing this constrained Hamiltonian Monte Carlo, I introduce a general implementation of the nested sampling algorithm.
Directory of Open Access Journals (Sweden)
E.R. Bittner
2016-03-01
Full Text Available We present here a formally exact model for electronic transitions between an initial (donor and final (acceptor states linked by an intermediate (bridge state. Our model incorporates a common set of vibrational modes that are coupled to the donor, bridge, and acceptor states and serves as a dissipative bath that destroys quantum coherence between the donor and acceptor. Taking the memory time of the bath as a free parameter, we calculate transition rates for a heuristic 3-state/2 mode Hamiltonian system parameterized to represent the energetics and couplings in a typical organic photovoltaic system. Our results indicate that if the memory time of the bath is of the order of 10-100 fs, a two-state kinetic (i.e., incoherent hopping model will grossly underestimate overall transition rate.
Robust online Hamiltonian learning
International Nuclear Information System (INIS)
Granade, Christopher E; Ferrie, Christopher; Wiebe, Nathan; Cory, D G
2012-01-01
In this work we combine two distinct machine learning methodologies, sequential Monte Carlo and Bayesian experimental design, and apply them to the problem of inferring the dynamical parameters of a quantum system. We design the algorithm 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), avoiding the need for storage and 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. The algorithm also numerically estimates the Cramer–Rao lower bound, certifying its own performance. (paper)
Renormalization of Hamiltonian QCD
International Nuclear Information System (INIS)
Andrasi, A.; Taylor, John C.
2009-01-01
We study to one-loop order the renormalization of QCD in the Coulomb gauge using the Hamiltonian formalism. Divergences occur which might require counter-terms outside the Hamiltonian formalism, but they can be cancelled by a redefinition of the Yang-Mills electric field.
Magnetic field line Hamiltonian
International Nuclear Information System (INIS)
Boozer, A.H.
1984-03-01
The magnetic field line Hamiltonian and the associated canonical form for the magnetic field are important concepts both for understanding toroidal plasma physics and for practical calculations. A number of important properties of the canonical or Hamiltonian representation are derived and their importance is explained
DEFF Research Database (Denmark)
Horwitz, Lawrence; Zion, Yossi Ben; Lewkowicz, Meir
2007-01-01
The characterization of chaotic Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor in the structure of the Hamiltonian is extended to a wide class of potential models of standard form through definition of a conformal metric. The geodesic equations reproduce ...
Magnetic field line Hamiltonian
International Nuclear Information System (INIS)
Boozer, A.H.
1985-02-01
The basic properties of the Hamiltonian representation of magnetic fields in canonical form are reviewed. The theory of canonical magnetic perturbation theory is then developed and applied to the time evolution of a magnetic field embedded in a toroidal plasma. Finally, the extension of the energy principle to tearing modes, utilizing the magnetic field line Hamiltonian, is outlined
Diagonalization of Hamiltonian; Diagonalization of Hamiltonian
Energy Technology Data Exchange (ETDEWEB)
Garrido, L M; Pascual, P
1960-07-01
We present a general method to diagonalized the Hamiltonian of particles of arbitrary spin. In particular we study the cases of spin 0,1/2, 1 and see that for spin 1/2 our transformation agrees with Foldy's and obtain the expression for different observables for particles of spin C and 1 in the new representation. (Author) 7 refs.
International Nuclear Information System (INIS)
Kersten, P; Krasil'shchik, I; Verbovetsky, A
2004-01-01
Using methods of Kersten et al (2004 J. Geom. Phys. 50 273-302) and Krasil'shchik and Kersten (2000 Symmetries and Recursion Operators for Classical and Supersymmetric Differential Equations (Dordrecht: Kluwer)), we accomplish an extensive study of the N = 1 supersymmetric Korteweg-de Vries (KdV) equation. The results include a description of local and nonlocal Hamiltonian and symplectic structures, five hierarchies of symmetries, the corresponding hierarchies of conservation laws, recursion operators for symmetries and generating functions of conservation laws. We stress that the main point of the paper is not just the results on super-KdV equation itself, but merely exposition of the efficiency of the geometrical approach and of the computational algorithms based on it
Quantum entangling power of adiabatically connected Hamiltonians
International Nuclear Information System (INIS)
Hamma, Alioscia; Zanardi, Paolo
2004-01-01
The space of quantum Hamiltonians has a natural partition in classes of operators that can be adiabatically deformed into each other. We consider parametric families of Hamiltonians acting on a bipartite quantum state space. When the different Hamiltonians in the family fall in the same adiabatic class, one can manipulate entanglement by moving through energy eigenstates corresponding to different values of the control parameters. We introduce an associated notion of adiabatic entangling power. This novel measure is analyzed for general dxd quantum systems, and specific two-qubit examples are studied
Witnessing eigenstates for quantum simulation of Hamiltonian spectra
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
Renormalization of Hamiltonians
International Nuclear Information System (INIS)
Glazek, S.D.; Wilson, K.G.
1993-01-01
This paper presents a new renormalization procedure for Hamiltonians such as those of light-front field theory. The bare Hamiltonian with an arbitrarily large, but finite cutoff, is transformed by a specially chosen similarity transformation. The similarity transformation has two desirable features. First, the transformed Hamiltonian is band diagonal: in particular, all matrix elements vanish which would otherwise have caused transitions with big energy jumps, such as from a state of bounded energy to a state with an energy of the order of the cutoff. At the same time, neither the similarity transformation nor the transformed Hamiltonian, computed in perturbation theory, contain vanishing or near-vanishing energy denominators. Instead, energy differences in denominators can be replaced by energy sums for purposes of order of magnitude estimates needed to determine cutoff dependences. These two properties make it possible to determine relatively easily the list of counterterms needed to obtain finite low energy results (such as for eigenvalues). A simple model Hamiltonian is discussed to illustrate the method
Theory of collective Hamiltonian
Energy Technology Data Exchange (ETDEWEB)
Zhang Qingying
1982-02-01
Starting from the cranking model, we derive the nuclear collective Hamiltonian. We expand the total energy of the collective motion of the ground state of even--even nuclei in powers of the deformation parameter ..beta... In the first approximation, we only take the lowest-order non-vanished terms in the expansion. The collective Hamiltonian thus obtained rather differs from the A. Bohr's Hamiltonian obtained by the irrotational incompressible liquid drop model. If we neglect the coupling term between ..beta..-and ..gamma..-vibration, our Hamiltonian then has the same form as that of A. Bohr. But there is a difference between these collective parameters. Our collective parameters are determined by the state of motion of the nucleous in the nuclei. They are the microscopic expressions. On the contrary, A. Bohr's collective parameters are only the simple functions of the microscopic physical quantities (such as nuclear radius and surface tension, etc.), and independent of the state of motion of the nucleons in the nuclei. Furthermore, there exist the coupling term between ..beta..-and ..gamma..-vibration and the higher-order terms in our expansion. They can be treated as the perturbations. There are no such terms in A. Bohr's Hamiltonian. These perturbation terms will influence the rotational, vibrational spectra and the ..gamma..-transition process, etc.
Hamiltonian dynamics of preferential attachment
International Nuclear Information System (INIS)
Zuev, Konstantin; Papadopoulos, Fragkiskos; Krioukov, Dmitri
2016-01-01
Prediction and control of network dynamics are grand-challenge problems in network science. The lack of understanding of fundamental laws driving the dynamics of networks is among the reasons why many practical problems of great significance remain unsolved for decades. Here we study the dynamics of networks evolving according to preferential attachment (PA), known to approximate well the large-scale growth dynamics of a variety of real networks. We show that this dynamics is Hamiltonian, thus casting the study of complex networks dynamics to the powerful canonical formalism, in which the time evolution of a dynamical system is described by Hamilton’s equations. We derive the explicit form of the Hamiltonian that governs network growth in PA. This Hamiltonian turns out to be nearly identical to graph energy in the configuration model, which shows that the ensemble of random graphs generated by PA is nearly identical to the ensemble of random graphs with scale-free degree distributions. In other words, PA generates nothing but random graphs with power-law degree distribution. The extension of the developed canonical formalism for network analysis to richer geometric network models with non-degenerate groups of symmetries may eventually lead to a system of equations describing network dynamics at small scales. (paper)
Time dependent drift Hamiltonian
International Nuclear Information System (INIS)
Boozer, A.H.
1982-04-01
The motion of individual charged particles in a given magnetic and an electric fields is discussed. An idea of a guiding center distribution function f is introduced. The guiding center distribution function is connected to the asymptotic Hamiltonian through the drift kinetic equation. The general non-stochastic magnetic field can be written in a contravariant and a covariant forms. The drift Hamiltonian is proposed, and the canonical gyroradius is presented. The proposed drift Hamiltonian agrees with Alfven's drift velocity to lowest non-vanishing order in the gyroradius. The relation between the exact, time dependent equations of motion and the guiding center equation is clarified by a Lagrangian analysis. The deduced Lagrangian represents the drift motion. (Kato, T.)
Lagrangian and Hamiltonian dynamics
Mann, Peter
2018-01-01
An introductory textbook exploring the subject of Lagrangian and Hamiltonian dynamics, with a relaxed and self-contained setting. Lagrangian and Hamiltonian dynamics is the continuation of Newton's classical physics into new formalisms, each highlighting novel aspects of mechanics that gradually build in complexity to form the basis for almost all of theoretical physics. Lagrangian and Hamiltonian dynamics also acts as a gateway to more abstract concepts routed in differential geometry and field theories and can be used to introduce these subject areas to newcomers. Journeying in a self-contained manner from the very basics, through the fundamentals and onwards to the cutting edge of the subject, along the way the reader is supported by all the necessary background mathematics, fully worked examples, thoughtful and vibrant illustrations as well as an informal narrative and numerous fresh, modern and inter-disciplinary applications. The book contains some unusual topics for a classical mechanics textbook. Mo...
Energy Technology Data Exchange (ETDEWEB)
Albert, Christopher G.; Heyn, Martin F.; Kapper, Gernot; Kernbichler, Winfried; Martitsch, Andreas F. [Fusion@ÖAW, Institut für Theoretische Physik - Computational Physics, Technische Universität Graz, Petersgasse 16, 8010 Graz (Austria); Kasilov, Sergei V. [Fusion@ÖAW, Institut für Theoretische Physik - Computational Physics, Technische Universität Graz, Petersgasse 16, 8010 Graz (Austria); Institute of Plasma Physics, National Science Center “Kharkov Institute of Physics and Technology,” ul. Akademicheskaya 1, 61108 Kharkov (Ukraine)
2016-08-15
Toroidal torque generated by neoclassical viscosity caused by external non-resonant, non-axisymmetric perturbations has a significant influence on toroidal plasma rotation in tokamaks. In this article, a derivation for the expressions of toroidal torque and radial transport in resonant regimes is provided within quasilinear theory in canonical action-angle variables. The proposed approach treats all low-collisional quasilinear resonant neoclassical toroidal viscosity regimes including superbanana-plateau and drift-orbit resonances in a unified way and allows for magnetic drift in all regimes. It is valid for perturbations on toroidally symmetric flux surfaces of the unperturbed equilibrium without specific assumptions on geometry or aspect ratio. The resulting expressions are shown to match the existing analytical results in the large aspect ratio limit. Numerical results from the newly developed code NEO-RT are compared to calculations by the quasilinear version of the code NEO-2 at low collisionalities. The importance of the magnetic shear term in the magnetic drift frequency and a significant effect of the magnetic drift on drift-orbit resonances are demonstrated.
Effective magnetic Hamiltonians
Czech Academy of Sciences Publication Activity Database
Drchal, Václav; Kudrnovský, Josef; Turek, I.
2013-01-01
Roč. 26, č. 5 (2013), s. 1997-2000 ISSN 1557-1939 R&D Projects: GA ČR GA202/09/0775 Institutional support: RVO:68378271 Keywords : effective magnetic Hamiltonian * ab initio * magnetic structure Subject RIV: BE - Theoretical Physics Impact factor: 0.930, year: 2013
Dissipative systems and Bateman's Hamiltonian
International Nuclear Information System (INIS)
Pedrosa, I.A.; Baseia, B.
1983-01-01
It is shown, by using canonical transformations, that one can construct Bateman's Hamiltonian from a Hamiltonian for a conservative system and obtain a clear physical interpretation which explains the ambiguities emerging from its application to describe dissipative systems. (Author) [pt
Optimal Control Approaches to the Aggregate Production Planning Problem
Directory of Open Access Journals (Sweden)
Yasser A. Davizón
2015-12-01
Full Text Available In the area of production planning and control, the aggregate production planning (APP problem represents a great challenge for decision makers in production-inventory systems. Tradeoff between inventory-capacity is known as the APP problem. To address it, static and dynamic models have been proposed, which in general have several shortcomings. It is the premise of this paper that the main drawback of these proposals is, that they do not take into account the dynamic nature of the APP. For this reason, we propose the use of an Optimal Control (OC formulation via the approach of energy-based and Hamiltonian-present value. The main contribution of this paper is the mathematical model which integrates a second order dynamical system coupled with a first order system, incorporating production rate, inventory level, and capacity as well with the associated cost by work force in the same formulation. Also, a novel result in relation with the Hamiltonian-present value in the OC formulation is that it reduces the inventory level compared with the pure energy based approach for APP. A set of simulations are provided which verifies the theoretical contribution of this work.
International Nuclear Information System (INIS)
Bourdier, A.; Patin, D.
2005-01-01
The basic physical processes in laser-matter interaction, up to 10 17 W/cm 2 (for a neodymium laser) are now well understood, on the other hand, new phenomena evidenced in particle-in-cell code simulations have to be investigated above 10 18 W/cm 2 . Thus, the relativistic motion of a charged particle in a linearly polarized homogeneous electromagnetic wave is studied, here, using the Hamiltonian formalism. First, the motion of a single particle in a linearly polarized traveling wave propagating in a non-magnetized space is explored. The problem is shown to be integrable. The results obtained are compared to those derived considering a cold electron plasma model. When the phase velocity is close to c, it is shown that the two approaches are in good agreement during a finite time. After this short time, when the plasma response is taken into account no chaos take place at least when considering low densities and/or high wave intensities. The case of a charged particle in a traveling wave propagating along a constant homogeneous magnetic field is then considered. The problem is shown to be integrable when the wave propagates in vacuum. The existence of a synchronous solution is shown very simply. In the case when the wave propagates in a low density plasma, using a simplifying Lorentz transformation, it is shown that the system can be reduced to a time-dependent system with two degrees of freedom. The system is shown to be non-integrable, chaos appears when a secondary resonance and a primary resonance overlap. Finally, stochastic instabilities are studied by considering the motion of one particle in a very high intensity wave perturbed by one or two low intensity traveling waves. Resonances are identified and conditions for resonance overlap are studied. (authors)
Instability in Hamiltonian systems
Directory of Open Access Journals (Sweden)
A. Pumarino
2005-11-01
Besides proving the existence of Arnold diffusion for a new family of three degrees of freedom Hamiltonian systems, another goal of this book is not only to show how Arnold-like results can be extended to substantially larger sets of parameters, but also how to obtain effective estimates on the splitting of separatrices size when the frequency of the perturbation belongs to open real sets.
Equivalence of Lagrangian and Hamiltonian BRST quantizations
International Nuclear Information System (INIS)
Grigoryan, G.V.; Grigoryan, R.P.; Tyutin, I.V.
1992-01-01
Two approaches to the quantization of gauge theories using BRST symmetry are widely used nowadays: the Lagrangian quantization, developed in (BV-quantization) and Hamiltonian quantization, formulated in (BFV-quantization). For all known examples of field theory (Yang-Mills theory, gravitation etc.) both schemes give equivalent results. However the equivalence of these approaches in general wasn't proved. The main obstacle in comparing of these formulations consists in the fact, that in Hamiltonian approach the number of ghost fields is equal to the number of all first-class constraints, while in the Lagrangian approach the number of ghosts is equal to the number of independent gauge symmetries, which is equal to the number of primary first-class constraints only. This paper is devoted to the proof of the equivalence of Lagrangian and Hamiltonian quantizations for the systems with first-class constraints only. This is achieved by a choice of special gauge in the Hamiltonian approach. It's shown, that after integration over redundant variables on the functional integral we come to effective action which is constructed according to rules for construction of the effective action in Lagrangian quantization scheme
Approximate symmetries of Hamiltonians
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.
Effective Hamiltonian within the microscopic unitary nuclear model
International Nuclear Information System (INIS)
Filippov, G.F.; Blokhin, A.L.
1989-01-01
A technique of projecting the microscopic nuclear Hamiltonian on the SU(3)-group enveloping algebra is developed. The approach proposed is based on the effective Hamiltonian restored from the matrix elements between the coherent states of the SU(3) irreducible representations. The technique is displayed for almost magic nuclei within the mixed representation basis, and for arbitrary nuclei within the single representation. 40 refs
Noncanonical Hamiltonian methods in plasma dynamics
International Nuclear Information System (INIS)
Kaufman, A.N.
1982-01-01
A Hamiltonian approach to plasma dynamics is described. The Poisson bracket of two observables g 1 and g 2 is given by using an antisymmetric tensor J, and must satisfy the Jacobi condition. The J can be obtained by elementary tensor analysis. The evolution in time of an observable g is given in terms of the Poisson bracket and a Hamiltonian H(Z). The guiding-center description of particle motion was presented by Littlejohn. The ponderomotive drift and force, the wave-induced oscillation-center velocity, and the gyrofrequency shift are obtained. The Lie transform yields the wave-induced increment to the gyromomentum. In the coulomb model for a Vlasov system, the dynamical variable is the Vlasov distribution f(z). The Hamiltonian functional and the Poisson bracket are obtained. The coupling of f(z) to the Maxwell field appears in the Poisson bracket. The evolution equation yields the Vlasov-Maxwell system. (Kato, T.)
Hamiltonian formulation of reduced magnetohydrodynamics
International Nuclear Information System (INIS)
Morrison, P.J.; Hazeltine, R.D.
1983-07-01
Reduced magnetohydrodynamics (RMHD) has become a principal tool for understanding nonlinear processes, including disruptions, in tokamak plasmas. Although analytical studies of RMHD turbulence have been useful, the model's impressive ability to simulate tokamak fluid behavior has been revealed primarily by numerical solution. The present work describes a new analytical approach, not restricted to turbulent regimes, based on Hamiltonian field theory. It is shown that the nonlinear (ideal) RMHD system, in both its high-beta and low-beta versions, can be expressed in Hanmiltonian form. Thus a Poisson bracket, [ , ], is constructed such that each RMHD field quantitity, xi/sub i/, evolves according to xi/sub i/ = [xi/sub i/,H], where H is the total field energy. The new formulation makes RMHD accessible to the methodology of Hamiltonian mechanics; it has lead, in particular, to the recognition of new RMHD invariants and even exact, nonlinear RMHD solutions. A canonical version of the Poisson bracket, which requires the introduction of additional fields, leads to a nonlinear variational principle for time-dependent RMHD
Discrete variable representation for singular Hamiltonians
DEFF Research Database (Denmark)
Schneider, B. I.; Nygaard, Nicolai
2004-01-01
We discuss the application of the discrete variable representation (DVR) to Schrodinger problems which involve singular Hamiltonians. Unlike recent authors who invoke transformations to rid the eigenvalue equation of singularities at the cost of added complexity, we show that an approach based...
Transparency in port-Hamiltonian based telemanipulation
Secchi, C; Stramigioli, Stefano; Fantuzzi, C.
2005-01-01
After stability, transparency is the major issue in the design of a telemanipulation system. In this paper we exploit a behavioral approach in order to provide an index for the evaluation of transparency in port-Hamiltonian based teleoperators. Furthermore we provide a transparency analysis of
Transparency in Port-Hamiltonian-Based Telemanipulation
Secchi, Cristian; Stramigioli, Stefano; Fantuzzi, Cesare
After stability, transparency is the major issue in the design of a telemanipulation system. In this paper, we exploit the behavioral approach in order to provide an index for the evaluation of transparency in port-Hamiltonian-based teleoperators. Furthermore, we provide a transparency analysis of
Structure preserving port-Hamiltonian model reduction of electrical circuits
Polyuga, R.; Schaft, van der A.J.; Benner, P.; Hinze, M.; Maten, ter E.J.W.
2011-01-01
This paper discusses model reduction of electrical circuits based on a port-Hamiltonian representation. It is shown that by the use of the Kalman decomposition an uncontrollable and/or unobservable port-Hamiltonian system is reduced to a controllable/observable system that inherits the
International Nuclear Information System (INIS)
Prokhorov, L.V.
1982-01-01
Problems related to consideration of operator nonpermutability in Hamiltonian path integral (HPI) are considered in the review. Integrals are investigated using trajectories in configuration space (nonrelativistic quantum mechanics). Problems related to trajectory integrals in HPI phase space are discussed: the problem of operator nonpermutability consideration (extra terms problem) and corresponding equivalence rules; ambiguity of HPI usual recording; transition to curvilinear coordinates. Problem of quantization of dynamical systems with couplings has been studied. As in the case of canonical transformations, quantization of the systems with couplings of the first kind requires the consideration of extra terms
Quantum bootstrapping via compressed quantum Hamiltonian learning
International Nuclear Information System (INIS)
Wiebe, Nathan; Granade, Christopher; Cory, D G
2015-01-01
A major problem facing the development of quantum computers or large scale quantum simulators is that general methods for characterizing and controlling are intractable. We provide a new approach to this problem that uses small quantum simulators to efficiently characterize and learn control models for larger devices. Our protocol achieves this by using Bayesian inference in concert with Lieb–Robinson bounds and interactive quantum learning methods to achieve compressed simulations for characterization. We also show that the Lieb–Robinson velocity is epistemic for our protocol, meaning that information propagates at a rate that depends on the uncertainty in the system Hamiltonian. We illustrate the efficiency of our bootstrapping protocol by showing numerically that an 8 qubit Ising model simulator can be used to calibrate and control a 50 qubit Ising simulator while using only about 750 kilobits of experimental data. Finally, we provide upper bounds for the Fisher information that show that the number of experiments needed to characterize a system rapidly diverges as the duration of the experiments used in the characterization shrinks, which motivates the use of methods such as ours that do not require short evolution times. (fast track communication)
Chromatic roots and hamiltonian paths
DEFF Research Database (Denmark)
Thomassen, Carsten
2000-01-01
We present a new connection between colorings and hamiltonian paths: If the chromatic polynomial of a graph has a noninteger root less than or equal to t(n) = 2/3 + 1/3 (3)root (26 + 6 root (33)) + 1/3 (3)root (26 - 6 root (33)) = 1.29559.... then the graph has no hamiltonian path. This result...
The Hamiltonian structure of general relativistic perfect fluids
International Nuclear Information System (INIS)
Bao, D.; Houston Univ., TX; Marsden, J.; Walton, R.
1985-01-01
We show that the evolution equations for a perfect fluid coupled to general relativity in a general lapse and shift, are Hamiltonian relative to a certain Poisson structure. For the fluid variables, a Lie-Poisson structure associated to the dual of a semi-direct product Lie algebra is used, while the bracket for the gravitational variables has the usual canonical symplectic structure. The evolution is governed by a Hamiltonian which is equivalent to that obtained from a canonical analysis. The relationship of our Hamiltonian structure with other approaches in the literature, such as Clebsch potentials, Lagrangian to Eulerian transformations, and its use in clarifying linearization stability, are discussed. (orig.)
Model Hamiltonian Calculations of the Nonlinear Polarizabilities of Conjugated Molecules.
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
Linear Port-Hamiltonian Systems on Infinite-dimensional Spaces
Jacob, Birgit
2012-01-01
This book provides a self-contained introduction to the theory of infinite-dimensional systems theory and its applications to port-Hamiltonian systems. The textbook starts with elementary known results, then progresses smoothly to advanced topics in current research. Many physical systems can be formulated using a Hamiltonian framework, leading to models described by ordinary or partial differential equations. For the purpose of control and for the interconnection of two or more Hamiltonian systems it is essential to take into account this interaction with the environment. This book is the fir
Alternative Hamiltonian representation for gravity
Energy Technology Data Exchange (ETDEWEB)
Rosas-RodrIguez, R [Instituto de Fisica, Universidad Autonoma de Puebla, Apdo. Postal J-48, 72570, Puebla, Pue. (Mexico)
2007-11-15
By using a Hamiltonian formalism for fields wider than the canonical one, we write the Einstein vacuum field equations in terms of alternative variables. This variables emerge from the Ashtekar's formalism for gravity.
Alternative Hamiltonian representation for gravity
International Nuclear Information System (INIS)
Rosas-RodrIguez, R
2007-01-01
By using a Hamiltonian formalism for fields wider than the canonical one, we write the Einstein vacuum field equations in terms of alternative variables. This variables emerge from the Ashtekar's formalism for gravity
Construction of alternative Hamiltonian structures for field equations
Energy Technology Data Exchange (ETDEWEB)
Herrera, Mauricio [Departamento de Fisica, Facultad de Ciencias Fisicas y Matematicas, Universidad de Chile, Santiago (Chile); Hojman, Sergio A. [Departamento de Fisica, Facultad de Ciencias, Universidad de Chile, Santiago (Chile); Facultad de Educacion, Universidad Nacional Andres Bello, Santiago (Chile); Centro de Recursos Educativos Avanzados, CREA, Santiago (Chile)
2001-08-10
We use symmetry vectors of nonlinear field equations to build alternative Hamiltonian structures. We construct such structures even for equations which are usually believed to be non-Hamiltonian such as heat, Burger and potential Burger equations. We improve on a previous version of the approach using recursion operators to increase the rank of the Poisson bracket matrices. Cole-Hopf and Miura-type transformations allow the mapping of these structures from one equation to another. (author)
Scattering theory for Stark Hamiltonians
International Nuclear Information System (INIS)
Jensen, Arne
1994-01-01
An introduction to the spectral and scattering theory for Schroedinger operators is given. An abstract short range scattering theory is developed. It is applied to perturbations of the Laplacian. Particular attention is paid to the study of Stark Hamiltonians. The main result is an explanation of the discrepancy between the classical and the quantum scattering theory for one-dimensional Stark Hamiltonians. (author). 47 refs
Boundary Hamiltonian Theory for Gapped Topological Orders
Hu, Yuting; Wan, Yidun; Wu, Yong-Shi
2017-06-01
We report our systematic construction of the lattice Hamiltonian model of topological orders on open surfaces, with explicit boundary terms. We do this mainly for the Levin-Wen string-net model. The full Hamiltonian in our approach yields a topologically protected, gapped energy spectrum, with the corresponding wave functions robust under topology-preserving transformations of the lattice of the system. We explicitly present the wavefunctions of the ground states and boundary elementary excitations. The creation and hopping operators of boundary quasi-particles are constructed. It is found that given a bulk topological order, the gapped boundary conditions are classified by Frobenius algebras in its input data. Emergent topological properties of the ground states and boundary excitations are characterized by (bi-) modules over Frobenius algebras.
Hamiltonian reduction of Kac-Moody algebras
International Nuclear Information System (INIS)
Kimura, Kazuhiro
1991-01-01
Feigin-Fucks construction provides us methods to treat rational conformal theories in terms of free fields. This formulation enables us to describe partition functions and correlation functions in the Fock space of free fields. There are several attempt extending to supersymmetric theories. In this report authors present an explicit calculation of the Hamiltonian reduction based on the free field realization. In spite of the results being well-known, the relations can be clearly understood in the language of bosons. Authors perform the hamiltonian reduction by imposing a constraint with appropriate gauge transformations which preserve the constraint. This approaches enables us to gives the geometric interpretation of super Virasoro algebras and relations of the super gravity. In addition, author discuss the properties of quantum groups by using the explicit form of the group element. It is also interesting to extend to super Kac-Moody algebras. (M.N.)
NLO renormalization in the Hamiltonian truncation
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.
Hamiltonian description of the ideal fluid
International Nuclear Information System (INIS)
Morrison, P.J.
1994-01-01
Fluid mechanics is examined from a Hamiltonian perspective. The Hamiltonian point of view provides a unifying framework; by understanding the Hamiltonian perspective, one knows in advance (within bounds) what answers to expect and what kinds of procedures can be performed. The material is organized into five lectures, on the following topics: rudiments of few-degree-of-freedom Hamiltonian systems illustrated by passive advection in two-dimensional fluids; functional differentiation, two action principles of mechanics, and the action principle and canonical Hamiltonian description of the ideal fluid; noncanonical Hamiltonian dynamics with examples; tutorial on Lie groups and algebras, reduction-realization, and Clebsch variables; and stability and Hamiltonian systems
Hamiltonian formalisms and symmetries of the Pais–Uhlenbeck oscillator
Directory of Open Access Journals (Sweden)
Krzysztof Andrzejewski
2014-12-01
Full Text Available The study of the symmetry of Pais–Uhlenbeck oscillator initiated in Andrzejewski et al. (2014 [24] is continued with special emphasis put on the Hamiltonian formalism. The symmetry generators within the original Pais and Uhlenbeck Hamiltonian approach as well as the canonical transformation to the Ostrogradski Hamiltonian framework are derived. The resulting algebra of generators appears to be the central extension of the one obtained on the Lagrangian level; in particular, in the case of odd frequencies one obtains the centrally extended l-conformal Newton–Hooke algebra. In this important case the canonical transformation to an alternative Hamiltonian formalism (related to the free higher derivatives theory is constructed. It is shown that all generators can be expressed in terms of the ones for the free theory and the result agrees with that obtained by the orbit method.
Quantum gates by inverse engineering of a Hamiltonian
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.
First principles of Hamiltonian medicine.
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.
Variational identities and Hamiltonian structures
International Nuclear Information System (INIS)
Ma Wenxiu
2010-01-01
This report is concerned with Hamiltonian structures of classical and super soliton hierarchies. In the classical case, basic tools are variational identities associated with continuous and discrete matrix spectral problems, targeted to soliton equations derived from zero curvature equations over general Lie algebras, both semisimple and non-semisimple. In the super case, a supertrace identity is presented for constructing Hamiltonian structures of super soliton equations associated with Lie superalgebras. We illustrate the general theories by the KdV hierarchy, the Volterra lattice hierarchy, the super AKNS hierarchy, and two hierarchies of dark KdV equations and dark Volterra lattices. The resulting Hamiltonian structures show the commutativity of each hierarchy discussed and thus the existence of infinitely many commuting symmetries and conservation laws.
Dynamical decoupling of unbounded Hamiltonians
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.
Invariant metrics for Hamiltonian systems
International Nuclear Information System (INIS)
Rangarajan, G.; Dragt, A.J.; Neri, F.
1991-05-01
In this paper, invariant metrics are constructed for Hamiltonian systems. These metrics give rise to norms on the space of homeogeneous polynomials of phase-space variables. For an accelerator lattice described by a Hamiltonian, these norms characterize the nonlinear content of the lattice. Therefore, the performance of the lattice can be improved by minimizing the norm as a function of parameters describing the beam-line elements in the lattice. A four-fold increase in the dynamic aperture of a model FODO cell is obtained using this procedure. 7 refs
Discrete variable representation for singular Hamiltonians
DEFF Research Database (Denmark)
Schneider, B. I.; Nygaard, Nicolai
2004-01-01
We discuss the application of the discrete variable representation (DVR) to Schrodinger problems which involve singular Hamiltonians. Unlike recent authors who invoke transformations to rid the eigenvalue equation of singularities at the cost of added complexity, we show that an approach based...... solely on an orthogonal polynomial basis is adequate, provided the Gauss-Lobatto or Gauss-Radau quadrature rule is used. This ensures that the mesh contains the singular points and by simply discarding the DVR functions corresponding to those points, all matrix elements become well behaved. the boundary...
Action-minimizing methods in Hamiltonian dynamics
Sorrentino, Alfonso
2015-01-01
John Mather's seminal works in Hamiltonian dynamics represent some of the most important contributions to our understanding of the complex balance between stable and unstable motions in classical mechanics. His novel approach-known as Aubry-Mather theory-singles out the existence of special orbits and invariant measures of the system, which possess a very rich dynamical and geometric structure. In particular, the associated invariant sets play a leading role in determining the global dynamics of the system. This book provides a comprehensive introduction to Mather's theory, and can serve as a
Derivation of Hamiltonians for accelerators
Energy Technology Data Exchange (ETDEWEB)
Symon, K.R.
1997-09-12
In this report various forms of the Hamiltonian for particle motion in an accelerator will be derived. Except where noted, the treatment will apply generally to linear and circular accelerators, storage rings, and beamlines. The generic term accelerator will be used to refer to any of these devices. The author will use the usual accelerator coordinate system, which will be introduced first, along with a list of handy formulas. He then starts from the general Hamiltonian for a particle in an electromagnetic field, using the accelerator coordinate system, with time t as independent variable. He switches to a form more convenient for most purposes using the distance s along the reference orbit as independent variable. In section 2, formulas will be derived for the vector potentials that describe the various lattice components. In sections 3, 4, and 5, special forms of the Hamiltonian will be derived for transverse horizontal and vertical motion, for longitudinal motion, and for synchrobetatron coupling of horizontal and longitudinal motions. Hamiltonians will be expanded to fourth order in the variables.
Hamiltonian cycles in polyhedral maps
Indian Academy of Sciences (India)
We present a necessary and sufficient condition for existence of a contractible, non-separating and non-contractible separating Hamiltonian cycle in the edge graph of polyhedral maps on surfaces.We also present algorithms to construct such cycles whenever it exists where one of them is linear time and another is ...
Maslov index for Hamiltonian systems
Directory of Open Access Journals (Sweden)
Alessandro Portaluri
2008-01-01
Full Text Available The aim of this article is to give an explicit formula for computing the Maslov index of the fundamental solutions of linear autonomous Hamiltonian systems in terms of the Conley-Zehnder index and the map time one flow.
Hamiltonian formulation of the supermembrane
International Nuclear Information System (INIS)
Bergshoeff, E.; Sezgin, E.; Tanii, Y.
1987-06-01
The Hamiltonian formulation of the supermembrane theory in eleven dimensions is given. The covariant split of the first and second class constraints is exhibited, and their Dirac brackets are computed. Gauge conditions are imposed in such a way that the reparametrizations of the membrane with divergence free 2-vectors are unfixed. (author). 10 refs
Relativistic non-Hamiltonian mechanics
International Nuclear Information System (INIS)
Tarasov, Vasily E.
2010-01-01
Relativistic particle subjected to a general four-force is considered as a nonholonomic system. The nonholonomic constraint in four-dimensional space-time represents the relativistic invariance by the equation for four-velocity u μ u μ + c 2 = 0, where c is the speed of light in vacuum. In the general case, four-forces are non-potential, and the relativistic particle is a non-Hamiltonian system in four-dimensional pseudo-Euclidean space-time. We consider non-Hamiltonian and dissipative systems in relativistic mechanics. Covariant forms of the principle of stationary action and the Hamilton's principle for relativistic mechanics of non-Hamiltonian systems are discussed. The equivalence of these principles is considered for relativistic particles subjected to potential and non-potential forces. We note that the equations of motion which follow from the Hamilton's principle are not equivalent to the equations which follow from the variational principle of stationary action. The Hamilton's principle and the principle of stationary action are not compatible in the case of systems with nonholonomic constraint and the potential forces. The principle of stationary action for relativistic particle subjected to non-potential forces can be used if the Helmholtz conditions are satisfied. The Hamilton's principle and the principle of stationary action are equivalent only for a special class of relativistic non-Hamiltonian systems.
Mathematical Modeling of Constrained Hamiltonian Systems
Schaft, A.J. van der; Maschke, B.M.
1995-01-01
Network modelling of unconstrained energy conserving physical systems leads to an intrinsic generalized Hamiltonian formulation of the dynamics. Constrained energy conserving physical systems are directly modelled as implicit Hamiltonian systems with regard to a generalized Dirac structure on the
Geometric Hamiltonian structures and perturbation theory
International Nuclear Information System (INIS)
Omohundro, S.
1984-08-01
We have been engaged in a program of investigating the Hamiltonian structure of the various perturbation theories used in practice. We describe the geometry of a Hamiltonian structure for non-singular perturbation theory applied to Hamiltonian systems on symplectic manifolds and the connection with singular perturbation techniques based on the method of averaging
Notch filters for port-Hamiltonian systems
Dirksz, D.A.; Scherpen, J.M.A.; van der Schaft, A.J.; Steinbuch, M.
2012-01-01
In this paper a standard notch filter is modeled in the port-Hamiltonian framework. By having such a port-Hamiltonian description it is proven that the notch filter is a passive system. The notch filter can then be interconnected with another (nonlinear) port-Hamiltonian system, while preserving the
Constructing Dense Graphs with Unique Hamiltonian Cycles
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…
The Hamiltonian of QED. Zero mode
International Nuclear Information System (INIS)
Zastavenko, L.G.
1990-01-01
We start with the standard QED Lagrangian. New derivation of the spinor QED Hamiltonian is given. We have taken into account the zero mode. Our derivation is faultless from the point of view of gauge invariance. It gives important corrections to the standard QED Hamiltonian. Our derivation of the Hamiltonian can be generalized to the case of QCD. 5 refs
Hamiltonian PDEs and Frobenius manifolds
International Nuclear Information System (INIS)
Dubrovin, Boris A
2008-01-01
In the first part of this paper the theory of Frobenius manifolds is applied to the problem of classification of Hamiltonian systems of partial differential equations depending on a small parameter. Also developed is a deformation theory of integrable hierarchies including the subclass of integrable hierarchies of topological type. Many well-known examples of integrable hierarchies, such as the Korteweg-de Vries, non-linear Schroedinger, Toda, Boussinesq equations, and so on, belong to this subclass that also contains new integrable hierarchies. Some of these new integrable hierarchies may be important for applications. Properties of the solutions to these equations are studied in the second part. Consideration is given to the comparative study of the local properties of perturbed and unperturbed solutions near a point of gradient catastrophe. A Universality Conjecture is formulated describing the various types of critical behaviour of solutions to perturbed Hamiltonian systems near the point of gradient catastrophe of the unperturbed solution.
Hamiltonian PDEs and Frobenius manifolds
Energy Technology Data Exchange (ETDEWEB)
Dubrovin, Boris A [Steklov Mathematical Institute, Russian Academy of Sciences, Moscow (Russian Federation)
2008-12-31
In the first part of this paper the theory of Frobenius manifolds is applied to the problem of classification of Hamiltonian systems of partial differential equations depending on a small parameter. Also developed is a deformation theory of integrable hierarchies including the subclass of integrable hierarchies of topological type. Many well-known examples of integrable hierarchies, such as the Korteweg-de Vries, non-linear Schroedinger, Toda, Boussinesq equations, and so on, belong to this subclass that also contains new integrable hierarchies. Some of these new integrable hierarchies may be important for applications. Properties of the solutions to these equations are studied in the second part. Consideration is given to the comparative study of the local properties of perturbed and unperturbed solutions near a point of gradient catastrophe. A Universality Conjecture is formulated describing the various types of critical behaviour of solutions to perturbed Hamiltonian systems near the point of gradient catastrophe of the unperturbed solution.
Weak KAM for commuting Hamiltonians
International Nuclear Information System (INIS)
Zavidovique, M
2010-01-01
For two commuting Tonelli Hamiltonians, we recover the commutation of the Lax–Oleinik semi-groups, a result of Barles and Tourin (2001 Indiana Univ. Math. J. 50 1523–44), using a direct geometrical method (Stoke's theorem). We also obtain a 'generalization' of a theorem of Maderna (2002 Bull. Soc. Math. France 130 493–506). More precisely, we prove that if the phase space is the cotangent of a compact manifold then the weak KAM solutions (or viscosity solutions of the critical stationary Hamilton–Jacobi equation) for G and for H are the same. As a corollary we obtain the equality of the Aubry sets and of the Peierls barrier. This is also related to works of Sorrentino (2009 On the Integrability of Tonelli Hamiltonians Preprint) and Bernard (2007 Duke Math. J. 136 401–20)
Hamiltonian dynamics of extended objects
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.
Hamiltonian description of bubble dynamics
International Nuclear Information System (INIS)
Maksimov, A. O.
2008-01-01
The dynamics of a nonspherical bubble in a liquid is described within the Hamiltonian formalism. Primary attention is focused on the introduction of the canonical variables into the computational algorithm. The expansion of the Dirichlet-Neumann operator in powers of the displacement of a bubble wall from an equilibrium position is obtained in the explicit form. The first three terms (more specifically, the second-, third-, and fourth-order terms) in the expansion of the Hamiltonian in powers of the canonical variables are determined. These terms describe the spectrum and interaction of three essentially different modes, i.e., monopole oscillations (pulsations), dipole oscillations (translational motions), and surface oscillations. The cubic nonlinearity is analyzed for the problem associated with the generation of Faraday ripples on the wall of a bubble in an acoustic field. The possibility of decay processes occurring in the course of interaction of surface oscillations for the first fifteen (experimentally observed) modes is investigated.
Hamiltonian dynamics of extended objects
International Nuclear Information System (INIS)
Capovilla, R; Guven, J; Rojas, E
2004-01-01
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
Hamiltonian dynamics of extended objects
Energy Technology Data Exchange (ETDEWEB)
Capovilla, R [Departamento de FIsica, Centro de Investigacion y de Estudios Avanzados del IPN, Apdo Postal 14-740, 07000 Mexico, DF (Mexico); Guven, J [School of Theoretical Physics, Dublin Institute for Advanced Studies, 10 Burlington Road, Dublin 4 (Ireland); Rojas, E [Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Apdo Postal 70-543, 04510 Mexico, DF (Mexico)
2004-12-07
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.
On the domain of the Nelson Hamiltonian
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.
Exercising self-control increases approach motivation.
Schmeichel, Brandon J; Harmon-Jones, Cindy; Harmon-Jones, Eddie
2010-07-01
The present research tested the hypothesis that exercising self-control causes an increase in approach motivation. Study 1 found that exercising (vs. not exercising) self-control increases self-reported approach motivation. Study 2a identified a behavior--betting on low-stakes gambles--that is correlated with approach motivation but is relatively uncorrelated with self-control, and Study 2b observed that exercising self-control temporarily increases this behavior. Last, Study 3 found that exercising self-control facilitates the perception of a reward-relevant symbol (i.e., a dollar sign) but not a reward-irrelevant symbol (i.e., a percent sign). Altogether, these results support the hypothesis that exercising self-control temporarily increases approach motivation. Failures of self-control that follow from prior efforts at self-control (i.e., ego depletion) may be explained in part by increased approach motivation.
Hamiltonian systems in accelerator physics
International Nuclear Information System (INIS)
Laslett, L.J.
1985-06-01
General features of the design of annular particle accelerators or storage rings are outlined and the Hamiltonian character of individual-ion motion is indicated. Examples of phase plots are presented, for the motion in one spatial degree of freedom, of an ion subject to a periodic nonlinear focusing force. A canonical transformation describing coupled nonlinear motion also is given, and alternative types of graphical display are suggested for the investigation of long-term stability in such cases. 7 figs
Contact symmetries and Hamiltonian thermodynamics
International Nuclear Information System (INIS)
Bravetti, A.; Lopez-Monsalvo, C.S.; Nettel, F.
2015-01-01
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 Legendre 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
Generic Local Hamiltonians are Gapless
Movassagh, Ramis
2017-12-01
We prove that generic quantum local Hamiltonians are gapless. In fact, we prove that there is a continuous density of states above the ground state. The Hamiltonian can be on a lattice in any spatial dimension or on a graph with a bounded maximum vertex degree. The type of interactions allowed for include translational invariance in a disorder (i.e., probabilistic) sense with some assumptions on the local distributions. Examples include many-body localization and random spin models. We calculate the scaling of the gap with the system's size when the local terms are distributed according to a Gaussian β orthogonal random matrix ensemble. As a corollary, there exist finite size partitions with respect to which the ground state is arbitrarily close to a product state. When the local eigenvalue distribution is discrete, in addition to the lack of an energy gap in the limit, we prove that the ground state has finite size degeneracies. The proofs are simple and constructive. This work excludes the important class of truly translationally invariant Hamiltonians where the local terms are all equal.
An extended discrete gradient formula for oscillatory Hamiltonian systems
International Nuclear Information System (INIS)
Liu Kai; Shi Wei; Wu Xinyuan
2013-01-01
In this paper, incorporating the idea of the discrete gradient method into the extended Runge–Kutta–Nyström integrator, we derive and analyze an extended discrete gradient formula for the oscillatory Hamiltonian system with the Hamiltonian H(p,q)= 1/2 p T p+ 1/2 q T Mq+U(q), where q:R→R d represents generalized positions, p:R→R d represents generalized momenta and M is an element of R dxd is a symmetric and positive semi-definite matrix. The solution of this system is a nonlinear oscillator. Basically, many nonlinear oscillatory mechanical systems with a partitioned Hamiltonian function lend themselves to this approach. The extended discrete gradient formula presented in this paper exactly preserves the energy H(p, q). We derive some properties of the new formula. The convergence is analyzed for the implicit schemes based on the discrete gradient formula, and it turns out that the convergence of the implicit schemes based on the extended discrete gradient formula is independent of ‖M‖, which is a significant property for the oscillatory Hamiltonian system. Thus, it transpires that a larger step size can be chosen for the new energy-preserving schemes than that for the traditional discrete gradient methods when applied to the oscillatory Hamiltonian system. Illustrative examples show the competence and efficiency of the new schemes in comparison with the traditional discrete gradient methods in the scientific literature. (paper)
Cluster expansion for ground states of local Hamiltonians
Directory of Open Access Journals (Sweden)
Alvise Bastianello
2016-08-01
Full Text Available 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.
Hamiltonian formalism of two-dimensional Vlasov kinetic equation.
Pavlov, Maxim V
2014-12-08
In this paper, the two-dimensional Benney system describing long wave propagation of a finite depth fluid motion and the multi-dimensional Russo-Smereka kinetic equation describing a bubbly flow are considered. The Hamiltonian approach established by J. Gibbons for the one-dimensional Vlasov kinetic equation is extended to a multi-dimensional case. A local Hamiltonian structure associated with the hydrodynamic lattice of moments derived by D. J. Benney is constructed. A relationship between this hydrodynamic lattice of moments and the two-dimensional Vlasov kinetic equation is found. In the two-dimensional case, a Hamiltonian hydrodynamic lattice for the Russo-Smereka kinetic model is constructed. Simple hydrodynamic reductions are presented.
Contamination Control: a systems approach
Donck, J.C.J. van der
2010-01-01
Contamination influences a wide variety of industrial processes. For complex systems, contamination control, the collective effort to control contamination to such a level that it guarantees or even improves process or product functionality, offers a way for finding workable solutions. Central in
Geometry and Hamiltonian mechanics on discrete spaces
International Nuclear Information System (INIS)
Talasila, V; Clemente-Gallardo, J; Schaft, A J van der
2004-01-01
Numerical simulation is often crucial for analysing the behaviour of many complex systems which do not admit analytic solutions. To this end, one either converts a 'smooth' model into a discrete (in space and time) model, or models systems directly at a discrete level. The goal of this paper is to provide a discrete analogue of differential geometry, and to define on these discrete models a formal discrete Hamiltonian structure-in doing so we try to bring together various fundamental concepts from numerical analysis, differential geometry, algebraic geometry, simplicial homology and classical Hamiltonian mechanics. For example, the concept of a twisted derivation is borrowed from algebraic geometry for developing a discrete calculus. The theory is applied to a nonlinear pendulum and we compare the dynamics obtained through a discrete modelling approach with the dynamics obtained via the usual discretization procedures. Also an example of an energy-conserving algorithm on a simple harmonic oscillator is presented, and its effect on the Poisson structure is discussed
Classical and quantum mechanics of complex Hamiltonian systems
Indian Academy of Sciences (India)
Certain aspects of classical and quantum mechanics of complex Hamiltonian systems in one dimension investigated within the framework of an extended complex phase space approach, characterized by the transformation = 1 + 2, = 1 + 2, are revisited. It is argued that Carl Bender inducted P T symmetry in ...
Hamiltonian circuited simulations in reactor physics
International Nuclear Information System (INIS)
Rio Hirowati Shariffudin
2002-01-01
In the assessment of suitability of reactor designs and in the investigations into reactor safety, the steady state of a nuclear reactor has to be studied carefully. The analysis can be done through mockup designs but this approach costs a lot of money and consumes a lot of time. A less expensive approach is via simulations where the reactor and its neutron interactions are modelled mathematically. Finite difference discretization of the diffusion operator has been used to approximate the steady state multigroup neutron diffusion equations. The steps include the outer scheme which estimates the resulting right hand side of the matrix equation, the group scheme which calculates the upscatter problem and the inner scheme which solves for the flux for a particular group. The Hamiltonian circuited simulations for the inner iterations of the said neutron diffusion equation enable the effective use of parallel computing, especially where the solutions of multigroup neutron diffusion equations involving two or more space dimensions are required. (Author)
Hamiltonian-Driven Adaptive Dynamic Programming for Continuous Nonlinear Dynamical Systems.
Yang, Yongliang; Wunsch, Donald; Yin, Yixin
2017-08-01
This paper presents a Hamiltonian-driven framework of adaptive dynamic programming (ADP) for continuous time nonlinear systems, which consists of evaluation of an admissible control, comparison between two different admissible policies with respect to the corresponding the performance function, and the performance improvement of an admissible control. It is showed that the Hamiltonian can serve as the temporal difference for continuous-time systems. In the Hamiltonian-driven ADP, the critic network is trained to output the value gradient. Then, the inner product between the critic and the system dynamics produces the value derivative. Under some conditions, the minimization of the Hamiltonian functional is equivalent to the value function approximation. An iterative algorithm starting from an arbitrary admissible control is presented for the optimal control approximation with its convergence proof. The implementation is accomplished by a neural network approximation. Two simulation studies demonstrate the effectiveness of Hamiltonian-driven ADP.
Hamiltonian Chaos and Fractional Dynamics
International Nuclear Information System (INIS)
Combescure, M
2005-01-01
This book provides an introduction and discussion of the main issues in the current understanding of classical Hamiltonian chaos, and of its fractional space-time structure. It also develops the most complex and open problems in this context, and provides a set of possible applications of these notions to some fundamental questions of dynamics: complexity and entropy of systems, foundation of classical statistical physics on the basis of chaos theory, and so on. Starting with an introduction of the basic principles of the Hamiltonian theory of chaos, the book covers many topics that can be found elsewhere in the literature, but which are collected here for the readers' convenience. In the last three parts, the author develops topics which are not typically included in the standard textbooks; among them are: - the failure of the traditional description of chaotic dynamics in terms of diffusion equations; - he fractional kinematics, its foundation and renormalization group analysis; - 'pseudo-chaos', i.e. kinetics of systems with weak mixing and zero Lyapunov exponents; - directional complexity and entropy. The purpose of this book is to provide researchers and students in physics, mathematics and engineering with an overview of many aspects of chaos and fractality in Hamiltonian dynamical systems. In my opinion it achieves this aim, at least provided researchers and students (mainly those involved in mathematical physics) can complement this reading with comprehensive material from more specialized sources which are provided as references and 'further reading'. Each section contains introductory pedagogical material, often illustrated by figures coming from several numerical simulations which give the feeling of what's going on, and thus is very useful to the reader who is not very familiar with the topics presented. Some problems are included at the end of most sections to help the reader to go deeper into the subject. My one regret is that the book does not
Coherent states for quadratic Hamiltonians
International Nuclear Information System (INIS)
Contreras-Astorga, Alonso; Fernandez C, David J; Velazquez, Mercedes
2011-01-01
The coherent states for a set of quadratic Hamiltonians in the trap regime are constructed. A matrix technique which allows us to directly identify the creation and annihilation operators will be presented. Then, the coherent states as simultaneous eigenstates of the annihilation operators will be derived, and will be compared with those attained through the displacement operator method. The corresponding wavefunction will be found, and a general procedure for obtaining several mean values involving the canonical operators in these states will be described. The results will be illustrated through the asymmetric Penning trap.
Perturbation theory of effective Hamiltonians
International Nuclear Information System (INIS)
Brandow, B.H.
1975-01-01
This paper constitutes a review of the many papers which have used perturbation theory to derive ''effective'' or ''model'' Hamiltonians. It begins with a brief review of nondegenerate and non-many-body perturbation theory, and then considers the degenerate but non-many-body problem in some detail. It turns out that the degenerate perturbation problem is not uniquely defined, but there are some practical criteria for choosing among the various possibilities. Finally, the literature dealing with the linked-cluster aspects of open-shell many-body systems is reviewed. (U.S.)
Integrable and nonintegrable Hamiltonian systems
International Nuclear Information System (INIS)
Percival, I.
1986-01-01
Traditionally Hamiltonian systems with a finite number of degrees of freedom have been divided into those with few degrees of freedom which were supposed to exhibit some kind of regular ordered motions and those with large numbers of degrees of freedom for which the methods of statistical mechanics should be used. The last few decades have seen a complete change of view. The change of view affects almost all the practical applications, particularly in mathematical physics, which has been dominated for many decades by linear mathematics, coming from quantum theory. The authors consider how this change of view affects some specific applications of dynamics and also the relation between dynamical theory and applications
Perspective: Quantum Hamiltonians for optical interactions
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.
Error Estimates for the Approximation of the Effective Hamiltonian
International Nuclear Information System (INIS)
Camilli, Fabio; Capuzzo Dolcetta, Italo; Gomes, Diogo A.
2008-01-01
We study approximation schemes for the cell problem arising in homogenization of Hamilton-Jacobi equations. We prove several error estimates concerning the rate of convergence of the approximation scheme to the effective Hamiltonian, both in the optimal control setting and as well as in the calculus of variations setting
STRUCTURAL APPROACH TO THE CONTROLLING
Directory of Open Access Journals (Sweden)
LOREDANA CIURLĂU
2016-10-01
Full Text Available Economic concentration has led to the emergence of large enterprises and complex that by the activities or the environment of their operation because of an activity of decentralization. The enterprise is cut in centers of responsibility which enjoys a autonomy more or less widely. The management control will be able to meet the needs of coordination of these organizations decentralised, orienting the "actors" within the meaning of the desired by the manager through the evaluation of the results obtained. The success of an enterprise requires a continuous adapting it to the environment or and competitiveness is transformed into a economic criterion by excellence.
Generalized oscillator representations for Calogero Hamiltonians
International Nuclear Information System (INIS)
Tyutin, I V; Voronov, B L
2013-01-01
This paper is a natural continuation of the previous paper (Gitman et al 2011 J. Phys. A: Math. Theor. 44 425204), where oscillator representations for nonnegative Calogero Hamiltonians with coupling constant α ⩾ − 1/4 were constructed. In this paper, we present generalized oscillator representations for all Calogero Hamiltonians with α ⩾ − 1/4. These representations are generally highly nonunique, but there exists an optimum representation for each Hamiltonian. (comment)
Effective hamiltonian calculations using incomplete model spaces
International Nuclear Information System (INIS)
Koch, S.; Mukherjee, D.
1987-01-01
It appears that the danger of encountering ''intruder states'' is substantially reduced if an effective hamiltonian formalism is developed for incomplete model spaces (IMS). In a Fock-space approach, the proof a ''connected diagram theorem'' is fairly straightforward with exponential-type of ansatze for the wave-operator W, provided the normalization chosen for W is separable. Operationally, one just needs a suitable categorization of the Fock-space operators into ''diagonal'' and ''non-diagonal'' parts that is generalization of the corresponding procedure for the complete model space. The formalism is applied to prototypical 2-electron systems. The calculations have been performed on the Cyber 205 super-computer. The authors paid special attention to an efficient vectorization for the construction and solution of the resulting coupled non-linear equations
General technique to produce isochronous Hamiltonians
International Nuclear Information System (INIS)
Calogero, F; Leyvraz, F
2007-01-01
We introduce a new technique-characterized by an arbitrary positive constant Ω, with which we associate the period T = 2π/Ω-to 'Ω-modify' a Hamiltonian so that the new Hamiltonian thereby obtained is entirely isochronous, namely it yields motions all of which (except possibly for a lower dimensional set of singular motions) are periodic with the same fixed period T in all their degrees of freedom. This technique transforms real autonomous Hamiltonians into Ω-modified Hamiltonians which are also real and autonomous, and it is widely applicable, for instance, to the most general many-body problem characterized by Newtonian equations of motion ('acceleration equal force') provided it is translation invariant. The Ω-modified Hamiltonians are of course not translation invariant, but for Ω = 0 they reduce (up to marginal changes) to the unmodified Hamiltonians they were obtained from. Hence, when this technique is applied to translation-invariant Hamiltonians yielding, in their center-of-mass systems, chaotic motions with a natural time scale much smaller than T, the corresponding Ω-modified Hamiltonians shall display a chaotic behavior for quite some time before the isochronous character of the motions takes over. We moreover show that the quantized versions of these Ω-modified Hamiltonians feature equispaced spectra
Collective Hamiltonians for dipole giant resonances
International Nuclear Information System (INIS)
Weiss, L.I.
1991-07-01
The collective hamiltonian for the Giant Dipole resonance (GDR), in the Goldhaber-Teller-Model, is analytically constructed using the semiclassical and generator coordinates method. Initially a conveniently parametrized set of many body wave functions and a microscopic hamiltonian, the Skyrme hamiltonian - are used. These collective Hamiltonians are applied to the investigation of the GDR, in He 4 , O 16 and Ca 40 nuclei. Also the energies and spectra of the GDR are obtained in these nuclei. The two sets of results are compared, and the zero point energy effects analysed. (author)
Canonical transformations and hamiltonian path integrals
International Nuclear Information System (INIS)
Prokhorov, L.V.
1982-01-01
Behaviour of the Hamiltonian path integrals under canonical transformations produced by a generator, is investigated. An exact form is determined for the kernel of the unitary operator realizing the corresponding quantum transformation. Equivalence rules are found (the Hamiltonian formalism, one-dimensional case) enabling one to exclude non-standard terms from the action. It is shown that the Hamiltonian path integral changes its form under cononical transformations: in the transformed expression besides the classical Hamiltonian function there appear some non-classical terms
A Generic Approach to Parameter Control
Karafotias, G.; Smit, S.K.; Eiben, A.E.
2012-01-01
On-line control of EA parameters is an approach to parameter setting that offers the advantage of values changing during the run. In this paper, we investigate parameter control from a generic and parameter-independent perspective. We propose a generic control mechanism that is targeted to
Topological color codes and two-body quantum lattice Hamiltonians
Kargarian, M.; Bombin, H.; Martin-Delgado, M. A.
2010-02-01
fermionized Hamiltonian from being reduced to a quadratic form owing to interacting gauge fields. We also propose another construction for the two-body Hamiltonian based on the connection between color codes and cluster states. The corresponding two-body Hamiltonian encodes a cluster state defined on a bipartite lattice as its low-energy spectrum, and subsequent selective measurements give rise to the color code model. We discuss this latter approach along with the construction based on the ruby lattice.
Identity of the SU(3) model phenomenological hamiltonian and the hamiltonian of nonaxial rotator
International Nuclear Information System (INIS)
Filippov, G.F.; Avramenko, V.I.; Sokolov, A.M.
1984-01-01
Interpretation of nonspheric atomic nuclei spectra on the basis of phenomenological hamiltonians of SU(3) model showed satisfactory agreement of simulation calculations with experimental data. Meanwhile physical sense of phenomenological hamiltonians was not yet discussed. It is shown that phenomenological hamiltonians of SU(3) model are reduced to hamiltonian of nonaxial rotator but with additional items of the third and fourth powers angular momentum operator of rotator
Hamiltonian closures in fluid models for plasmas
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
Flight Test Approach to Adaptive Control Research
Pavlock, Kate Maureen; Less, James L.; Larson, David Nils
2011-01-01
The National Aeronautics and Space Administration s Dryden Flight Research Center completed flight testing of adaptive controls research on a full-scale F-18 testbed. The validation of adaptive controls has the potential to enhance safety in the presence of adverse conditions such as structural damage or control surface failures. This paper describes the research interface architecture, risk mitigations, flight test approach and lessons learned of adaptive controls research.
Hamiltonian analysis of Plebanski theory
International Nuclear Information System (INIS)
Buffenoir, E; Henneaux, M; Noui, K; Roche, Ph
2004-01-01
We study the Hamiltonian formulation of Plebanski theory in both the Euclidean and Lorentzian cases. A careful analysis of the constraints shows that the system is non-regular, i.e., the rank of the Dirac matrix is non-constant on the non-reduced phase space. We identify the gravitational and topological sectors which are regular subspaces of the non-reduced phase space. The theory can be restricted to the regular subspace which contains the gravitational sector. We explicitly identify first- and second-class constraints in this case. We compute the determinant of the Dirac matrix and the natural measure for the path integral of the Plebanski theory (restricted to the gravitational sector). This measure is the analogue of the Leutwyler-Fradkin-Vilkovisky measure of quantum gravity
Quantum Statistical Operator and Classically Chaotic Hamiltonian ...
African Journals Online (AJOL)
Quantum Statistical Operator and Classically Chaotic Hamiltonian System. ... Journal of the Nigerian Association of Mathematical Physics ... In a Hamiltonian system von Neumann Statistical Operator is used to tease out the quantum consequence of (classical) chaos engendered by the nonlinear coupling of system to its ...
A Direct Method of Hamiltonian Structure
International Nuclear Information System (INIS)
Li Qi; Chen Dengyuan; Su Shuhua
2011-01-01
A direct method of constructing the Hamiltonian structure of the soliton hierarchy with self-consistent sources is proposed through computing the functional derivative under some constraints. The Hamiltonian functional is related with the conservation densities of the corresponding hierarchy. Three examples and their two reductions are given. (general)
Hamiltonian representation of divergence-free fields
International Nuclear Information System (INIS)
Boozer, A.H.
1984-11-01
Globally divergence-free fields, such as the magnetic field and the vorticity, can be described by a two degree of freedom Hamiltonian. The Hamiltonian function provides a complete topological description of the field lines. The formulation also separates the dissipative and inertial time scale evolution of the magnetic and the vorticity fields
Hamiltonian structure of linearly extended Virasoro algebra
International Nuclear Information System (INIS)
Arakelyan, T.A.; Savvidi, G.K.
1991-01-01
The Hamiltonian structure of linearly extended Virasoro algebra which admits free bosonic field representation is described. An example of a non-trivial extension is found. The hierarchy of integrable non-linear equations corresponding to this Hamiltonian structure is constructed. This hierarchy admits the Lax representation by matrix Lax operator of second order
Momentum and hamiltonian in complex action theory
DEFF Research Database (Denmark)
Nagao, Keiichi; Nielsen, Holger Frits Bech
2012-01-01
$-parametrized wave function, which is a solution to an eigenvalue problem of a momentum operator $\\hat{p}$, in FPI with a starting Lagrangian. Solving the eigenvalue problem, we derive the momentum and Hamiltonian. Oppositely, starting from the Hamiltonian we derive the Lagrangian in FPI, and we are led...
A parcel formulation for Hamiltonian layer models
Bokhove, Onno; Oliver, M.
Starting from the three-dimensional hydrostatic primitive equations, we derive Hamiltonian N-layer models with isentropic tropospheric and isentropic or isothermal stratospheric layers. Our construction employs a new parcel Hamiltonian formulation which describes the fluid as a continuum of
On Distributed Port-Hamiltonian Process Systems
Lopezlena, Ricardo; Scherpen, Jacquelien M.A.
2004-01-01
In this paper we use the term distributed port-Hamiltonian Process Systems (DPHPS) to refer to the result of merging the theory of distributed Port-Hamiltonian systems (DPHS) with the theory of process systems (PS). Such concept is useful for combining the systematic interconnection of PHS with the
Relativistic magnetohydrodynamics as a Hamiltonian system
International Nuclear Information System (INIS)
Holm, D.D.; Kupershmidt, A.
1985-01-01
The equations of ideal relativistic magnetohydrodynamics in the laboratory frame form a noncanonical Hamiltonian system with the same Poisson bracket as for the nonrelativistic system, but with dynamical variables and Hamiltonian obtained via a regular deformation of their nonrelativistic counterparts [fr
Hamiltonian Cycles on Random Eulerian Triangulations
DEFF Research Database (Denmark)
Guitter, E.; Kristjansen, C.; Nielsen, Jakob Langgaard
1998-01-01
. Considering the case n -> 0, this implies that the system of random Eulerian triangulations equipped with Hamiltonian cycles describes a c=-1 matter field coupled to 2D quantum gravity as opposed to the system of usual random triangulations equipped with Hamiltonian cycles which has c=-2. Hence, in this case...
Xie, Yu; Jiang, Shengshi; Zheng, Jie; Lan, Zhenggang
2017-12-21
Photoinduced excited-state electron and energy transfer processes are crucial in biological photoharvesting systems and organic photovoltaic devices. We discuss the construction of a diabatic vibronic Hamiltonian for the proper treatment of these processes involving the projection approach acting on both electronic wave functions and vibrational modes. In the electronic part, the wave function projection approach is used to construct the diabatic Hamiltonian in which both local excited states and charge-transfer states are included on the same footing. For the vibrational degrees of freedom, the vibronic couplings in the diabatic Hamiltonian are obtained in the basis of the pseudonormal modes localized on each monomer site by applying delocalized-to-localized mode projection. This systematic approach allows us to construct the vibronic diabatic Hamiltonian in molecular aggregates.
Entangled trajectories Hamiltonian dynamics for treating quantum nuclear effects
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.
The mathematics of a quantum Hamiltonian computing half adder Boolean logic gate
International Nuclear Information System (INIS)
Dridi, G; Julien, R; Hliwa, M; Joachim, C
2015-01-01
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. (paper)
The mathematics of a quantum Hamiltonian computing half adder Boolean logic gate.
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.
Effective Hamiltonian theory: recent formal results and non-nuclear applications
International Nuclear Information System (INIS)
Brandow, B.H.
1981-01-01
Effective Hamiltonian theory is discussed from the points of view of the unitary transformation method and degenerate perturbation theory. It is shown that the two approaches are identical term by term. The main features of a formulation of the coupled-cluster method for open-shell systems are outlined. Finally, recent applications of the many-body linked-cluster form of degenerate perturbation theory are described: the derivation of effective spin Hamiltonians in magnetic insulator systems, the derivation and calculation ab initio of effective π-electron Hamiltonians for planar conjugated hydrocarbon molecules, and understanding the so-called valence fluctuation phenomenon exhibited by certain rare earth compounds
Approaches to tobacco control: the evidence base.
Aquilino, M Lober; Lowe, J B
2004-02-01
Tobacco production, distribution, and use are international issues with significant health and economic implications. This paper provides an overview of the effective approaches to tobacco control including decreasing demand for tobacco products through taxation, consumer education, research, bans on advertising and promotion, warning labels, and restrictions on public smoking. The effectiveness of reducing the supply of tobacco products through prohibition, restrictions on youth access, crop substitution, trade restrictions, and control of smuggling, will also be discussed. Decreasing smoking, particularly among young people, by preventing or delaying initiation, preventing regular use, and increasing cessation through behavioural approaches for all ages is reviewed. Cessation methods including pharmacological approaches, 'quitlines', Internet programmes, and the targeting of specific populations are discussed. Internet availability of tobacco products and sustainability of current efforts are presented as continuing challenges to tobacco control.
Systems Approach to Arms Control Verification
Energy Technology Data Exchange (ETDEWEB)
Allen, K; Neimeyer, I; Listner, C; Stein, G; Chen, C; Dreicer, M
2015-05-15
Using the decades of experience of developing concepts and technologies for verifying bilateral and multilateral arms control agreements, a broad conceptual systems approach is being developed that takes into account varying levels of information and risk. The IAEA has already demonstrated the applicability of a systems approach by implementing safeguards at the State level, with acquisition path analysis as the key element. In order to test whether such an approach could also be implemented for arms control verification, an exercise was conducted in November 2014 at the JRC ITU Ispra. Based on the scenario of a hypothetical treaty between two model nuclear weapons states aimed at capping their nuclear arsenals at existing levels, the goal of this exercise was to explore how to use acquisition path analysis in an arms control context. Our contribution will present the scenario, objectives and results of this exercise, and attempt to define future workshops aimed at further developing verification measures that will deter or detect treaty violations.
Preliminary Results on Asymptotic Stabilization of Hamiltonian Systems with Nonholonomic Constraints
Khennouf, H.; Canudas de Wit, C.; Schaft, A.J. van der
1995-01-01
This paper presents some preliminary results on asymptotic stabilization of nonholonomic mechanical systems using the Hamiltonian formulation proposed previously. Our work seeks to establish a general formulation for designing time-varying controllers for some mechanical system described in the
Indirect quantum tomography of quadratic Hamiltonians
Energy Technology Data Exchange (ETDEWEB)
Burgarth, Daniel [Institute for Mathematical Sciences, Imperial College London, London SW7 2PG (United Kingdom); Maruyama, Koji; Nori, Franco, E-mail: daniel@burgarth.de, E-mail: kmaruyama@riken.jp [Advanced Science Institute, RIKEN, Wako-shi, Saitama 351-0198 (Japan)
2011-01-15
A number of many-body problems can be formulated using Hamiltonians that are quadratic in the creation and annihilation operators. Here, we show how such quadratic Hamiltonians can be efficiently estimated indirectly, employing very few resources. We found that almost all the properties of the Hamiltonian are determined by its surface and that these properties can be measured even if the system can only be initialized to a mixed state. Therefore, our method can be applied to various physical models, with important examples including coupled nano-mechanical oscillators, hopping fermions in optical lattices and transverse Ising chains.
Single-particle dynamics - Hamiltonian formulation
International Nuclear Information System (INIS)
Montague, B.W.
1977-01-01
In this paper the Hamiltonian formalism is applied to the linear theory of accelerator dynamics. The reasons for the introduction of this method rather than the more straightforward use of second order differential equations of motion are briefly discussed. An outline of Lagrangian and Hamiltonian formalism is given, some properties of the Hamiltonian are discussed and canonical transformations are illustrated. The methods are demonstrated using elementary examples such as the simple pendulum and the procedures adopted to handle specific problems in accelerator theory are indicated. (B.D.)
Incomplete Dirac reduction of constrained Hamiltonian systems
Energy Technology Data Exchange (ETDEWEB)
Chandre, C., E-mail: chandre@cpt.univ-mrs.fr
2015-10-15
First-class constraints constitute a potential obstacle to the computation of a Poisson bracket in Dirac’s theory of constrained Hamiltonian systems. Using the pseudoinverse instead of the inverse of the matrix defined by the Poisson brackets between the constraints, we show that a Dirac–Poisson bracket can be constructed, even if it corresponds to an incomplete reduction of the original Hamiltonian system. The uniqueness of Dirac brackets is discussed. The relevance of this procedure for infinite dimensional Hamiltonian systems is exemplified.
Quantum Hamiltonian Physics with Supercomputers
International Nuclear Information System (INIS)
Vary, James P.
2014-01-01
The vision of solving the nuclear many-body problem in a Hamiltonian framework with fundamental interactions tied to QCD via Chiral Perturbation Theory is gaining support. The goals are to preserve the predictive power of the underlying theory, to test fundamental symmetries with the nucleus as laboratory and to develop new understandings of the full range of complex quantum phenomena. Advances in theoretical frameworks (renormalization and many-body methods) as well as in computational resources (new algorithms and leadership-class parallel computers) signal a new generation of theory and simulations that will yield profound insights into the origins of nuclear shell structure, collective phenomena and complex reaction dynamics. Fundamental discovery opportunities also exist in such areas as physics beyond the Standard Model of Elementary Particles, the transition between hadronic and quark–gluon dominated dynamics in nuclei and signals that characterize dark matter. I will review some recent achievements and present ambitious consensus plans along with their challenges for a coming decade of research that will build new links between theory, simulations and experiment. Opportunities for graduate students to embark upon careers in the fast developing field of supercomputer simulations is also discussed
Quantum Hamiltonian Physics with Supercomputers
Energy Technology Data Exchange (ETDEWEB)
Vary, James P.
2014-06-15
The vision of solving the nuclear many-body problem in a Hamiltonian framework with fundamental interactions tied to QCD via Chiral Perturbation Theory is gaining support. The goals are to preserve the predictive power of the underlying theory, to test fundamental symmetries with the nucleus as laboratory and to develop new understandings of the full range of complex quantum phenomena. Advances in theoretical frameworks (renormalization and many-body methods) as well as in computational resources (new algorithms and leadership-class parallel computers) signal a new generation of theory and simulations that will yield profound insights into the origins of nuclear shell structure, collective phenomena and complex reaction dynamics. Fundamental discovery opportunities also exist in such areas as physics beyond the Standard Model of Elementary Particles, the transition between hadronic and quark–gluon dominated dynamics in nuclei and signals that characterize dark matter. I will review some recent achievements and present ambitious consensus plans along with their challenges for a coming decade of research that will build new links between theory, simulations and experiment. Opportunities for graduate students to embark upon careers in the fast developing field of supercomputer simulations is also discussed.
Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity
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.
International Nuclear Information System (INIS)
Struckmeier, Juergen
2005-01-01
We will present a consistent description of Hamiltonian dynamics on the 'symplectic extended phase space' that is analogous to that of a time-independent Hamiltonian system on the conventional symplectic phase space. The extended Hamiltonian H 1 and the pertaining extended symplectic structure that establish the proper canonical extension of a conventional Hamiltonian H will be derived from a generalized formulation of Hamilton's variational principle. The extended canonical transformation theory then naturally permits transformations that also map the time scales of the original and destination system, while preserving the extended Hamiltonian H 1 , and hence the form of the canonical equations derived from H 1 . The Lorentz transformation, as well as time scaling transformations in celestial mechanics, will be shown to represent particular canonical transformations in the symplectic extended phase space. Furthermore, the generalized canonical transformation approach allows us to directly map explicitly time-dependent Hamiltonians into time-independent ones. An 'extended' generating function that defines transformations of this kind will be presented for the time-dependent damped harmonic oscillator and for a general class of explicitly time-dependent potentials. In the appendix, we will re-establish the proper form of the extended Hamiltonian H 1 by means of a Legendre transformation of the extended Lagrangian L 1
Optimal protocols for Hamiltonian and Schrödinger dynamics
International Nuclear Information System (INIS)
Schmiedl, Tim; Dieterich, Eckhard; Dieterich, Peter-Simon; Seifert, Udo
2009-01-01
For systems in an externally controllable time dependent potential, the optimal protocol minimizes the mean work spent in a finite time transition between given initial and final values of a control parameter. For an initially thermalized ensemble, we consider both Hamiltonian evolution for classical systems and Schrödinger evolution for quantum systems. In both cases, we show that for harmonic potentials, the optimal work is given by the adiabatic work even in the limit of short transition times. This result is counter-intuitive because the adiabatic work is substantially smaller than the work for an instantaneous jump. We also perform numerical calculations for the optimal protocol for Hamiltonian dynamics in an anharmonic quartic potential. For a two-level spin system, we give examples where the adiabatic work can be reached in either a finite or an arbitrarily short transition time depending on the allowed parameter space
A Modular Approach to Redundant Robot Control
International Nuclear Information System (INIS)
Anderson, R.J.
1997-12-01
This paper describes a modular approach for computing redundant robot kinematics. First some conventional redundant control methods are presented and shown to be 'passive control laws', i.e. they can be represented by a network consisting of passive elements. These networks are then put into modular form by applying scattering operator techniques. Additional subnetwork modules can then be added to further shape the motion. Modules for obstacle detection, joint limit avoidance, proximity sensing, and for imposing nonlinear velocity constraints are presented. The resulting redundant robot control system is modular, flexible and robust
Jacobi fields of completely integrable Hamiltonian systems
International Nuclear Information System (INIS)
Giachetta, G.; Mangiarotti, L.; Sardanashvily, G.
2003-01-01
We show that Jacobi fields of a completely integrable Hamiltonian system of m degrees of freedom make up an extended completely integrable system of 2m degrees of freedom, where m additional first integrals characterize a relative motion
Quantum Hamiltonian reduction in superspace formalism
International Nuclear Information System (INIS)
Madsen, J.O.; Ragoucy, E.
1994-02-01
Recently the quantum Hamiltonian reduction was done in the case of general sl(2) embeddings into Lie algebras and superalgebras. The results are extended to the quantum Hamiltonian reduction of N=1 affine Lie superalgebras in the superspace formalism. It is shown that if we choose a gauge for the supersymmetry, and consider only certain equivalence classes of fields, then our quantum Hamiltonian reduction reduces to quantum Hamiltonian reduction of non-supersymmetric Lie superalgebras. The super energy-momentum tensor is constructed explicitly as well as all generators of spin 1 (and 1/2); thus all generators in the superconformal, quasi-superconformal and Z 2 *Z 2 superconformal algebras are constructed. (authors). 21 refs
Integrable Hamiltonian systems and spectral theory
Moser, J
1981-01-01
Classical integrable Hamiltonian systems and isospectral deformations ; geodesics on an ellipsoid and the mechanical system of C. Neumann ; the Schrödinger equation for almost periodic potentials ; finite band potentials ; limit cases, Bargmann potentials.
Spectral properties of almost-periodic Hamiltonians
International Nuclear Information System (INIS)
Lima, R.
1983-12-01
We give a description of some spectral properties of almost-periodic hamiltonians. We put the stress on some particular points of the proofs of the existence of absolutely continuous or pure point spectrum [fr
Air parcels and air particles: Hamiltonian dynamics
Bokhove, Onno; Lynch, Peter
We present a simple Hamiltonian formulation of the Euler equations for fluid flow in the Lagrangian framework. In contrast to the conventional formulation, which involves coupled partial differential equations, our "innovative'' mathematical formulation involves only ordinary differential equations
Discrete Hamiltonian evolution and quantum gravity
International Nuclear Information System (INIS)
Husain, Viqar; Winkler, Oliver
2004-01-01
We study constrained Hamiltonian systems by utilizing general forms of time discretization. We show that for explicit discretizations, the requirement of preserving the canonical Poisson bracket under discrete evolution imposes strong conditions on both allowable discretizations and Hamiltonians. These conditions permit time discretizations for a limited class of Hamiltonians, which does not include homogeneous cosmological models. We also present two general classes of implicit discretizations which preserve Poisson brackets for any Hamiltonian. Both types of discretizations generically do not preserve first class constraint algebras. Using this observation, we show that time discretization provides a complicated time gauge fixing for quantum gravity models, which may be compared with the alternative procedure of gauge fixing before discretization
Classical mechanics Hamiltonian and Lagrangian formalism
Deriglazov, Alexei
2016-01-01
This account of the fundamentals of Hamiltonian mechanics also covers related topics such as integral invariants and the Noether theorem. With just the elementary mathematical methods used for exposition, the book is suitable for novices as well as graduates.
Hamiltonian cycle problem and Markov chains
Borkar, Vivek S; Filar, Jerzy A; Nguyen, Giang T
2014-01-01
This book summarizes a line of research that maps certain classical problems of discrete mathematics and operations research - such as the Hamiltonian cycle and the Travelling Salesman problems - into convex domains where continuum analysis can be carried out.
Variable Delay in port-Hamiltonian Telemanipulation
Secchi, C; Stramigioli, Stefano; Fantuzzi, C.
2006-01-01
In several applications involving bilateral telemanipulation, master and slave act at different power scales. In this paper a strategy for passively dealing with variable communication delay in scaled port-Hamiltonian based telemanipulation over packet switched networks is proposed.
Superradiance, disorder, and the non-Hermitian Hamiltonian in open quantum systems
Energy Technology Data Exchange (ETDEWEB)
Celardo, G. L.; Biella, A.; Giusteri, G. G.; Mattiotti, F. [Dipartimento di Matematica e Fisica and Interdisciplinary Laboratories for Advanced Materials Physics, Università Cattolica, via Musei 41, 25121 Brescia (Italy); Zhang, Y.; Kaplan, L. [Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118 (United States)
2014-10-15
We first briefly review the non-Hermitian effective Hamiltonian approach to open quantum systems and the associated phenomenon of superradiance. We next discuss the superradiance crossover in the presence of disorder and the relationship between superradiance and the localization transition. Finally, we investigate the regime of validity of the energy-independent effective Hamiltonian approximation and show that the results obtained by these methods are applicable to realistic physical systems.
Controllable Load Management Approaches in Smart Grids
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Jingshuang Shen
2015-10-01
Full Text Available With rapid smart grid technology development, the customer can actively participate in demand-side management (DSM with the mutual information communication between the distributor operation company and the smart devices in real-time. Controllable load management not only has the advantage of peak shaving, load balance, frequency regulation, and voltage stability, but is also effective at providing fast balancing services to the renewable energy grid in the distributed power system. The load management faces an enormous challenge as the customer has a large number of both small residential loads and dispersed renewable sources. In this paper, various controllable load management approaches are discussed. The traditional controllable load approaches such as the end users’ controllable appliances, storage battery, Vehicle-to-Grid (V2G, and heat storage are reviewed. The “broad controllable loads” management, such as the microgrid, Virtual Power Plant (VPP, and the load aggregator are also presented. Furthermore, the load characteristics, control strategies, and control effectiveness are analyzed.
Towards a nonperturbative calculation of weak Hamiltonian Wilson coefficients
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.
On local Hamiltonians and dissipative systems
Energy Technology Data Exchange (ETDEWEB)
Castagnino, M. [CONICET-Institutos de Fisica Rosario y de Astronomia y Fisica del Espacio Casilla de Correos 67, Sucursal 28, 1428, Buenos Aires (Argentina); Gadella, M. [Facultad de Ciencias Exactas, Ingenieria y Agrimensura UNR, Rosario (Argentina) and Departamento de Fisica Teorica, Facultad de Ciencias c. Real de Burgos, s.n., 47011 Valladolid (Spain)]. E-mail: manuelgadella@yahoo.com.ar; Lara, L.P. [Facultad de Ciencias Exactas, Ingenieria y Agrimensura UNR, Rosario (Argentina)
2006-11-15
We study a type of one-dimensional dynamical systems on the corresponding two-dimensional phase space. By using arguments related to the existence of integrating factors for Pfaff equations, we show that some one-dimensional non-Hamiltonian systems like dissipative systems, admit a Hamiltonian description by sectors on the phase plane. This picture is not uniquely defined and is coordinate dependent. A simple example is exhaustively discussed. The method, is not always applicable to systems with higher dimensions.
A phenomenological Hamiltonian for the Lotka-Volterra problem
International Nuclear Information System (INIS)
Georgian, T.; Findley, G.L.
1996-01-01
We have presented a Hamiltonian theory of phenomenological chemical kinetics. In the present paper, we extend this treatment to the Lotka-Volterra model of sustained oscillations. Our approach begins with the usual definition of an intrinsic reaction coordinate space (x 1 ,x 2 ) for the Lotka-Volterra problem, which leads to the rate equations x 1 =ax 1 -bx 1 x 2 , x 2 =-cx 2 +bx 1 x 2 , with a,b and c being real constants. We thereafter present a Hamiltonian function H(x,y)[y 1 = x 1 and y 2 = x 2 ] and an associated holonomic constraint, which give rise to the above rates as half of Hamilton's equations. We provide trajectories by numerical integration (4th order Runge-Kutta) and show that H(x,y) is a constant of the motion. Finally, issues involved in developing an analytic solution to this problem are discussed
Hamiltonian Dynamics of Doubly-Foliable Space-Times
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Cecília Gergely
2018-01-01
Full Text Available The 2 + 1 + 1 decomposition of space-time is useful in monitoring the temporal evolution of gravitational perturbations/waves in space-times with a spatial direction singled-out by symmetries. Such an approach based on a perpendicular double foliation has been employed in the framework of dark matter and dark energy-motivated scalar-tensor gravitational theories for the discussion of the odd sector perturbations of spherically-symmetric gravity. For the even sector, however, the perpendicularity has to be suppressed in order to allow for suitable gauge freedom, recovering the 10th metric variable. The 2 + 1 + 1 decomposition of the Einstein–Hilbert action leads to the identification of the canonical pairs, the Hamiltonian and momentum constraints. Hamiltonian dynamics is then derived via Poisson brackets.
Extended hamiltonian formalism and Lorentz-violating lagrangians
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Don Colladay
2017-09-01
Full Text Available 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.
Quadratic time dependent Hamiltonians and separation of variables
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.
Extended hamiltonian formalism and Lorentz-violating lagrangians
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.
Symplectic and Hamiltonian structures of nonlinear evolution equations
International Nuclear Information System (INIS)
Dorfman, I.Y.
1993-01-01
A Hamiltonian structure on a finite-dimensional manifold can be introduced either by endowing it with a (pre)symplectic structure, or by describing the Poisson bracket with the help of a tensor with two upper indices named the Poisson structure. Under the assumption of nondegeneracy, the Poisson structure is nothing else than the inverse of the symplectic structure. Also in the degenerate case the distinction between the two approaches is almost insignificant, because both presymplectic and Poisson structures split into symplectic structures on leaves of appropriately chosen foliations. Hamiltonian structures that arise in the theory of evolution equations demonstrate something new in this respect: trying to operate in local terms, one is induced to develop both approaches independently. Hamiltonian operators, being the infinite-dimensional counterparts of Poisson structures, were the first to become the subject of investigations. A considerable period of time passed before the papers initiated research in the theory of symplectic operators, being the counterparts of presymplectic structures. In what follows, we focus on the main achievements in this field
Relativistic and separable classical hamiltonian particle dynamics
International Nuclear Information System (INIS)
Sazdjian, H.
1981-01-01
We show within the Hamiltonian formalism the existence of classical relativistic mechanics of N scalar particles interacting at a distance which satisfies the requirements of Poincare invariance, separability, world-line invariance and Einstein causality. The line of approach which is adopted here uses the methods of the theory of systems with constraints applied to manifestly covariant systems of particles. The study is limited to the case of scalar interactions remaining weak in the whole phase space and vanishing at large space-like separation distances of the particles. Poincare invariance requires the inclusion of many-body, up to N-body, potentials. Separability requires the use of individual or two-body variables and the construction of the total interaction from basic two-body interactions. Position variables of the particles are constructed in terms of the canonical variables of the theory according to the world-line invariance condition and the subsidiary conditions of the non-relativistic limit and separability. Positivity constraints on the interaction masses squared of the particles ensure that the velocities of the latter remain always smaller than the velocity of light
Solving a Hamiltonian Path Problem with a bacterial computer
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
Solving a Hamiltonian Path Problem with a bacterial computer
Directory of Open Access Journals (Sweden)
Treece Jessica
2009-07-01
Full Text Available Abstract 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
Focal points and principal solutions of linear Hamiltonian systems revisited
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.
Operator approach to linear control systems
Cheremensky, A
1996-01-01
Within the framework of the optimization problem for linear control systems with quadratic performance index (LQP), the operator approach allows the construction of a systems theory including a number of particular infinite-dimensional optimization problems with hardly visible concreteness. This approach yields interesting interpretations of these problems and more effective feedback design methods. This book is unique in its emphasis on developing methods for solving a sufficiently general LQP. Although this is complex material, the theory developed here is built on transparent and relatively simple principles, and readers with less experience in the field of operator theory will find enough material to give them a good overview of the current state of LQP theory and its applications. Audience: Graduate students and researchers in the fields of mathematical systems theory, operator theory, cybernetics, and control systems.
Quadratic time dependent Hamiltonians and separation of variables
International Nuclear Information System (INIS)
Anzaldo-Meneses, A.
2017-01-01
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. - Highlights: • Exact unitary transformation reducing time dependent quadratic quantum Hamiltonian to zero. • New separation of variables method and simultaneous uncoupling of modes. • Explicit examples of transformations for one to four dimensional problems. • New general evolution equation for quadratic form in the action, respectively Green’s function.
Existence of 121 limit cycles in a perturbed planar polynomial Hamiltonian vector field of degree 11
International Nuclear Information System (INIS)
Wang, S.; Yu, P.
2006-01-01
In this article, a systematic procedure has been explored to studying general Z q -equivariant planar polynomial Hamiltonian vector fields for the maximal number of closed orbits and the maximal number of limit cycles after perturbation. Following the procedure by taking special consideration of Z 12 -equivariant vector fields of degree 11, the maximal of 99 closed orbits are obtained under a well-defined coefficient group. Consequently, perturbation parameter control in limit cycle computation leads to the existence of 121 limit cycles in the perturbed Hamiltonian vector field, which gives rise to the lower bound of Hilbert number of 11th-order systems as H(11) ≥ 11 2 . Two conjectures are proposed regarding the maximal number of closed orbits for equivariant polynomial Hamiltonian vector fields and the maximal number of limit cycles bifurcated from the well defined Hamiltonian vector fields after perturbation
Comparison of Routable Control System Security Approaches
Energy Technology Data Exchange (ETDEWEB)
Edgar, Thomas W.; Hadley, Mark D.; Carroll, Thomas E.; Manz, David O.; Winn, Jennifer D.
2011-06-01
This document is an supplement to the 'Secure and Efficient Routable Control Systems.' It addressed security in routable control system communication. The control system environment that monitors and manages the power grid historically has utilized serial communication mechanisms. Leased-line serial communication environments operating at 1200 to 9600 baud rates are common. However, recent trends show that communication media such as fiber, optical carrier 3 (OC-3) speeds, mesh-based high-speed wireless, and the Internet are becoming the media of choice. In addition, a dichotomy has developed between the electrical transmission and distribution environments, with more modern communication infrastructures deployed by transmission utilities. The preceding diagram represents a typical control system. The Communication Links cloud supports all of the communication mechanisms a utility might deploy between the control center and devices in the field. Current methodologies used for security implementations are primarily led by single vendors or standards bodies. However, these entities tend to focus on individual protocols. The result is an environment that contains a mixture of security solutions that may only address some communication protocols at an increasing operational burden for the utility. A single approach is needed that meets operational requirements, is simple to operate, and provides the necessary level of security for all control system communication. The solution should be application independent (e.g., Distributed Network Protocol/Internet Protocol [DNP/IP], International Electrotechnical Commission [IEC] C37.118, Object Linking and Embedding for Process Control [OPC], etc.) and focus on the transport layer. In an ideal setting, a well-designed suite of standards for control system communication will be used for vendor implementation and compliance testing. An expected outcome of this effort is an international standard.
A probabilistic approach to controlling crevice chemistry
International Nuclear Information System (INIS)
Millett, P.J.; Brobst, G.E.; Riddle, J.
1995-01-01
It has been generally accepted that the corrosion of steam generator tubing could be reduced if the local pH in regions where impurities concentrate could be controlled. The practice of molar ratio control is based on this assumption. Unfortunately, due to the complexity of the crevice concentration process, efforts to model the crevice chemistry based on bulk water conditions are quite uncertain. In-situ monitoring of the crevice chemistry is desirable, but may not be achievable in the near future. The current methodology for assessing the crevice chemistry is to monitor the hideout return chemistry when the plant shuts down. This approach also has its shortcomings, but may provide sufficient data to evaluate whether the crevice pH is in a desirable range. In this paper, an approach to controlling the crevice chemistry based on a target molar ratio indicator is introduced. The molar ratio indicator is based on what is believed to be the most reliable hideout return data. Probabilistic arguments are then used to show that the crevice pH will most likely be in a desirable range when the target molar ratio is achieved
Large Scale Emerging Properties from Non Hamiltonian Complex Systems
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Marco Bianucci
2017-06-01
Full Text Available The concept of “large scale” depends obviously on the phenomenon we are interested in. For example, in the field of foundation of Thermodynamics from microscopic dynamics, the spatial and time large scales are order of fraction of millimetres and microseconds, respectively, or lesser, and are defined in relation to the spatial and time scales of the microscopic systems. In large scale oceanography or global climate dynamics problems the time scales of interest are order of thousands of kilometres, for space, and many years for time, and are compared to the local and daily/monthly times scales of atmosphere and ocean dynamics. In all the cases a Zwanzig projection approach is, at least in principle, an effective tool to obtain class of universal smooth “large scale” dynamics for few degrees of freedom of interest, starting from the complex dynamics of the whole (usually many degrees of freedom system. The projection approach leads to a very complex calculus with differential operators, that is drastically simplified when the basic dynamics of the system of interest is Hamiltonian, as it happens in Foundation of Thermodynamics problems. However, in geophysical Fluid Dynamics, Biology, and in most of the physical problems the building block fundamental equations of motions have a non Hamiltonian structure. Thus, to continue to apply the useful projection approach also in these cases, we exploit the generalization of the Hamiltonian formalism given by the Lie algebra of dissipative differential operators. In this way, we are able to analytically deal with the series of the differential operators stemming from the projection approach applied to these general cases. Then we shall apply this formalism to obtain some relevant results concerning the statistical properties of the El Niño Southern Oscillation (ENSO.
Gravitational surface Hamiltonian and entropy quantization
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Ashish Bakshi
2017-02-01
Full Text Available 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.
Effective Hamiltonian for travelling discrete breathers
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.
Hamiltonian boundary term and quasilocal energy flux
International Nuclear Information System (INIS)
Chen, C.-M.; Nester, James M.; Tung, R.-S.
2005-01-01
The Hamiltonian for a gravitating region includes a boundary term which determines not only the quasilocal values but also, via the boundary variation principle, the boundary conditions. Using our covariant Hamiltonian formalism, we found four particular quasilocal energy-momentum boundary term expressions; each corresponds to a physically distinct and geometrically clear boundary condition. Here, from a consideration of the asymptotics, we show how a fundamental Hamiltonian identity naturally leads to the associated quasilocal energy flux expressions. For electromagnetism one of the four is distinguished: the only one which is gauge invariant; it gives the familiar energy density and Poynting flux. For Einstein's general relativity two different boundary condition choices correspond to quasilocal expressions which asymptotically give the ADM energy, the Trautman-Bondi energy and, moreover, an associated energy flux (both outgoing and incoming). Again there is a distinguished expression: the one which is covariant
Path-integral isomorphic Hamiltonian for including nuclear quantum effects in non-adiabatic dynamics
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.
Bäcklund transformations and Hamiltonian flows
International Nuclear Information System (INIS)
Zullo, Federico
2013-01-01
In this work we show that, under certain conditions, parametric Bäcklund transformations for a finite dimensional integrable system can be interpreted as solutions to the equations of motion defined by an associated non-autonomous Hamiltonian. The two systems share the same constants of motion. This observation leads to the identification of the Hamiltonian interpolating the iteration of the discrete map defined by the transformations, which indeed in numerical applications can be considered a linear combination of the integrals appearing in the spectral curve of the Lax matrix. An example with the periodic Toda lattice is given. (paper)
Hamiltonian dynamics for complex food webs
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.
Convergence to equilibrium under a random Hamiltonian
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.
Suppression of work fluctuations by optimal control: An approach based on Jarzynski's equality
Xiao, Gaoyang; Gong, Jiangbin
2014-11-01
Understanding and manipulating work fluctuations in microscale and nanoscale systems are of both fundamental and practical interest. For example, aspects of work fluctuations will be an important factor in designing nanoscale heat engines. In this work, an optimal control approach directly exploiting Jarzynski's equality is proposed to effectively suppress the fluctuations in the work statistics, for systems (initially at thermal equilibrium) subject to a work protocol but isolated from a bath during the protocol. The control strategy is to minimize the deviations of individual values of e-β W from their ensemble average given by e-β Δ F, where W is the work, β is the inverse temperature, and Δ F is the free energy difference between two equilibrium states. It is further shown that even when the system Hamiltonian is not fully known, it is still possible to suppress work fluctuations through a feedback loop, by refining the control target function on the fly through Jarzynski's equality itself. Numerical experiments are based on linear and nonlinear parametric oscillators. Optimal control results for linear parametric oscillators are also benchmarked with early results based on shortcuts to adiabaticity.
Nuclear outages: an approach to project controls
International Nuclear Information System (INIS)
Bryson, R.
1985-01-01
The annual budget for maintaining and operating a nuclear power plant has risen dramatically over the past 5 years. NRC-mandated plant improvements and outage related expenses are often cited to be the main contributors to these escalating budgets. Nuclear utilities have responded by developing programs to improve plant availability and outage costs through improved outage performance. Utilities recognize that for capital improvements the program to control costs does no begin with outage planning, but rather more appropriately up front during the engineering phase. To support their management objectives, utilities have been developing comprehensive project control systems for concurrently reducing capital expenditures, outage-related costs, and time. This paper provides an approach to project controls that, rather than using one all inclusive comprehensive system, requires five separate monitoring systems - one for each phase of an activity's life cycle. Through the integration of these discrete but interrelated systems, utility management acquires the necessary tools for comprehensive planning and control of their modification program and effective detailed monitoring for all outage-related activities
Approaches to Learning to Control Dynamic Uncertainty
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Magda Osman
2015-10-01
Full Text Available In dynamic environments, when faced with a choice of which learning strategy to adopt, do people choose to mostly explore (maximizing their long term gains or exploit (maximizing their short term gains? More to the point, how does this choice of learning strategy influence one’s later ability to control the environment? In the present study, we explore whether people’s self-reported learning strategies and levels of arousal (i.e., surprise, stress correspond to performance measures of controlling a Highly Uncertain or Moderately Uncertain dynamic environment. Generally, self-reports suggest a preference for exploring the environment to begin with. After which, those in the Highly Uncertain environment generally indicated they exploited more than those in the Moderately Uncertain environment; this difference did not impact on performance on later tests of people’s ability to control the dynamic environment. Levels of arousal were also differentially associated with the uncertainty of the environment. Going beyond behavioral data, our model of dynamic decision-making revealed that, in actual fact, there was no difference in exploitation levels between those in the highly uncertain or moderately uncertain environments, but there were differences based on sensitivity to negative reinforcement. We consider the implications of our findings with respect to learning and strategic approaches to controlling dynamic uncertainty.
Immunocontraceptives: New Approaches to Fertility Control
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Kiranjeet Kaur
2014-01-01
Full Text Available The rapidly increasing global population has bowed the attention of family planning and associated reproductive health programmes in the direction of providing a safe and reliable method which can be used to limit family size. The world population is estimated to exceed a phenomenal 10 billion by the year 2050 A.D., thus presenting a real jeopardy of overpopulation with severe implications for the future. Despite the availability of contraceptive methods, there are over one million elective abortions globally each year due to unintended pregnancies, having devastating impact on reproductive health of women worldwide. This highlights the need for the development of newer and improved contraceptive methods. A novel contraceptive approach that is gaining substantial attention is “immunocontraception” targeting gamete production, gamete outcome, or gamete function. Amongst these, use of sperm antigens (gamete function seems to be an exciting and feasible approach. However, the variability of immune response and time lag to attain titer among vaccinated individuals after active immunization has highlighted the potential relevance of preformed antibodies in this league. This review is an attempt to analyze the current status and progress of immunocontraceptive approaches with respect to their establishment as a future fertility control agent.
Renormalization Group Reduction of Non Integrable Hamiltonian Systems
International Nuclear Information System (INIS)
Tzenov, Stephan I.
2002-01-01
Based on Renormalization Group method, a reduction of non integratable multi-dimensional Hamiltonian systems has been performed. The evolution equations for the slowly varying part of the angle-averaged phase space density and for the amplitudes of the angular modes have been derived. It has been shown that these equations are precisely the Renormalization Group equations. As an application of the approach developed, the modulational diffusion in one-and-a-half degrees of freedom dynamical system has been studied in detail
Iterated Hamiltonian type systems and applications
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.
Symmetry and resonance in Hamiltonian systems
Tuwankotta, J.M.; Verhulst, F.
2000-01-01
In this paper we study resonances in two degrees of freedom, autonomous, hamiltonian systems. Due to the presence of a symmetry condition on one of the degrees of freedom, we show that some of the resonances vanish as lower order resonances. After giving a sharp estimate of the resonance domain, we
Symmetry and resonance in Hamiltonian systems
Tuwankotta, J.M.; Verhulst, F.
1999-01-01
In this paper we study resonances in two degrees of freedom, autonomous, hamiltonian systems. Due to the presence of a symmetry condition on one of the degrees of freedom, we show that some of the resonances vanish as lower order resonances. After determining the size of the resonance domain, we
Hamiltonian evolutions of twisted polygons in RPn
International Nuclear Information System (INIS)
Beffa, Gloria Marì; Wang, Jing Ping
2013-01-01
In this paper we find a discrete moving frame and their associated invariants along projective polygons in RP n , and we use them to describe invariant evolutions of projective N-gons. We then apply a reduction process to obtain a natural Hamiltonian structure on the space of projective invariants for polygons, establishing a close relationship between the projective N-gon invariant evolutions and the Hamiltonian evolutions on the invariants of the flow. We prove that any Hamiltonian evolution is induced on invariants by an invariant evolution of N-gons—what we call a projective realization—and both evolutions are connected explicitly in a very simple way. Finally, we provide a completely integrable evolution (the Boussinesq lattice related to the lattice W 3 -algebra), its projective realization in RP 2 and its Hamiltonian pencil. We generalize both structures to n-dimensions and we prove that they are Poisson, defining explicitly the n-dimensional generalization of the planar evolution (a discretization of the W n -algebra). We prove that the generalization is completely integrable, and we also give its projective realization, which turns out to be very simple. (paper)
The hamiltonian structures of the KP hierarchy
International Nuclear Information System (INIS)
Das, A.; Panda, S.; Huang Wenjui
1991-01-01
We obtain the two hamiltonian structures of the KP hierarchy following the method of Drinfeld and Sokolov. We point out how the second structure of Drinfeld and Sokolov needs to be modified in the present case. We briefly comment on the connection between these structures and the W 1+∞ algebra. (orig.)
Hamiltonian structure for rescaled integrable Lorenz systems
International Nuclear Information System (INIS)
Haas, F.; Goedert, J.
1993-01-01
It is shown that three among the known invariants for the Lorenz system recast the original equations into a Hamiltonian form. This is made possible by an appropriate time-dependent rescaling and the use of a generalized formalism with non-trivial structure functions. (author)
Singularities of Poisson structures and Hamiltonian bifurcations
Meer, van der J.C.
2010-01-01
Consider a Poisson structure on C8(R3,R) with bracket {, } and suppose that C is a Casimir function. Then {f, g} =<¿C, (¿g x ¿f) > is a possible Poisson structure. This confirms earlier observations concerning the Poisson structure for Hamiltonian systems that are reduced to a one degree of freedom
Hamiltonian formulation of anomaly free chiral bosons
International Nuclear Information System (INIS)
Abdalla, E.; Abdalla, M.C.B.; Devecchi, F.P.; Zadra, A.
1988-01-01
Starting out of an anomaly free Lagrangian formulation for chiral scalars, which a Wess-Zumino Term (to cancel the anomaly), we formulate the corresponding hamiltonian problem. Ther we use the (quantum) Siegel invariance to choose a particular, which turns out coincide with the obtained by Floreanini and Jackiw. (author) [pt
Hamiltonian structure of gravitational field theory
International Nuclear Information System (INIS)
Rayski, J.
1992-01-01
Hamiltonian generalizations of Einstein's theory of gravitation introducing a laminar structure of spacetime are discussed. The concepts of general relativity and of quasi-inertial coordinate systems are extended beyond their traditional scope. Not only the metric, but also the coordinate system, if quantized, undergoes quantum fluctuations
Port-Hamiltonian Systems on Open Graphs
Schaft, A.J. van der; Maschke, B.M.
2010-01-01
In this talk we discuss how to define in an intrinsic manner port-Hamiltonian dynamics on open graphs. Open graphs are graphs where some of the vertices are boundary vertices (terminals), which allow interconnection with other systems. We show that a directed graph carries two natural Dirac
Gauge theories of infinite dimensional Hamiltonian superalgebras
International Nuclear Information System (INIS)
Sezgin, E.
1989-05-01
Symplectic diffeomorphisms of a class of supermanifolds and the associated infinite dimensional Hamiltonian superalgebras, H(2M,N) are discussed. Applications to strings, membranes and higher spin field theories are considered: The embedding of the Ramond superconformal algebra in H(2,1) is obtained. The Chern-Simons gauge theory of symplectic super-diffeomorphisms is constructed. (author). 29 refs
The Hamiltonian structures of the KP hierarchy
International Nuclear Information System (INIS)
Das, A.; Panda, S.; Huang Wenjui
1991-08-01
We obtain the two Hamiltonian structures of the KP hierarchy following the method of Drinfeld and Sokolov. We point out how the second structure of Drinfeld and Sokolov needs to be modified in the present case. We briefly comment on the connection between these structures and the W 1+∞ algebra. (author). 18 refs
Quasi exact solution of the Rabi Hamiltonian
Koç, R; Tuetuencueler, H
2002-01-01
A method is suggested to obtain the quasi exact solution of the Rabi Hamiltonian. It is conceptually simple and can be easily extended to other systems. The analytical expressions are obtained for eigenstates and eigenvalues in terms of orthogonal polynomials. It is also demonstrated that the Rabi system, in a particular case, coincides with the quasi exactly solvable Poeschl-Teller potential.
Edge-disjoint Hamiltonian cycles in hypertournaments
DEFF Research Database (Denmark)
Thomassen, Carsten
2006-01-01
We introduce a method for reducing k-tournament problems, for k >= 3, to ordinary tournaments, that is, 2-tournaments. It is applied to show that a k-tournament on n >= k + 1 + 24d vertices (when k >= 4) or on n >= 30d + 2 vertices (when k = 3) has d edge-disjoint Hamiltonian cycles if and only...
Hamiltonian constraint in polymer parametrized field theory
International Nuclear Information System (INIS)
Laddha, Alok; Varadarajan, Madhavan
2011-01-01
Recently, a generally covariant reformulation of two-dimensional flat spacetime free scalar field theory known as parametrized field theory was quantized using loop quantum gravity (LQG) type ''polymer'' representations. Physical states were constructed, without intermediate regularization structures, by averaging over the group of gauge transformations generated by the constraints, the constraint algebra being a Lie algebra. We consider classically equivalent combinations of these constraints corresponding to a diffeomorphism and a Hamiltonian constraint, which, as in gravity, define a Dirac algebra. Our treatment of the quantum constraints parallels that of LQG and obtains the following results, expected to be of use in the construction of the quantum dynamics of LQG: (i) the (triangulated) Hamiltonian constraint acts only on vertices, its construction involves some of the same ambiguities as in LQG and its action on diffeomorphism invariant states admits a continuum limit, (ii) if the regulating holonomies are in representations tailored to the edge labels of the state, all previously obtained physical states lie in the kernel of the Hamiltonian constraint, (iii) the commutator of two (density weight 1) Hamiltonian constraints as well as the operator correspondent of their classical Poisson bracket converge to zero in the continuum limit defined by diffeomorphism invariant states, and vanish on the Lewandowski-Marolf habitat, (iv) the rescaled density 2 Hamiltonian constraints and their commutator are ill-defined on the Lewandowski-Marolf habitat despite the well-definedness of the operator correspondent of their classical Poisson bracket there, (v) there is a new habitat which supports a nontrivial representation of the Poisson-Lie algebra of density 2 constraints.
Control-matrix approach to stellarator design and control
International Nuclear Information System (INIS)
Mynick, H. E.; Pomphrey, N.
2000-01-01
The full space Z(equivalent to){Z j=1,...,Nz } of independent variables defining a stellarator configuration is large. To find attractive design points in this space, or to understand operational flexibility about a given design point, one needs insight into the topography in Z-space of the physics figures of merit P i which characterize the machine performance, and means of determining those directions in Z-space which give one independent control over the P i , as well as those which affect none of them, and so are available for design flexibility. The control matrix (CM) approach described here provides a mathematical means of obtaining these. In this work, the CM approach is described and used in studying some candidate Quasi-Axisymmetric (QA) stellarator configurations the National Compact Stellarator Experiment design group has been considering. In the process of the analysis, a first exploration of the topography of the configuration space in the vicinity of these candidate systems has been performed, whose character is discussed
Control-matrix approach to stellarator design and control
International Nuclear Information System (INIS)
Mynick, H.E.; Pomphrey, N.
2000-01-01
The full space Z always equal to {Zj=1,..Nz} of independent variables defining a stellarator configuration is large. To find attractive design points in this space, or to understand operational flexibility about a given design point, one needs insight into the topography in Z-space of the physics figures of merit Pi which characterize the machine performance, and means of determining those directions in Z-space which give one independent control over the Pi, as well as those which affect none of them, and so are available for design flexibility. The control matrix (CM) approach described here provides a mathematical means of obtaining these. In this work, the authors describe the CM approach and use it in studying some candidate Quasi-Axisymmetric (QA) stellarator configurations the NCSX design group has been considering. In the process of the analysis, a first exploration of the topography of the configuration space in the vicinity of these candidate systems has been performed, whose character is discussed
The group of Hamiltonian automorphisms of a star product
La Fuente-Gravy, Laurent
2015-01-01
We deform the group of Hamiltonian diffeomorphisms into the group of Hamiltonian automorphisms of a formal star product on a symplectic manifold. We study the geometry of that group and deform the Flux morphism in the framework of deformation quantization.
QCD string with quarks. 2. Light cone Hamiltonian
International Nuclear Information System (INIS)
Dubin, A.Yu.; Kaidalov, A.B.; Simonov, Yu.A.
1994-01-01
The light-cone Hamiltonian is derived from the general gauge - and Lorentz - invariant expression for the qq-bar Green function. The resulting Hamiltonian contains in a non-additive way contributions from quark and string degrees of freedom
Discrete port-Hamiltonian systems
Talasila, V.; Clemente-Gallardo, J.; Schaft, A.J. van der
2006-01-01
Either from a control theoretic viewpoint or from an analysis viewpoint it is necessary to convert smooth systems to discrete systems, which can then be implemented on computers for numerical simulations. Discrete models can be obtained either by discretizing a smooth model, or by directly modeling
Hamiltonian analysis of transverse dynamics in axisymmetric rf photoinjectors
International Nuclear Information System (INIS)
Wang, C.-x.
2006-01-01
A general Hamiltonian that governs the beam dynamics in an rf photoinjector is derived from first principles. With proper choice of coordinates, the resulting Hamiltonian has a simple and familiar form, while taking into account the rapid acceleration, rf focusing, magnetic focusing, and space-charge forces. From the linear Hamiltonian, beam-envelope evolution is readily obtained, which better illuminates the theory of emittance compensation. Preliminary results on the third-order nonlinear Hamiltonian will be given as well.
On integrable Hamiltonians for higher spin XXZ chain
International Nuclear Information System (INIS)
Bytsko, Andrei G.
2003-01-01
Integrable Hamiltonians for higher spin periodic XXZ chains are constructed in terms of the spin generators; explicit examples for spins up to (3/2) are given. Relations between Hamiltonians for some U q (sl 2 )-symmetric and U(1)-symmetric universal r-matrices are studied; their properties are investigated. A certain modification of the higher spin periodic chain Hamiltonian is shown to be an integrable U q (sl 2 )-symmetric Hamiltonian for an open chain
DETECTING ALIEN LIMIT CYCLES NEAR A HAMILTONIAN 2-SADDLE CYCLE
LUCA, Stijn; DUMORTIER, Freddy; Caubergh, M.; Roussarie, R.
2009-01-01
This paper aims at providing and example of a cubic Hamiltonian 2-saddle cycle that after bifurcation can give rise to an alien limit cycle; this is a limit cycle that is not controlled by a zero of the related Abelian integral. To guarantee the existence of an alien limit cycle one can verify generic conditions on the Abelian integral and on the transition map associated to the connections of the 2-saddle cycle. In this paper, a general method is developed to compute the first and second der...
Numerical determination of the magnetic field line Hamiltonian
International Nuclear Information System (INIS)
Kuo-Petravic, G.; Boozer, A.H.
1986-03-01
The structure of a magnetic field is determined by a one-degree of freedom, time-dependent Hamiltonian. This Hamiltonian is evaluated for a given field in a perturbed action-angle form. The location and the size of magnetic islands in the given field are determined from Hamiltonian perturbation theory and from an ordinary Poincare plot of the field line trajectories
Effective Hamiltonians in quantum physics: resonances and geometric phase
International Nuclear Information System (INIS)
Rau, A R P; Uskov, D
2006-01-01
Effective Hamiltonians are often used in quantum physics, both in time-dependent and time-independent contexts. Analogies are drawn between the two usages, the discussion framed particularly for the geometric phase of a time-dependent Hamiltonian and for resonances as stationary states of a time-independent Hamiltonian
Theoretical approaches to control spin dynamics in solid-state ...
Indian Academy of Sciences (India)
We present fundamental theories in the history of NMR, namely, the average Hamiltonian and Floquet theories. We also ..... The results are better illustrated in a double ...... Matter 17 4501. 94. Ernst M 2006 Germany: Solid-State NMR Summer.
Coherent states of systems with quadratic Hamiltonians
Energy Technology Data Exchange (ETDEWEB)
Bagrov, V.G., E-mail: bagrov@phys.tsu.ru [Department of Physics, Tomsk State University, Tomsk (Russian Federation); Gitman, D.M., E-mail: gitman@if.usp.br [Tomsk State University, Tomsk (Russian Federation); Pereira, A.S., E-mail: albertoufcg@hotmail.com [Universidade de Sao Paulo (USP), Sao Paulo, SP (Brazil). Instituto de Fisica
2015-06-15
Different families of generalized coherent states (CS) for one-dimensional systems with general time-dependent quadratic Hamiltonian are constructed. In principle, all known CS of systems with quadratic Hamiltonian are members of these families. Some of the constructed generalized CS are close enough to the well-known due to Schroedinger and Glauber CS of a harmonic oscillator; we call them simply CS. However, even among these CS, there exist different families of complete sets of CS. These families differ by values of standard deviations at the initial time instant. According to the values of these initial standard deviations, one can identify some of the families with semiclassical CS. We discuss properties of the constructed CS, in particular, completeness relations, minimization of uncertainty relations and so on. As a unknown application of the general construction, we consider different CS of an oscillator with a time dependent frequency. (author)
Coherent states of systems with quadratic Hamiltonians
International Nuclear Information System (INIS)
Bagrov, V.G.; Gitman, D.M.; Pereira, A.S.
2015-01-01
Different families of generalized coherent states (CS) for one-dimensional systems with general time-dependent quadratic Hamiltonian are constructed. In principle, all known CS of systems with quadratic Hamiltonian are members of these families. Some of the constructed generalized CS are close enough to the well-known due to Schroedinger and Glauber CS of a harmonic oscillator; we call them simply CS. However, even among these CS, there exist different families of complete sets of CS. These families differ by values of standard deviations at the initial time instant. According to the values of these initial standard deviations, one can identify some of the families with semiclassical CS. We discuss properties of the constructed CS, in particular, completeness relations, minimization of uncertainty relations and so on. As a unknown application of the general construction, we consider different CS of an oscillator with a time dependent frequency. (author)
Effective Hamiltonian for high Tc Cu oxides
International Nuclear Information System (INIS)
Fukuyama, H.; Matsukawa, H.
1989-01-01
Effective Hamiltonian has been derived for CuO 2 layers in the presence of extra holes doped mainly into O-sites by taking both on-site and intersite Coulomb interaction into account. A special case with a single hole has been examined in detail. It is found that there exist various types of bound states, singlet and triplet with different spatial symmetry, below the hole bank continuum. The spatial extent of the Zhang-Rice singlet state, which is most stabilized, and the effective transfer integral between these singlet states are seen to be very sensitive to the relative magnitude of the direct and the indirect transfer integrals between O-sites. Effective Hamiltonian for the case of electron doping has also been derived
Partial quantization of Lagrangian-Hamiltonian systems
International Nuclear Information System (INIS)
Amaral, C.M. do; Soares Filho, P.C.
1979-05-01
A classical variational principle is constructed in the Weiss form, for dynamical systems with support spaces of the configuration-phase kind. This extended principle rules the dynamics of classical systems, partially Hamiltonian, in interaction with Lagrangean parameterized subsidiary dynamics. The variational family of equations obtained, consists of an equation of the Hamilton-Jacobi type, coupled to a family of differential equations of the Euler-Lagrange form. The basic dynamical function appearing in the equations is a function of the Routh kind. By means of an ansatz induced by the variationally obtained family, a generalized set of equation, is proposed constituted by a wave equation of Schroedinger type, coupled to a family of equations formaly analog to those Euler-Lagrange equations. A basic operator of Routh type appears in our generalized set of equations. This operator describes the interaction between a quantized Hamiltonian dynamics, with a parameterized classical Lagrangean dynamics in semi-classical closed models. (author) [pt
Quadratic hamiltonians and relativistic quantum mechanics
International Nuclear Information System (INIS)
Razumov, A.V.; Solov'ev, V.O.; Taranov, A.Yu.
1981-01-01
For the case of a charged scalar field described by a quadratic hamiltonian the equivalent relativistic quantum mechanics is constructed in one-particle sector. Complete investigation of a charged relativistic particle motion in the Coulomb field is carried out. Subcritical as well as supercritical cases are considered. In the course of investigation of the charged scalar particle in the Coulomb field the diagonalization of the quadratic hamiltonian describing the charged scalar quantized field interaction with the external Coulomb field has taken place. Mathematically this problem is bound to the construction of self-conjugated expansions of the symmetric operator. The construction of such expansion is necessary at any small external field magnitude [ru
Hamiltonian mechanics and divergence-free fields
International Nuclear Information System (INIS)
Boozer, A.H.
1986-08-01
The field lines, or integral curves, of a divergence-free field in three dimensions are shown to be topologically equivalent to the trajectories of a Hamiltonian with two degrees of freedom. The consideration of fields that depend on a parameter allow the construction of a canonical perturbation theory which is valid even if the perturbation is large. If the parametric dependence of the magnetic, or the vorticity field is interpreted as time dependence, evolution equations are obtained which give Kelvin's theorem or the flux conservation theorem for ideal fluids and plasmas. The Hamiltonian methods prove especially useful for study of fields in which the field lines must be known throughout a volume of space
Quantum mechanical Hamiltonian models of discrete processes
International Nuclear Information System (INIS)
Benioff, P.
1981-01-01
Here the results of other work on quantum mechanical Hamiltonian models of Turing machines are extended to include any discrete process T on a countably infinite set A. The models are constructed here by use of scattering phase shifts from successive scatterers to turn on successive step interactions. Also a locality requirement is imposed. The construction is done by first associating with each process T a model quantum system M with associated Hilbert space H/sub M/ and step operator U/sub T/. Since U/sub T/ is not unitary in general, M, H/sub M/, and U/sub T/ are extended into a (continuous time) Hamiltonian model on a larger space which satisfies the locality requirement. The construction is compared with the minimal unitary dilation of U/sub T/. It is seen that the model constructed here is larger than the minimal one. However, the minimal one does not satisfy the locality requirement
Phase transitions in the Hubbard Hamiltonian
International Nuclear Information System (INIS)
Chaves, C.M.; Lederer, P.; Gomes, A.A.
1977-05-01
Phase transition in the isotropic non-degenerate Hubbard Hamiltonian within the renormalization group techniques is studied, using the epsilon = 4 - d expansion to first order in epsilon. The functional obtained from the Hubbard Hamiltonian displays full rotation symmetry and describes two coupled fields: a vector spin field, with n components and a non-soft scalar charge field. This coupling is pure imaginary, which has interesting consequences on the critical properties of this coupled field system. The effect of simple constraints imposed on the charge field is considered. The relevance of the coupling between the fields in producing Fisher renormalization of the critical exponents is discussed. The possible singularities introduced in the charge-charge correlation function by the coupling are also discussed
Hamiltonian partial differential equations and applications
Nicholls, David; Sulem, Catherine
2015-01-01
This book is a unique selection of work by world-class experts exploring the latest developments in Hamiltonian partial differential equations and their applications. Topics covered within are representative of the field’s wide scope, including KAM and normal form theories, perturbation and variational methods, integrable systems, stability of nonlinear solutions as well as applications to cosmology, fluid mechanics and water waves. The volume contains both surveys and original research papers and gives a concise overview of the above topics, with results ranging from mathematical modeling to rigorous analysis and numerical simulation. It will be of particular interest to graduate students as well as researchers in mathematics and physics, who wish to learn more about the powerful and elegant analytical techniques for Hamiltonian partial differential equations.
A diagrammatic construction of formal E-independent model hamiltonian
International Nuclear Information System (INIS)
Kvasnicka, V.
1977-01-01
A diagrammatic construction of formal E-independent model interaction (i.e., without second-quantization formalism) is suggested. The construction starts from the quasi-degenerate Brillouin-Wigner perturbation theory, in the framework of which an E-dependent model Hamiltonian is simply constructed. Applying the ''E-removing'' procedure to this E-dependent model Hamiltonian, the E-independent formal model Hamiltonian either Hermitian or non-Hermitian can diagrammatically be easily derived. For the formal E-independent model Hamiltonian the separability theorem is proved, which can be profitably used for a rather ''formalistic ''construction of a many-body E-independent model Hamiltonian
Boson mapping and the microscopic collective nuclear Hamiltonian
International Nuclear Information System (INIS)
Dobes, J.; Ivanova, S.P.; Dzholos, R.V.; Pedrosa, R.
1990-01-01
Starting with the mapping of the quadrupole collective states in the fermion space onto the boson space, the fermion nuclear problem is transformed into the boson one. The boson images of the bifermion operators and of the fermion Hamiltonian are found. Recurrence relations are used to obtain approximately the norm matrix which appears in the boson-fermion mapping. The resulting boson Hamiltonian contains terms which go beyond the ordinary SU(6) symmetry Hamiltonian of the interacting boson model. Calculations, however, suggest that on the phenomenological level the differences between the mapped Hamiltonian and the SU(6) Hamiltonian are not too important. 18 refs.; 2 figs
Hamiltonian mechanics limits microscopic engines
Anglin, James; Gilz, Lukas; Thesing, Eike
2015-05-01
We propose a definition of fully microscopic engines (micro-engines) in terms of pure mechanics, without reference to thermodynamics, equilibrium, or cycles imposed by external control, and without invoking ergodic theory. This definition is pragmatically based on the observation that what makes engines useful is energy transport across a large ratio of dynamical time scales. We then prove that classical and quantum mechanics set non-trivial limits-of different kinds-on how much of the energy that a micro-engine extracts from its fuel can be converted into work. Our results are not merely formal; they imply manageable design constraints on micro-engines. They also suggest the novel possibility that thermodynamics does not emerge from mechanics in macroscopic regimes, but rather represents the macroscopic limit of a generalized theory, valid on all scales, which governs the important phenomenon of energy transport across large time scale ratios. We propose experimental realizations of the dynamical mechanisms we identify, with trapped ions and in Bose-Einstein condensates (``motorized bright solitons'').
Recursive tridiagonalization of infinite dimensional Hamiltonians
International Nuclear Information System (INIS)
Haydock, R.; Oregon Univ., Eugene, OR
1989-01-01
Infinite dimensional, computable, sparse Hamiltonians can be numerically tridiagonalized to finite precision using a three term recursion. Only the finite number of components whose relative magnitude is greater than the desired precision are stored at any stage in the computation. Thus the particular components stored change as the calculation progresses. This technique avoids errors due to truncation of the orbital set, and makes terminators unnecessary in the recursion method. (orig.)
Hamiltonian theory of guiding-center motion
International Nuclear Information System (INIS)
Littlejohn, R.G.
1980-05-01
A Hamiltonian treatment of the guiding center problem is given which employs noncanonical coordinates in phase space. Separation of the unperturbed system from the perturbation is achieved by using a coordinate transformation suggested by a theorem of Darboux. As a model to illustrate the method, motion in the magnetic field B=B(x,y)z is studied. Lie transforms are used to carry out the perturbation expansion
Hamiltonian kinetic theory of plasma ponderomotive processes
International Nuclear Information System (INIS)
McDonald, S.W.; Kaufman, A.N.
1982-01-01
The nonlinear nonresonant interaction of plasma waves and particles is formulated in Hamiltonian kinetic theory which treats the wave-action and particle distributions on an equal footing, thereby displaying reciprocity relations. In the quasistatic limit, a nonlinear wave-kinetic equation is obtained. The generality of the formalism allows for applications to arbitrary geometry, with the nonlinear effects expressed in terms of the linear susceptibility
Symplectic Geometric Algorithms for Hamiltonian Systems
Feng, Kang
2010-01-01
"Symplectic Geometry Algorithms for Hamiltonian Systems" will be useful not only for numerical analysts, but also for those in theoretical physics, computational chemistry, celestial mechanics, etc. The book generalizes and develops the generating function and Hamilton-Jacobi equation theory from the perspective of the symplectic geometry and symplectic algebra. It will be a useful resource for engineers and scientists in the fields of quantum theory, astrophysics, atomic and molecular dynamics, climate prediction, oil exploration, etc. Therefore a systematic research and development
Dynamical invariants for variable quadratic Hamiltonians
International Nuclear Information System (INIS)
Suslov, Sergei K
2010-01-01
We consider linear and quadratic integrals of motion for general variable quadratic Hamiltonians. Fundamental relations between the eigenvalue problem for linear dynamical invariants and solutions of the corresponding Cauchy initial value problem for the time-dependent Schroedinger equation are emphasized. An eigenfunction expansion of the solution of the initial value problem is also found. A nonlinear superposition principle for generalized Ermakov systems is established as a result of decomposition of the general quadratic invariant in terms of the linear ones.
The Effective Hamiltonian in the Scalar Electrodynamics
Dineykhan, M D; Zhaugasheva, S A; Sakhyev, S K
2002-01-01
On the basis of an investigation of the asymptotic behaviour of the polarization loop for the scalar particles in the external electromagnetic field the relativistic corrections to the Hamiltonian are determined. The constituent mass of the particles in the bound state is analytically derived. It is shown that the constituent mass of the particles differs from the mass of the particles in the free state. The corrections connected with the Thomas precession have been calculated.
Quantization of non-Hamiltonian physical systems
International Nuclear Information System (INIS)
Bolivar, A.O.
1998-09-01
We propose a general method of quantization of non-Hamiltonian physical systems. Applying it, for example, to a dissipative system coupled to a thermal reservoir described by the Fokker-Planck equation, we are able to obtain the Caldeira-Leggett master equation, the non-linear Schroedinger-Langevin equation and Caldirola-Kanai equation (with an additional term), as particular cases. (author)
Hamiltonian kinetic theory of plasma ponderomotive processes
International Nuclear Information System (INIS)
McDonald, S.W.; Kaufman, A.N.
1981-12-01
The nonlinear nonresonant interaction of plasma waves and particles is formulated in a Hamiltonian kinetic theory which treats the wave-action and particle distributions on an equal footing, thereby displaying reciprocity relations. In the quasistatic limit, a nonlinear wave-kinetic equation is obtained. The generality of the formalism allows for applications to arbitrary geometry, with the nonlinear effects expressed in terms of the linear susceptibility
Symplectic topology of integrable Hamiltonian systems
International Nuclear Information System (INIS)
Nguyen Tien Zung.
1993-08-01
We study the topology of integrable Hamiltonian systems, giving the main attention to the affine structure of their orbit spaces. In particular, we develop some aspects of Fomenko's theory about topological classification of integrable non-degenerate systems, and consider some relations between such systems and ''pure'' contact and symplectic geometry. We give a notion of integrable surgery and use it to obtain some interesting symplectic structures. (author). Refs, 10 figs
Hamiltonian description and quantization of dissipative systems
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.
Hamiltonian theory of guiding-center motion
Energy Technology Data Exchange (ETDEWEB)
Littlejohn, R.G.
1980-05-01
A Hamiltonian treatment of the guiding center problem is given which employs noncanonical coordinates in phase space. Separation of the unperturbed system from the perturbation is achieved by using a coordinate transformation suggested by a theorem of Darboux. As a model to illustrate the method, motion in the magnetic field B=B(x,y)z is studied. Lie transforms are used to carry out the perturbation expansion.
Hamiltonian description of the ideal fluid
International Nuclear Information System (INIS)
Morrison, P.J.
1998-01-01
The Hamiltonian viewpoint of fluid mechanical systems with few and infinite number of degrees of freedom is described. Rudimentary concepts of finite-degree-of-freedom Hamiltonian dynamics are reviewed, in the context of the passive advection of a scalar or tracer field by a fluid. The notions of integrability, invariant-tori, chaos, overlap criteria, and invariant-tori breakup are described in this context. Preparatory to the introduction of field theories, systems with an infinite number of degrees of freedom, elements of functional calculus and action principles of mechanics are reviewed. The action principle for the ideal compressible fluid is described in terms of Lagrangian or material variables. Hamiltonian systems in terms of noncanonical variables are presented, including several examples of Eulerian or inviscid fluid dynamics. Lie group theory sufficient for the treatment of reduction is reviewed. The reduction from Lagrangian to Eulerian variables is treated along with Clebsch variable decompositions. Stability in the canonical and noncanonical Hamiltonian contexts is described. Sufficient conditions for stability, such as Rayleigh-like criteria, are seen to be only sufficient in the general case because of the existence of negative-energy modes, which are possessed by interesting fluid equilibria. Linearly stable equilibria with negative energy modes are argued to be unstable when nonlinearity or dissipation is added. The energy-Casimir method is discussed and a variant of it that depends upon the notion of dynamical accessibility is described. The energy content of a perturbation about a general fluid equilibrium is calculated using three methods. copyright 1998 The American Physical Society
An integrated approach to process control
Schippers, W.A.J.
2001-01-01
The control of production processes is the subject of several disciplines, such as statistical process control (SPC), total productive maintenance (TPM), and automated process control (APC). Although these disciplines are traditionally separated (both in science and in business practice), their
Large-scale stochasticity in Hamiltonian systems
International Nuclear Information System (INIS)
Escande, D.F.
1982-01-01
Large scale stochasticity (L.S.S.) in Hamiltonian systems is defined on the paradigm Hamiltonian H(v,x,t) =v 2 /2-M cos x-P cos k(x-t) which describes the motion of one particle in two electrostatic waves. A renormalization transformation Tsub(r) is described which acts as a microscope that focusses on a given KAM (Kolmogorov-Arnold-Moser) torus in phase space. Though approximate, Tsub(r) yields the threshold of L.S.S. in H with an error of 5-10%. The universal behaviour of KAM tori is predicted: for instance the scale invariance of KAM tori and the critical exponent of the Lyapunov exponent of Cantori. The Fourier expansion of KAM tori is computed and several conjectures by L. Kadanoff and S. Shenker are proved. Chirikov's standard mapping for stochastic layers is derived in a simpler way and the width of the layers is computed. A simpler renormalization scheme for these layers is defined. A Mathieu equation for describing the stability of a discrete family of cycles is derived. When combined with Tsub(r), it allows to prove the link between KAM tori and nearby cycles, conjectured by J. Greene and, in particular, to compute the mean residue of a torus. The fractal diagrams defined by G. Schmidt are computed. A sketch of a methodology for computing the L.S.S. threshold in any two-degree-of-freedom Hamiltonian system is given. (Auth.)
Redesign of the DFT/MRCI Hamiltonian
Energy Technology Data Exchange (ETDEWEB)
Lyskov, Igor; Kleinschmidt, Martin; Marian, Christel M., E-mail: Christel.Marian@hhu.de [Institute of Theoretical and Computational Chemistry, Heinrich-Heine-University Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf (Germany)
2016-01-21
The combined density functional theory and multireference configuration interaction (DFT/MRCI) method of Grimme and Waletzke [J. Chem. Phys. 111, 5645 (1999)] is a well-established semi-empirical quantum chemical method for efficiently computing excited-state properties of organic molecules. As it turns out, the method fails to treat bi-chromophores owing to the strong dependence of the parameters on the excitation class. In this work, we present an alternative form of correcting the matrix elements of a MRCI Hamiltonian which is built from a Kohn-Sham set of orbitals. It is based on the idea of constructing individual energy shifts for each of the state functions of a configuration. The new parameterization is spin-invariant and incorporates less empirism compared to the original formulation. By utilizing damping techniques together with an algorithm of selecting important configurations for treating static electron correlation, the high computational efficiency has been preserved. The robustness of the original and redesigned Hamiltonians has been tested on experimentally known vertical excitation energies of organic molecules yielding similar statistics for the two parameterizations. Besides that, our new formulation is free from artificially low-lying doubly excited states, producing qualitatively correct and consistent results for excimers. The way of modifying matrix elements of the MRCI Hamiltonian presented here shall be considered as default choice when investigating photophysical processes of bi-chromophoric systems such as singlet fission or triplet-triplet upconversion.
Controller synthesis for negative imaginary systems: a data driven approach
Mabrok, Mohamed; Petersen, Ian R.
2016-01-01
-driven controller synthesis methodology for NI systems is presented. In this approach, measured frequency response data of the plant is used to construct the controller frequency response at every frequency by minimising a cost function. Then, this controller
Construction of Hamiltonians by supervised learning of energy and entanglement spectra
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.
Exact solution of the generalized time-dependent Jaynes-Cummings Hamiltonian
International Nuclear Information System (INIS)
Gruver, J.L.; Aliaga, J.; Cerdeira, H.A.; Proto, A.N.
1993-04-01
A time-dependent generalization of the Jaynes-Cummings Hamiltonian is studied using the maximum entropy formalism. The approach, related to a semi-Lie algebra, allows to find three different sets of physical relevant operators which describe the dynamics of the system for any temporal dependence. It is shown how the initial conditions of the operators are determined via the maximum entropy principle density operator, where the inclusion of the temperature turns the description of the problem into a thermodynamical one. The generalized time-independent Jaynes-Cummings Hamiltonian is exactly solved as a particular example. (author). 14 refs
Reaction Hamiltonian and state-to-state description of chemical reactions
International Nuclear Information System (INIS)
Ruf, B.A.; Kresin, V.Z.; Lester, W.A. Jr.
1985-08-01
A chemical reaction is treated as a quantum transition from reactants to products. A specific reaction Hamiltonian (in second quantization formalism) is introduced. The approach leads to Franck-Condon-like factor, and adiabatic method in the framework of the nuclear motion problems. The influence of reagent vibrational state on the product energy distribution has been studied following the reaction Hamiltonian method. Two different cases (fixed available energy and fixed translational energy) are distinguished. Results for several biomolecular reactions are presented. 40 refs., 5 figs
Radiopharmaceutical quality control-Pragmatic approach
International Nuclear Information System (INIS)
Barbier, Y.
1994-01-01
The quality control must be considered in a practical manner. The radiopharmaceuticals are drugs. They must satisfy the quality assurance control. These products are then conform to Pharmacopeia. But sometimes the user must control some data especially radiochemical purity and pH value. On all the administered solutions four controls are compulsory: radionuclide identity, administered radioactivity, organoleptic character and pH
A unified theoretical framework for mapping models for the multi-state Hamiltonian.
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.
International Nuclear Information System (INIS)
Chiappe, G; Louis, E; San-Fabián, E; Vergés, J A
2015-01-01
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
Covariant description of Hamiltonian form for field dynamics
International Nuclear Information System (INIS)
Ozaki, Hiroshi
2005-01-01
Hamiltonian form of field dynamics is developed on a space-like hypersurface in space-time. A covariant Poisson bracket on the space-like hypersurface is defined and it plays a key role to describe every algebraic relation into a covariant form. It is shown that the Poisson bracket has the same symplectic structure that was brought in the covariant symplectic approach. An identity invariant under the canonical transformations is obtained. The identity follows a canonical equation in which the interaction Hamiltonian density generates a deformation of the space-like hypersurface. The equation just corresponds to the Yang-Feldman equation in the Heisenberg pictures in quantum field theory. By converting the covariant Poisson bracket on the space-like hypersurface to four-dimensional commutator, we can pass over to quantum field theory in the Heisenberg picture without spoiling the explicit relativistic covariance. As an example the canonical QCD is displayed in a covariant way on a space-like hypersurface
Hamiltonian description of toroidal magnetic fields in vacuum
International Nuclear Information System (INIS)
Lewis, H.R.; Bates, J.W.
1996-01-01
An investigation of vacuum magnetic fields in toroidal geometry has been initiated. Previously, the general form of the magnetic scalar potential for fields regular at the poloidal axis was given. Here, these results have been expanded to obtain the magnetic scalar potential in a vacuum region that may surround a toroidal current distribution. Using this generalized magnetic scalar potential in conjunction with Boozer's canonical representation of a magnetic field, a field-line Hamiltonian for nonaxisymmetric vacuum fields has been derived. These fields axe being examined using a novel, open-quotes time-dependentclose quotes perturbation theory, which permits the iterative construction of invariants associated with magnetic field-line Hamiltonians that consist of an axisymmetric zeroth-order term, plus a nonaxisymmetric perturbation. By choosing appropriate independent variables, an explicit constructive procedure is developed which involves only a single canonical transformation. Such invariants are of interest because they provide a means of investigating the topology of magnetic field lines. Our objective is to elucidate the existence of magnetic surfaces for nonaxisymmetric vacuum configurations, as well as to provide an approach for studying the onset of stochastic behavior
Escobar, Gerardo; van der Schaft, Arjan; Ortega, Romeo
1999-01-01
In this paper we show how, using the Hamiltonian formalism, we can systematically derive mathematical models that describe the behaviour of a large class of switching power converters, including the “Boost”, “Buck”, “Buck-Boost”, “ uk” and “Flyback” converters. We follow the approach proposed by van
Generation of quantum logic operations from physical Hamiltonians
International Nuclear Information System (INIS)
Zhang Jun; Whaley, K. Birgitta
2005-01-01
We provide a systematic analysis of the physical generation of single- and two-qubit quantum operations from Hamiltonians available in various quantum systems for scalable quantum information processing. We show that generation of single-qubit operations can be transformed into a steering problem on the Bloch sphere, which represents all R z -equivalence classes of single-qubit operations, whereas the two-qubit problem can be generally transformed into a steering problem in a tetrahedron representing all the local-equivalence classes of two-qubit operations (the Weyl chamber). We use this approach to investigate several physical examples for the generation of two-qubit operations. The steering approach provides useful guidance for the realization of various quantum computation schemes
Systems approach for design control at Monitored Retrievable Storage Project
International Nuclear Information System (INIS)
Kumar, P.N.; Williams, J.R.
1994-01-01
This paper describes the systems approach in establishing design control for the Monitored Retrievable Storage Project design development. Key elements in design control are enumerated and systems engineering aspects are detailed. Application of lessons learned from the Yucca Mountain Project experience is addressed. An integrated approach combining quality assurance and systems engineering requirements is suggested to practice effective design control
Quantum Hamiltonian reduction and conformal field theories
International Nuclear Information System (INIS)
Bershadsky, M.
1991-01-01
It is proved that irreducible representation of the Virasoro algebra can be extracted from an irreducible representation space of the SL (2, R) current algebra by putting a constraint on the latter using the BRST formalism. Thus there is a SL(2, R) symmetry in the Virasoro algebra which is gauged and hidden. This construction of the Virasoro algebra is the quantum analog of the Hamiltonian reduction. The author then naturally leads to consider an SL(2, R) Wess-Zumino-Witten model. This system is related to the quantum field theory of the coadjoint orbit of the Virasoro group. Based on this result he presents the canonical derivation of the SL(2, R) current algebra in Polyakov's theory of two dimensional gravity; it is manifestation of the SL(2, R) symmetry in the conformal field theory hidden by the quantum Hamiltonian reduction. He discusses the quantum Hamiltonian reduction of the SL(n, R) current algebra for the general type of constraints labeled by index 1 ≤ l ≤ (n - 1) and claim that it leads to the new extended conformal algebras W n l . For l = 1 he recovers the well known W n algebra introduced by A. Zamolodchikov. For SL(3, R) Wess-Zumino-Witten model there are two different possibilities of constraining it. The first possibility gives the W 3 algebra, while the second leads to the new chiral algebra W 3 2 generated by the stress-energy tensor, two bosonic supercurrents with spins 3/2 and the U(1) current. He conjectures a Kac formula that describes the highly reducible representation for this algebra. He also makes some speculations concerning the structure of W gravity
Quantum Monte Carlo studies in Hamiltonian lattice gauge theory
International Nuclear Information System (INIS)
Hamer, C.J.; Samaras, M.; Bursill, R.J.
2000-01-01
Full text: The application of Monte Carlo methods to the 'Hamiltonian' formulation of lattice gauge theory has been somewhat neglected, and lags at least ten years behind the classical Monte Carlo simulations of Euclidean lattice gauge theory. We have applied a Green's Function Monte Carlo algorithm to lattice Yang-Mills theories in the Hamiltonian formulation, combined with a 'forward-walking' technique to estimate expectation values and correlation functions. In this approach, one represents the wave function in configuration space by a discrete ensemble of random walkers, and application of the time development operator is simulated by a diffusion and branching process. The approach has been used to estimate the ground-state energy and Wilson loop values in the U(1) theory in (2+1)D, and the SU(3) Yang-Mills theory in (3+1)D. The finite-size scaling behaviour has been explored, and agrees with the predictions of effective Lagrangian theory, and weak-coupling expansions. Crude estimates of the string tension are derived, which agree with previous results at intermediate couplings; but more accurate results for larger loops will be required to establish scaling behaviour at weak couplings. A drawback to this method is that it is necessary to introduce a 'trial' or 'guiding wave function' to guide the walkers towards the most probable regions of configuration space, in order to achieve convergence and accuracy. The 'forward-walking' estimates should be independent of this guidance, but in fact for the SU(3) case they turn out to be sensitive to the choice of trial wave function. It would be preferable to use some sort of Metropolis algorithm instead to produce a correct distribution of walkers: this may point in the direction of a Path Integral Monte Carlo approach
Access control, security, and trust a logical approach
Chin, Shiu-Kai
2010-01-01
Access Control, Security, Trust, and Logic Deconstructing Access Control Decisions A Logical Approach to Access Control PRELIMINARIES A Language for Access ControlSets and Relations Syntax SemanticsReasoning about Access Control Logical RulesFormal Proofs and Theorems Soundness of Logical RulesBasic Concepts Reference Monitors Access Control Mechanisms: Tickets and Lists Authentication Security PoliciesConfidentiality, Integrity, and Availability Discretionary Security Policies Mandatory Security Policies Military Security Policies Commercial PoliciesDISTRIBUTED ACCESS CONTROL Digital Authenti
Integrable Time-Dependent Quantum Hamiltonians
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.
Resonant driving of a nonlinear Hamiltonian system
International Nuclear Information System (INIS)
Palmisano, Carlo; Gervino, Gianpiero; Balma, Massimo; Devona, Dorina; Wimberger, Sandro
2013-01-01
As a proof of principle, we show how a classical nonlinear Hamiltonian system can be driven resonantly over reasonably long times by appropriately shaped pulses. To keep the parameter space reasonably small, we limit ourselves to a driving force which consists of periodic pulses additionally modulated by a sinusoidal function. The main observables are the average increase of kinetic energy and of the action variable (of the non-driven system) with time. Applications of our scheme aim for driving high frequencies of a nonlinear system with a fixed modulation signal.
Nonabelian N=2 superstrings: Hamiltonian structure
International Nuclear Information System (INIS)
Isaev, A.P.; Ivanov, E.A.
1991-04-01
We examine the Hamiltonian structure of nonabelian N=2 superstring models which are the supergroup manifold extensions of N=2 Green-Schwarz superstring. We find the Kac-Moody and Virasoro type superalgebras of the relevant constraints and present elements of the corresponding quantum theory. A comparison with the type IIA Green-Schwarz superstring moving in a general curved 10-d supergravity background is also given. We find that nonabelian superstrings (for d=10) present a particular case of this general system corresponding to a special choice of the background. (author). 22 refs
Effective Hamiltonians for phosphorene and silicene
DEFF Research Database (Denmark)
Voon, L. C. Lew Yan; Lopez-Bezanilla, A.; Wang, J.
2015-01-01
We derived the effective Hamiltonians for silicene and phosphorene with strain, electric field andmagnetic field using the method of invariants. Our paper extends the work of Geissler et al 2013 (NewJ. Phys. 15 085030) on silicene, and Li and Appelbaum 2014 (Phys. Rev. B 90, 115439) on phosphorene.......For phosphorene, it is shown that the bands near the Brillouin zone center only have terms ineven powers of the wave vector. We predict that the energies change quadratically in the presence of aperpendicular external electric field but linearly in a perpendicular magnetic field, as opposed to thosefor silicene...
Hamiltonian Description of Convective-cell Generation
International Nuclear Information System (INIS)
Krommes, J.A.; Kolesnikov, R.A.
2004-01-01
The nonlinear statistical growth rate eq for convective cells driven by drift-wave (DW) interactions is studied with the aid of a covariant Hamiltonian formalism for the gyrofluid nonlinearities. A statistical energy theorem is proven that relates eq to a second functional tensor derivative of the DW energy. This generalizes to a wide class of systems of coupled partial differential equations a previous result for scalar dynamics. Applications to (i) electrostatic ion-temperature-gradient-driven modes at small ion temperature, and (ii) weakly electromagnetic collisional DW's are noted
Eigenfunctions of quadratic hamiltonians in Wigner representation
International Nuclear Information System (INIS)
Akhundova, Eh.A.; Dodonov, V.V.; Man'ko, V.I.
1984-01-01
Exact solutions of the Schroedinger equation in Wigner representation are obtained for an arbitrary non-stationary N-dimensional quadratic Hamiltonian. It is shown that the complete system of the solutions can always be chosen in the form of the products of Laguerre polynomials, the arguments of which are the quadratic integrals of motion of the corresponding classical problem. The generating function is found for the transition probabilities between Fock states which represent a many-dimensional generatization of a well-known Husimi formula for the oscillator of variable frequency. As an example, the motion of a charged particle in an uniform alternate electromagnetic field is considered in detail
A new perturbative treatment of pentadiagonal Hamiltonians
International Nuclear Information System (INIS)
Znojil, M.
1987-01-01
A new formulation of the Rayleich - Schroedinger perturbation theory is proposed. It is inspired by a recurent construction of propagators, and its main idea lies in a replacement of the auxiliary matrix elements (generalized continued fractions) by their non-numerical approximants. In a test of convergence (the anharmonic oscillator), the asymptotic fixed-point approximation scheme is used. The results indicate a good applicability of this fixed-point version of our formalism to systems with a band-matrix structure of the Hamiltonian
Configurations of Control: A Transaction Cost Approach
R.F. Speklé (Roland)
2003-01-01
textabstractIn this paper, I present a theory of management control based on Transaction Cost Economics. This theory seeks to integrate into a single framework a set of insights as to the nature of the organization's activities, the control problems that are inherent in these activities, and the
Hamiltonians and variational principles for Alfvén simple waves
International Nuclear Information System (INIS)
Webb, G M; Hu, Q; Roux, J A le; Dasgupta, B; Zank, G P
2012-01-01
The evolution equations for the magnetic field induction B with the wave phase for Alfvén simple waves are expressed as variational principles and in the Hamiltonian form. The evolution of B with the phase (which is a function of the space and time variables) depends on the generalized Frenet–Serret equations, in which the wave normal n (which is a function of the phase) is taken to be tangent to a curve X, in a 3D Cartesian geometry vector space. The physical variables (the gas density, fluid velocity, gas pressure and magnetic field induction) in the wave depend only on the phase. Three approaches are developed. One approach exploits the fact that the Frenet equations may be written as a 3D Hamiltonian system, which can be described using the Nambu bracket. It is shown that B as a function of the phase satisfies a modified version of the Frenet equations, and hence the magnetic field evolution equations can be expressed in the Hamiltonian form. A second approach develops an Euler–Poincaré variational formulation. A third approach uses the Frenet frame formulation, in which the hodograph of B moves on a sphere of constant radius and uses a stereographic projection transformation due to Darboux. The equations for the projected field components reduce to a complex Riccati equation. By using a Cole–Hopf transformation, the Riccati equation reduces to a linear second order differential equation for the new variable. A Hamiltonian formulation of the second order differential equation then allows the system to be written in the Hamiltonian form. Alignment dynamics equations for Alfvén simple waves give rise to a complex Riccati equation or, equivalently, to a quaternionic Riccati equation, which can be mapped onto the Riccati equation obtained by stereographic projection. (paper)
Effective hamiltonian within the microscopic unitary nuclear model
International Nuclear Information System (INIS)
Avramenko, V.I.; Blokhin, A.L.
1989-01-01
Within the microscopic version of the unitary collective model with the horizontal mixing the effective Hamiltonian for 18 O and 18 Ne nuclei is constructed. The algebraic structure of the Hamiltonian is compared to the familiar phenomenological ones with the SU(3)-mixing terms which describe the coupled rotational and vibrational spectra. The Hamiltonian, including central nuclear and Coulomb interaction, is diagonalized on the basis of three SU(3) irreducible representations with two orbital symmetries. 32 refs.; 2 figs.; 4 tabs
A Hamiltonian functional for the linearized Einstein vacuum field equations
International Nuclear Information System (INIS)
Rosas-RodrIguez, R
2005-01-01
By considering the Einstein vacuum field equations linearized about the Minkowski metric, the evolution equations for the gauge-invariant quantities characterizing the gravitational field are written in a Hamiltonian form by using a conserved functional as Hamiltonian; this Hamiltonian is not the analog of the energy of the field. A Poisson bracket between functionals of the field, compatible with the constraints satisfied by the field variables, is obtained. The generator of spatial translations associated with such bracket is also obtained
Introduction to thermodynamics of spin models in the Hamiltonian limit
Energy Technology Data Exchange (ETDEWEB)
Berche, Bertrand [Groupe M, Laboratoire de Physique des Materiaux, UMR CNRS No 7556, Universite Henri Poincare, Nancy 1, BP 239, F-54506 Vandoeuvre les Nancy, (France); Lopez, Alexander [Instituto Venezolano de Investigaciones CientIficas, Centro de Fisica, Carr. Panamericana, km 11, Altos de Pipe, Aptdo 21827, 1020-A Caracas, (Venezuela)
2006-01-01
A didactic description of the thermodynamic properties of classical spin systems is given in terms of their quantum counterpart in the Hamiltonian limit. Emphasis is on the construction of the relevant Hamiltonian and the calculation of thermal averages is explicitly done in the case of small systems described, in Hamiltonian field theory, by small matrices. The targeted students are those of a graduate statistical physics course.
Hamiltonian structure of the Lotka-Volterra equations
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.
Hamiltonian structures of some non-linear evolution equations
International Nuclear Information System (INIS)
Tu, G.Z.
1983-06-01
The Hamiltonian structure of the O(2,1) non-linear sigma model, generalized AKNS equations, are discussed. By reducing the O(2,1) non-linear sigma model to its Hamiltonian form some new conservation laws are derived. A new hierarchy of non-linear evolution equations is proposed and shown to be generalized Hamiltonian equations with an infinite number of conservation laws. (author)
Implementation Guide for Approaching Ship Floor Control
National Research Council Canada - National Science Library
Folz, Darrold; Diedrick, Karen
1992-01-01
.... Since the shipbuilding job shop environment revolves around the assembly of a single product, it is difficult to bring in "off the shelf" production control software which will speak to shipbuilding's unique needs...
Sustainable malaria control: transdisciplinary approaches for translational applications
2012-01-01
With the adoption of the Global Malaria Action Plan, several countries are moving from malaria control towards elimination and eradication. However, the sustainability of some of the approaches taken may be questionable. Here, an overview of malaria control and elimination strategies is provided and the sustainability of each in context of vector- and parasite control is assessed. From this, it can be concluded that transdisciplinary approaches are essential for sustained malaria control and elimination in malaria-endemic communities. PMID:23268712
Sustainable malaria control: transdisciplinary approaches for translational applications
Directory of Open Access Journals (Sweden)
Birkholtz Lyn-Marie
2012-12-01
Full Text Available Abstract With the adoption of the Global Malaria Action Plan, several countries are moving from malaria control towards elimination and eradication. However, the sustainability of some of the approaches taken may be questionable. Here, an overview of malaria control and elimination strategies is provided and the sustainability of each in context of vector- and parasite control is assessed. From this, it can be concluded that transdisciplinary approaches are essential for sustained malaria control and elimination in malaria-endemic communities.
Mesh-free Hamiltonian implementation of two dimensional Darwin model
Siddi, Lorenzo; Lapenta, Giovanni; Gibbon, Paul
2017-08-01
A new approach to Darwin or magnetoinductive plasma simulation is presented, which combines a mesh-free field solver with a robust time-integration scheme avoiding numerical divergence errors in the solenoidal field components. The mesh-free formulation employs an efficient parallel Barnes-Hut tree algorithm to speed up the computation of fields summed directly from the particles, avoiding the necessity of divergence cleaning procedures typically required by particle-in-cell methods. The time-integration scheme employs a Hamiltonian formulation of the Lorentz force, circumventing the development of violent numerical instabilities associated with time differentiation of the vector potential. It is shown that a semi-implicit scheme converges rapidly and is robust to further numerical instabilities which can develop from a dominant contribution of the vector potential to the canonical momenta. The model is validated by various static and dynamic benchmark tests, including a simulation of the Weibel-like filamentation instability in beam-plasma interactions.
Superconducting tunneling with the tunneling Hamiltonian. II. Subgap harmonic structure
International Nuclear Information System (INIS)
Arnold, G.B.
1987-01-01
The theory of superconducting tunneling without the tunneling Hamiltonian is extended to treat superconductor/insulator/superconductor junctions in which the transmission coefficient of the insulating barrier approaches unity. The solution for the current in such junctions is obtained by solving the problem of a particle hopping in a one-dimensional lattice of sites, with forward and reverse transfer integrals that depend on the site. The results are applied to the problem of subgap harmonic structure in superconducting tunneling. The time-dependent current at finite voltage through a junction exhibiting subgap structure is found to have terms that oscillate at all integer multiples of the Josephson frequency, n(2eV/h). The amplitudes of these new, and as yet unmeasured, ac current contributions as a function of voltage are predicted
Hamiltonian lattice studies of chiral meson field theories
International Nuclear Information System (INIS)
Chin, S.A.
1998-01-01
The latticization of the non-linear sigma model reduces a chiral meson field theory to an O(4) spin lattice system with quantum fluctuations. The result is an interesting marriage between quantum many-body theory and classical spin systems. By solving the resulting lattice Hamiltonian by Monte Carlo methods, the dynamics and thermodynamics of pions can be determined non-perturbatively. In a variational 16 3 lattice study, the ground state chiral phase transition is shown to be first order. Moreover, as the chiral phase transition is approached, the mass gap of pionic collective modes with quantum number of the ω vector meson drops toward zero. (Copyright (1998) World Scientific Publishing Co. Pte. Ltd)
IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence
Borisov, Alexey V; Mamaev, Ivan S; Sokolovskiy, Mikhail A; IUTAM BOOKSERIES : Volume 6
2008-01-01
This work brings together previously unpublished notes contributed by participants of the IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence (Moscow, 25-30 August 2006). The study of vortex motion is of great interest to fluid and gas dynamics: since all real flows are vortical in nature, applications of the vortex theory are extremely diverse, many of them (e.g. aircraft dynamics, atmospheric and ocean phenomena) being especially important. The last few decades have shown that serious possibilities for progress in the research of real turbulent vortex motions are essentially related to the combined use of mathematical methods, computer simulation and laboratory experiments. These approaches have led to a series of interesting results which allow us to study these processes from new perspectives. Based on this principle, the papers collected in this proceedings volume present new results on theoretical and applied aspects of the processes of formation and evolution of various flows, wave a...
Thermalization Time Bounds for Pauli Stabilizer Hamiltonians
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.
Normal form for mirror machine Hamiltonians
International Nuclear Information System (INIS)
Dragt, A.J.; Finn, J.M.
1979-01-01
A systematic algorithm is developed for performing canonical transformations on Hamiltonians which govern particle motion in magnetic mirror machines. These transformations are performed in such a way that the new Hamiltonian has a particularly simple normal form. From this form it is possible to compute analytic expressions for gyro and bounce frequencies. In addition, it is possible to obtain arbitrarily high order terms in the adiabatic magnetic moment expansion. The algorithm makes use of Lie series, is an extension of Birkhoff's normal form method, and has been explicitly implemented by a digital computer programmed to perform the required algebraic manipulations. Application is made to particle motion in a magnetic dipole field and to a simple mirror system. Bounce frequencies and locations of periodic orbits are obtained and compared with numerical computations. Both mirror systems are shown to be insoluble, i.e., trajectories are not confined to analytic hypersurfaces, there is no analytic third integral of motion, and the adiabatic magnetic moment expansion is divergent. It is expected also that the normal form procedure will prove useful in the study of island structure and separatrices associated with periodic orbits, and should facilitate studies of breakdown of adiabaticity and the onset of ''stochastic'' behavior
Nonextensive formalism and continuous Hamiltonian systems
International Nuclear Information System (INIS)
Boon, Jean Pierre; Lutsko, James F.
2011-01-01
A recurring question in nonequilibrium statistical mechanics is what deviation from standard statistical mechanics gives rise to non-Boltzmann behavior and to nonlinear response, which amounts to identifying the emergence of 'statistics from dynamics' in systems out of equilibrium. Among several possible analytical developments which have been proposed, the idea of nonextensive statistics introduced by Tsallis about 20 years ago was to develop a statistical mechanical theory for systems out of equilibrium where the Boltzmann distribution no longer holds, and to generalize the Boltzmann entropy by a more general function S q while maintaining the formalism of thermodynamics. From a phenomenological viewpoint, nonextensive statistics appeared to be of interest because maximization of the generalized entropy S q yields the q-exponential distribution which has been successfully used to describe distributions observed in a large class of phenomena, in particular power law distributions for q>1. Here we re-examine the validity of the nonextensive formalism for continuous Hamiltonian systems. In particular we consider the q-ideal gas, a model system of quasi-particles where the effect of the interactions are included in the particle properties. On the basis of exact results for the q-ideal gas, we find that the theory is restricted to the range q<1, which raises the question of its formal validity range for continuous Hamiltonian systems.
Hamiltonian Anomalies from Extended Field Theories
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.
Effective Hamiltonians for phosphorene and silicene
International Nuclear Information System (INIS)
Lew Yan Voon, L C; Lopez-Bezanilla, A; Wang, J; Zhang, Y; Willatzen, M
2015-01-01
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 of Geissler et al 2013 (New J. Phys. 15 085030) on silicene, and Li and Appelbaum 2014 (Phys. Rev. B 90, 115439) 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 the 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. (paper)
Phase space eigenfunctions of multidimensional quadratic Hamiltonians
International Nuclear Information System (INIS)
Dodonov, V.V.; Man'ko, V.I.
1986-01-01
We obtain the explicit expressions for phace space eigenfunctions (PSE),i.e. Weyl's symbols of dyadic operators like vertical stroken> ,vertical strokem>, being the solution of the Schroedinger equation with the Hamiltonian which is a quite arbitrary multidimensional quadratic form of the operators of Cartesian coordinates and conjugated to them momenta with time-dependent coefficients. It is shown that for an arbitrary quadratic Hamiltonian one can always construct the set of completely factorized PSE which are products of N factors, each factor being dependent only on two arguments for nnot=m and on a single argument for n=m. These arguments are nothing but constants of motion of the correspondent classical system. PSE are expressed in terms of the associated Laguerre polynomials in the case of a discrete spectrum and in terms of the Airy functions in the continuous spectrum case. Three examples are considered: a harmonic oscillator with a time-dependent frequency, a charged particle in a nonstationary uniform magnetic field, and a particle in a time-dependent uniform potential field. (orig.)
Diffeomorphism invariance in the Hamiltonian formulation of General Relativity
International Nuclear Information System (INIS)
Kiriushcheva, N.; Kuzmin, S.V.; Racknor, C.; Valluri, S.R.
2008-01-01
It is shown that when the Einstein-Hilbert Lagrangian is considered without any non-covariant modifications or change of variables, its Hamiltonian formulation leads to results consistent with principles of General Relativity. The first-class constraints of such a Hamiltonian formulation, with the metric tensor taken as a canonical variable, allow one to derive the generator of gauge transformations, which directly leads to diffeomorphism invariance. The given Hamiltonian formulation preserves general covariance of the transformations derivable from it. This characteristic should be used as the crucial consistency requirement that must be met by any Hamiltonian formulation of General Relativity
Matchings Extend to Hamiltonian Cycles in 5-Cube
Directory of Open Access Journals (Sweden)
Wang Fan
2018-02-01
Full Text Available Ruskey and Savage asked the following question: Does every matching in a hypercube Qn for n ≥ 2 extend to a Hamiltonian cycle of Qn? Fink confirmed that every perfect matching can be extended to a Hamiltonian cycle of Qn, thus solved Kreweras’ conjecture. Also, Fink pointed out that every matching can be extended to a Hamiltonian cycle of Qn for n ∈ {2, 3, 4}. In this paper, we prove that every matching in Q5 can be extended to a Hamiltonian cycle of Q5.
Squeezed states from a quantum deformed oscillator Hamiltonian
Energy Technology Data Exchange (ETDEWEB)
Ramírez, R. [IFLP, CONICET–Department of Mathematics, University of La Plata c.c. 67 1900, La Plata (Argentina); Reboiro, M., E-mail: marta.reboiro@gmail.com [IFLP, CONICET–Department of Physics, University of La Plata c.c. 67 1900, La Plata (Argentina)
2016-03-11
The spectrum and the time evolution of a system, which is modeled by a non-hermitian quantum deformed oscillator Hamiltonian, is analyzed. The proposed Hamiltonian is constructed from a non-standard realization of the algebra of Heisenberg. We show that, for certain values of the coupling constants and for a range of values of the deformation parameter, the deformed Hamiltonian is a pseudo-hermitic Hamiltonian. We explore the conditions under which the Hamiltonian is similar to a Swanson Hamiltonian. Also, we show that the lowest eigenstate of the system is a squeezed state. We study the time evolution of the system, for different initial states, by computing the corresponding Wigner functions. - Highlights: • A generalization of the squeezed harmonic oscillator is constructed from a non-standard realization of the Heisenberg algebra. • It is proved that, for certain values of the parameters of the model, the Hamiltonian is a pseudo-hermitian Hamiltonian. • It is shown that the lowest eigenstate of the Hamiltonian is a squeezed state. • The squeezing behavior of the associated Gazeau–Klauder state, as a function of time, is discussed.
Spectral and resonance properties of the Smilansky Hamiltonian
Energy Technology Data Exchange (ETDEWEB)
Exner, Pavel [Department of Theoretical Physics, Nuclear Physics Institute, Czech Academy of Sciences, 25068 Řež near Prague (Czech Republic); Doppler Institute for Mathematical Physics and Applied Mathematics, Czech Technical University, Břehová 7, 11519 Prague (Czech Republic); Lotoreichik, Vladimir [Department of Theoretical Physics, Nuclear Physics Institute, Czech Academy of Sciences, 25068 Řež near Prague (Czech Republic); Tater, Miloš, E-mail: tater@ujf.cas.cz [Department of Theoretical Physics, Nuclear Physics Institute, Czech Academy of Sciences, 25068 Řež near Prague (Czech Republic)
2017-02-26
We analyze the Hamiltonian proposed by Smilansky to describe irreversible dynamics in quantum graphs and studied further by Solomyak and others. We derive a weak-coupling asymptotics of the ground state and add new insights by finding the discrete spectrum numerically in the subcritical case. Furthermore, we show that the model then has a rich resonance structure. - Highlights: • We derive conditions on bound states and on resonances of the Smilansky Hamiltonian. • Using these conditions we find numerically discrete spectrum and resonances of this Hamiltonian. • Our numerical tests confirm known properties of the Hamiltonian and allow us to conjecture new ones.
The behavior-analytic approach to emotional self-control
Directory of Open Access Journals (Sweden)
Jussara Rocha Batista
2012-12-01
Full Text Available Some psychological approaches distinguish behavioral self-control from emotional self-control, the latter being approached with the reference to inside events controlled by the individual himself. This paper offers some directions to a behavior-analytic approach of what has been referred to as emotional self-control. According to Behavior Analysis, no new process is found in emotional self-control, but components that are additional to those found in behavioral self-control, which require appropriate treatment. The paper highlights some determinants of behavioral repertoires taken as instances of emotional self-control: the social context in which self-control is produced and maintained; the conflicts between consequences for the individual and for the group; and the degree of participation of the motor apparatus in the emission of emotional responses. Keywords: emotional self-control; emotional responses; inner world; behavior analysis.
Controller design approach based on linear programming.
Tanaka, Ryo; Shibasaki, Hiroki; Ogawa, Hiromitsu; Murakami, Takahiro; Ishida, Yoshihisa
2013-11-01
This study explains and demonstrates the design method for a control system with a load disturbance observer. Observer gains are determined by linear programming (LP) in terms of the Routh-Hurwitz stability criterion and the final-value theorem. In addition, the control model has a feedback structure, and feedback gains are determined to be the linear quadratic regulator. The simulation results confirmed that compared with the conventional method, the output estimated by our proposed method converges to a reference input faster when a load disturbance is added to a control system. In addition, we also confirmed the effectiveness of the proposed method by performing an experiment with a DC motor. © 2013 ISA. Published by ISA. All rights reserved.
Optical pulse shaping approaches to coherent control
International Nuclear Information System (INIS)
Goswami, Debabrata
2003-01-01
The last part of the twentieth century has experienced a huge resurge of activity in the field of coherent light-matter interaction, more so in attempting to exert control over such interactions. Birth of coherent control was originally spurred by the theoretical understanding of the quantum interferences that lead to energy randomization and experimental developments in ultrafast laser spectroscopy. The theoretical predictions on control of reaction channels or energy randomization processes are still more dramatic than the experimental demonstrations, though this gap between the two is consistently reducing over the recent years with realistic theoretical models and technological developments. Experimental demonstrations of arbitrary optical pulse shaping have made some of the previously impracticable theoretical predictions possible to implement. Starting with the simple laser modulation schemes to provide proof-of-the-principle demonstrations, feedback loop pulse shaping systems have been developed that can actively manipulate some atomic and molecular processes. This tremendous experimental boost of optical pulse shaping developments has prospects and implications into many more new directions, such as quantum computing and terabit/sec data communications. This review captures certain aspects and impacts of optical pulse shaping into the fast developing areas of coherent control and other related fields. Currently available reviews focus on one or the other detailed aspects of coherent control, and the reader will be referred to such details as and when necessary for issues that are dealt in brief here. We will focus on the current issues including control of intramolecular dynamics and make connections to the future concepts, such as, quantum computation, biomedical applications, etc
Statistical quality control a loss minimization approach
Trietsch, Dan
1999-01-01
While many books on quality espouse the Taguchi loss function, they do not examine its impact on statistical quality control (SQC). But using the Taguchi loss function sheds new light on questions relating to SQC and calls for some changes. This book covers SQC in a way that conforms with the need to minimize loss. Subjects often not covered elsewhere include: (i) measurements, (ii) determining how many points to sample to obtain reliable control charts (for which purpose a new graphic tool, diffidence charts, is introduced), (iii) the connection between process capability and tolerances, (iv)
International Nuclear Information System (INIS)
Reiher, Markus; Wolf, Alexander
2004-01-01
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
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.
Computer science approach to quantum control
International Nuclear Information System (INIS)
Janzing, D.
2006-01-01
Whereas it is obvious that every computation process is a physical process it has hardly been recognized that many complex physical processes bear similarities to computation processes. This is in particular true for the control of physical systems on the nanoscopic level: usually the system can only be accessed via a rather limited set of elementary control operations and for many purposes only a concatenation of a large number of these basic operations will implement the desired process. This concatenation is in many cases quite similar to building complex programs from elementary steps and principles for designing algorithm may thus be a paradigm for designing control processes. For instance, one can decrease the temperature of one part of a molecule by transferring its heat to the remaining part where it is then dissipated to the environment. But the implementation of such a process involves a complex sequence of electromagnetic pulses. This work considers several hypothetical control processes on the nanoscopic level and show their analogy to computation processes. We show that measuring certain types of quantum observables is such a complex task that every instrument that is able to perform it would necessarily be an extremely powerful computer. Likewise, the implementation of a heat engine on the nanoscale requires to process the heat in a way that is similar to information processing and it can be shown that heat engines with maximal efficiency would be powerful computers, too. In the same way as problems in computer science can be classified by complexity classes we can also classify control problems according to their complexity. Moreover, we directly relate these complexity classes for control problems to the classes in computer science. Unifying notions of complexity in computer science and physics has therefore two aspects: on the one hand, computer science methods help to analyze the complexity of physical processes. On the other hand, reasonable
Wind Turbine Control: Robust Model Based Approach
DEFF Research Database (Denmark)
Mirzaei, Mahmood
. Wind turbines are the most common wind energy conversion systems and are hoped to be able to compete economically with fossil fuel power plants in near future. However this demands better technology to reduce the price of electricity production. Control can play an essential part in this context....... This is because, on the one hand, control methods can decrease the cost of energy by keeping the turbine close to its maximum efficiency. On the other hand, they can reduce structural fatigue and therefore increase the lifetime of the wind turbine. The power produced by a wind turbine is proportional...... to the square of its rotor radius, therefore it seems reasonable to increase the size of the wind turbine in order to capture more power. However as the size increases, the mass of the blades increases by cube of the rotor size. This means in order to keep structural feasibility and mass of the whole structure...
Hamiltonian Dynamics of Spider-Type Multirotor Rigid Bodies Systems
International Nuclear Information System (INIS)
Doroshin, Anton V.
2010-01-01
This paper sets out to develop a spider-type multiple-rotor system which can be used for attitude control of spacecraft. The multirotor system contains a large number of rotor-equipped rays, so it was called a 'Spider-type System', also it can be called 'Rotary Hedgehog'. These systems allow using spinups and captures of conjugate rotors to perform compound attitude motion of spacecraft. The paper describes a new method of spacecraft attitude reorientation and new mathematical model of motion in Hamilton form. Hamiltonian dynamics of the system is investigated with the help of Andoyer-Deprit canonical variables. These variables allow obtaining exact solution for hetero- and homoclinic orbits in phase space of the system motion, which are very important for qualitative analysis.
A fatigue approach to wind turbine control
International Nuclear Information System (INIS)
Hammerum, K; Brath, P; Poulsen, N K
2007-01-01
Conventional design of wind turbine controllers is focused on speed and produced electric power. As fatigue loads is an important design consideration, the resulting design is evaluated also with respect to the fatigue loads inflicted on the turbine structure. This is normally done by performing simulations using tools like FLEX, HAWC or FAST, followed by rainflow counting in the resulting time series. This procedure constitutes an iterative design procedure involving realisations of the stress processes in order to obtain the time series needed for fatigue estimates. The focus of this paper is the elimination of the need for process realisation. To this end, known techniques for approximative fatigue load assesment based on the spectral moments of the inflicted stress histories are applied. Assuming a linearised system model, we present a novel scheme for efficient computation of these spectral moments. The scheme is applied to obtain rapid evaluation of cost functions including fatigue loads, hereby allowing efficient numerical optimisation of the controller. Three different controller design examples are given, all defined directly in terms of component life times
A plant control system development approach for IRIS
International Nuclear Information System (INIS)
Wood, R.T.; Brittain, C.R.; March-Leuba, J.A.; Conway, L.E.; Oriani, L.
2003-01-01
The plant control system concept for the International Reactor Innovative and Secure (IRIS) will make use of integrated control, diagnostic, and decision modules to provide a highly automated intelligent control capability. The plant control system development approach established for IRIS involves determination and verification of control strategies based on whole-plant simulation; identification of measurement, control, and diagnostic needs; development of an architectural framework in which to integrate an intelligent plant control system; and design of the necessary control and diagnostic elements for implementation and validation. This paper describes key elements of the plant control system development approach established for IRIS and presents some of the strategies and methods investigated to support the desired control capabilities. (author)
Different Approaches to Control of TISO Thermal System
Directory of Open Access Journals (Sweden)
Jaroslava KRÁLOVÁ
2009-06-01
Full Text Available The contribution is aimed on problematic of multivariable control. Multivariable system can be controlled by multivariable controller or we can use decentralized control. Control of thermal system with two inputs and one output is shown in the paper. The goal of paper is to find what sort of results we can get by classical approaches and by more sophisticated strategies. Two discrete-time PID controllers are selected as a representative of classical approach and split-range with discrete-time PID controller is selected as a representative of more sophisticated strategy. Control strategies are compared in the view of control quality and costs, information and knowledge required by control design and application.
An Approach to Naval Arms Control
1989-07-01
commentary pro and con on the control of SLCM’s has 9 I: been uttered by people not known to be expert on maritime strategy and the roles of navies in crisis ... transcultural misunderstanding is indeed deep and widespread (e.g., witness the surprise on the part of America’s leading television pundits that China’s...force on behalf of (U.S definition of) international order in situations short of war; 0 alliance cohesion; 37 i * crisis , arms race, and political
Future approaches to material control and accounting
International Nuclear Information System (INIS)
Sherr, T.S.; Smith, G.D.; Wirfs, L.F.
1978-01-01
This paper presents a short description of the safeguards responsibilities and activities of the U.S. Nuclear Regulatory Commission (NRC), the NRC regulatory requirements for safeguards in the area of material control and accounting (MCandA), and the current NRC efforts which may result in significant changes in the current U.S. safeguards system. The preliminary results of NRC staff and contractor MCandA activities are discussed, as well as the recommendations of a recent NRC task force on MCandA. 9 refs
Distributed Secondary Control for Islanded MicroGrids – A Networked Control Systems Approach
DEFF Research Database (Denmark)
Shafiee, Qobad; Vasquez, Juan Carlos; Guerrero, Josep M.
2012-01-01
This paper presents a novel approach to conceive the secondary control in droop-controlled MicroGrids. The conventional approach is based on restoring the frequency and amplitude deviations produced by the local droop controllers by using a MicroGrid Central Controller. A distributed networked...... control system is used in order to implement a distributed secondary control thus avoiding the use of a MicroGrid Central Control. The proposed approach is not only able to restore frequency and voltage of the MicroGrid but also ensures reactive power sharing. The distributed secondary control do...
A controllability approach to the control of a class of chaotic systems
International Nuclear Information System (INIS)
Bowong, Samuel; Moukam Kakmeni, F.M.; Tchawoua, Clement; Abdus Salam International Centre for Theoretical Physics, Trieste
2003-10-01
In this paper the exponential control problem for a class of chaotic systems with affine dependence on the control is addressed and solved by the controllability approach. It is shown that the controllability approach in conjunction with Lyapunov Direct Method yields a promising way of controlling chaotic dynamics. The proposed strategy is an input-output control scheme which comprises a state estimator and an exponential linearizing feedback. The proposed output feedback controller allows chaos suppression and can be applied to a large class of chaotic systems. Explicit expression of the control time is given. Computer simulations confirm the feasibility of the proposed approach. (author)
Tuberculosis control in the Americas: current approaches.
Pio, A; Western, K
1976-01-01
Tuberculosi remains a serious public health problem in the Americas, and it has not declined as rapidly or as much as experts projected it would in the 1940's. Scientific advances in control of the disease over the last three decades have produced effective chemotherapeutic agents, established the immunizing capacity of BCG vaccine, and demonstrated the superior value of bacteriologic diagnosis in symptomatic individuals over mass community x-ray surveys, which are both inefficient and costly. They have also shown that most cases can be treated on an ambulatory basis, obviating the need for the lengthy hospital stays which have heretofore weighed so heavily on budgets. By standardization of control methods, both for diagnosis and for chemotherapy, these tasks can be taken on by polyvalent staff in the general health services, whose wide coverage places them in a position to reach a much larger segment of the population than that attended by the traditional vertical system. To a greater or lesser degree, all the countries in the Americas are beginning to orient their strategies in this direction, and some of them already have considerable progress to report.
Artificial intelligence approach to accelerator control systems
International Nuclear Information System (INIS)
Schultz, D.E.; Hurd, J.W.; Brown, S.K.
1987-01-01
An experiment was recently started at LAMPF to evaluate the power and limitations of using artificial intelligence techniques to solve problems in accelerator control and operation. A knowledge base was developed to describe the characteristics and the relationships of the first 30 devices in the LAMPF H+ beam line. Each device was categorized and pertinent attributes for each category defined. Specific values were assigned in the knowledge base to represent each actual device. Relationships between devices are modeled using the artificial intelligence techniques of rules, active values, and object-oriented methods. This symbolic model, built using the Knowledge Engineering Environment (KEE) system, provides a framework for analyzing faults, tutoring trainee operators, and offering suggestions to assist in beam tuning. Based on information provided by the domain expert responsible for tuning this portion of the beam line, additional rules were written to describe how he tunes, how he analyzes what is actually happening, and how he deals with failures. Initial results have shown that artificial intelligence techniques can be a useful adjunct to traditional methods of numerical simulation. Successful and efficient operation of future accelerators may depend on the proper merging of symbolic reasoning and conventional numerical control algorithms
Geometric solitons of Hamiltonian flows on manifolds
Energy Technology Data Exchange (ETDEWEB)
Song, Chong, E-mail: songchong@xmu.edu.cn [School of Mathematical Sciences, Xiamen University, Xiamen 361005 (China); Sun, Xiaowei, E-mail: sunxw@cufe.edu.cn [School of Applied Mathematics, Central University of Finance and Economics, Beijing 100081 (China); Wang, Youde, E-mail: wyd@math.ac.cn [Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190 (China)
2013-12-15
It is well-known that the LIE (Locally Induction Equation) admit soliton-type solutions and same soliton solutions arise from different and apparently irrelevant physical models. By comparing the solitons of LIE and Killing magnetic geodesics, we observe that these solitons are essentially decided by two families of isometries of the domain and the target space, respectively. With this insight, we propose the new concept of geometric solitons of Hamiltonian flows on manifolds, such as geometric Schrödinger flows and KdV flows for maps. Moreover, we give several examples of geometric solitons of the Schrödinger flow and geometric KdV flow, including magnetic curves as geometric Schrödinger solitons and explicit geometric KdV solitons on surfaces of revolution.
Hamiltonian indices and rational spectral densities
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.
A Hamiltonian five-field gyrofluid model
Energy Technology Data Exchange (ETDEWEB)
Keramidas Charidakos, I.; Waelbroeck, F. L.; Morrison, P. J. [Institute for Fusion Studies and Department of Physics, The University of Texas at Austin, Austin, TX 78712 (United States)
2015-11-15
A Lie-Poisson bracket is presented for a five-field gyrofluid model, thereby showing the model to be Hamiltonian. The model includes the effects of magnetic field curvature and describes the evolution of the electron and ion gyro-center densities, the parallel component of the ion and electron velocities, and the ion temperature. The quasineutrality property and Ampère's law determine, respectively, the electrostatic potential and magnetic flux. The Casimir invariants are presented, and shown to be associated with five Lagrangian invariants advected by distinct velocity fields. A linear, local study of the model is conducted both with and without Landau and diamagnetic resonant damping terms. Stability criteria and dispersion relations for the electrostatic and the electromagnetic cases are derived and compared with their analogs for fluid and kinetic models.
Hamiltonian inclusive fitness: a fitter fitness concept.
Costa, James T
2013-01-01
In 1963-1964 W. D. Hamilton introduced the concept of inclusive fitness, the only significant elaboration of Darwinian fitness since the nineteenth century. I discuss the origin of the modern fitness concept, providing context for Hamilton's discovery of inclusive fitness in relation to the puzzle of altruism. While fitness conceptually originates with Darwin, the term itself stems from Spencer and crystallized quantitatively in the early twentieth century. Hamiltonian inclusive fitness, with Price's reformulation, provided the solution to Darwin's 'special difficulty'-the evolution of caste polymorphism and sterility in social insects. Hamilton further explored the roles of inclusive fitness and reciprocation to tackle Darwin's other difficulty, the evolution of human altruism. The heuristically powerful inclusive fitness concept ramified over the past 50 years: the number and diversity of 'offspring ideas' that it has engendered render it a fitter fitness concept, one that Darwin would have appreciated.
Renormalized semiclassical quantization for rescalable Hamiltonians
International Nuclear Information System (INIS)
Takahashi, Satoshi; Takatsuka, Kazuo
2004-01-01
A renormalized semiclassical quantization method for rescalable Hamiltonians is proposed. A classical Hamilton system having a potential function that consists of homogeneous polynomials like the Coulombic potential can have a scale invariance in its extended phase space (phase space plus time). Consequently, infinitely many copies of a single trajectory constitute a one-parameter family that is characterized in terms of a scaling factor. This scaling invariance in classical dynamics is lost in quantum mechanics due to the presence of the Planck constant. It is shown that in a system whose classical motions have a self-similarity in the above sense, classical trajectories adopted in the semiclassical scheme interact with infinitely many copies of their own that are reproduced by the relevant scaling procedure, thereby undergoing quantum interference among themselves to produce a quantized spectrum
Bifurcation of solutions to Hamiltonian boundary value problems
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.
Non-self-adjoint hamiltonians defined by Riesz bases
Energy Technology Data Exchange (ETDEWEB)
Bagarello, F., E-mail: fabio.bagarello@unipa.it [Dipartimento di Energia, Ingegneria dell' Informazione e Modelli Matematici, Facoltà di Ingegneria, Università di Palermo, I-90128 Palermo, Italy and INFN, Università di Torino, Torino (Italy); Inoue, A., E-mail: a-inoue@fukuoka-u.ac.jp [Department of Applied Mathematics, Fukuoka University, Fukuoka 814-0180 (Japan); Trapani, C., E-mail: camillo.trapani@unipa.it [Dipartimento di Matematica e Informatica, Università di Palermo, I-90123 Palermo (Italy)
2014-03-15
We discuss some features of non-self-adjoint Hamiltonians with real discrete simple spectrum under the assumption that the eigenvectors form a Riesz basis of Hilbert space. Among other things, we give conditions under which these Hamiltonians can be factorized in terms of generalized lowering and raising operators.
The Group of Hamiltonian Automorphisms of a Star Product
Energy Technology Data Exchange (ETDEWEB)
La Fuente-Gravy, Laurent, E-mail: lfuente@ulg.ac.be [Université de Liège, Département de Mathématique (Belgium)
2016-09-15
We deform the group of Hamiltonian diffeomorphisms into a group of Hamiltonian automorphisms, Ham(M,∗), of a formal star product ∗ on a symplectic manifold (M,ω). We study the geometry of that group and deform the Flux morphism in the framework of deformation quantization.
Hamiltonian formulation for the Martin-Taylor model
International Nuclear Information System (INIS)
Vasconcelos, D.B.; Viana, R.L.
1993-01-01
Locally stochastic layer and its optimization are studied. In order to accomplish this task, it is employed a Hamiltonian formulation of magnetic field line flow with a subsequent application of Escande-Doveil renormalization method which have been extensively used to obtain accurate estimates of stochasticity thresholds in systems exhibiting Hamiltonian chaos. (author)
Formulation of Hamiltonian mechanics with even and odd Poisson brackets
International Nuclear Information System (INIS)
Khudaverdyan, O.M.; Nersesyan, A.P.
1987-01-01
A possibility is studied as to constrict the odd Poisson bracket and odd Hamiltonian by the given dynamics in phase superspace - the even Poisson bracket and even Hamiltonian so the transition to the new structure does not change the equations of motion. 9 refs
Classical and quantum mechanics of complex Hamiltonian systems ...
Indian Academy of Sciences (India)
Vol. 73, No. 2. — journal of. August 2009 physics pp. 287–297. Classical and quantum mechanics of complex. Hamiltonian systems: An extended complex phase space ... 1Department of Physics, Ramjas College (University Enclave), University of Delhi,. Delhi 110 ... 1.1 Motivation behind the study of complex Hamiltonians.
Local Hamiltonians for maximally multipartite-entangled states
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.
Local Hamiltonians for maximally multipartite-entangled states
International Nuclear Information System (INIS)
Facchi, P.; Florio, G.; Pascazio, S.; Pepe, F.
2010-01-01
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.
Modelling chaotic Hamiltonian systems as a Markov Chain ...
African Journals Online (AJOL)
The behaviour of chaotic Hamiltonian system has been characterised qualitatively in recent times by its appearance on the Poincaré section and quantitatively by the Lyapunov exponent. Studying the dynamics of the two chaotic Hamiltonian systems: the Henon-Heiles system and non-linearly coupled oscillators as their ...
On the physical applications of hyper-Hamiltonian dynamics
International Nuclear Information System (INIS)
Gaeta, Giuseppe; Rodriguez, Miguel A
2008-01-01
An extension of Hamiltonian dynamics, defined on hyper-Kahler manifolds ('hyper-Hamiltonian dynamics') and sharing many of the attractive features of standard Hamiltonian dynamics, was introduced in previous work. In this paper, we discuss applications of the theory to physically interesting cases, dealing with the dynamics of particles with spin 1/2 in a magnetic field, i.e. the Pauli and the Dirac equations. While the free Pauli equation corresponds to a hyper-Hamiltonian flow, it turns out that the hyper-Hamiltonian description of the Dirac equation, and of the full Pauli one, is in terms of two commuting hyper-Hamiltonian flows. In this framework one can use a factorization principle discussed here (which is a special case of a general phenomenon studied by Walcher) and provide an explicit description of the resulting flow. On the other hand, by applying the familiar Foldy-Wouthuysen and Cini-Tousheck transformations (and the one recently introduced by Mulligan) which separate-in suitable limits-the Dirac equation into two equations, each of these turn out to be described by a single hyper-Hamiltonian flow. Thus the hyper-Hamiltonian construction is able to describe the fundamental dynamics for particles with spin
The Group of Hamiltonian Automorphisms of a Star Product
International Nuclear Information System (INIS)
La Fuente-Gravy, Laurent
2016-01-01
We deform the group of Hamiltonian diffeomorphisms into a group of Hamiltonian automorphisms, Ham(M,∗), of a formal star product ∗ on a symplectic manifold (M,ω). We study the geometry of that group and deform the Flux morphism in the framework of deformation quantization.
Hamiltonian reduction of SU(2) Yang-Mills field theory
International Nuclear Information System (INIS)
Khvedelidze, A.M.; Pavel, H.-P.
1998-01-01
The unconstrained system equivalent to SU (2) Yang-Mills field theory is obtained in the framework of the generalized Hamiltonian formalism using the method of Hamiltonian reduction. The reduced system is expressed in terms of fields with 'nonrelativistic' spin-0 and spin-2
Model reduction of port-Hamiltonian systems as structured systems
Polyuga, R.V.; Schaft, van der A.J.
2010-01-01
The goal of this work is to demonstrate that a specific projection-based model reduction method, which provides an H2 error bound, turns out to be applicable to port-Hamiltonian systems, preserving the port-Hamiltonian structure for the reduced order model, and, as a consequence, passivity.
Port Hamiltonian Formulation of Infinite Dimensional Systems I. Modeling
Macchelli, Alessandro; Schaft, Arjan J. van der; Melchiorri, Claudio
2004-01-01
In this paper, some new results concerning the modeling of distributed parameter systems in port Hamiltonian form are presented. The classical finite dimensional port Hamiltonian formulation of a dynamical system is generalized in order to cope with the distributed parameter and multi-variable case.
Residual gauge invariance of Hamiltonian lattice gauge theories
International Nuclear Information System (INIS)
Ryang, S.; Saito, T.; Shigemoto, K.
1984-01-01
The time-independent residual gauge invariance of Hamiltonian lattice gauge theories is considered. Eigenvalues and eigenfunctions of the unperturbed Hamiltonian are found in terms of Gegengauer's polynomials. Physical states which satisfy the subsidiary condition corresponding to Gauss' law are constructed systematically. (orig.)
Multiple Model Approaches to Modelling and Control,
DEFF Research Database (Denmark)
on the ease with which prior knowledge can be incorporated. It is interesting to note that researchers in Control Theory, Neural Networks,Statistics, Artificial Intelligence and Fuzzy Logic have more or less independently developed very similar modelling methods, calling them Local ModelNetworks, Operating......, and allows direct incorporation of high-level and qualitative plant knowledge into themodel. These advantages have proven to be very appealing for industrial applications, and the practical, intuitively appealing nature of the framework isdemonstrated in chapters describing applications of local methods...... to problems in the process industries, biomedical applications and autonomoussystems. The successful application of the ideas to demanding problems is already encouraging, but creative development of the basic framework isneeded to better allow the integration of human knowledge with automated learning...
A generalized AKNS hierarchy and its bi-Hamiltonian structures
International Nuclear Information System (INIS)
Xia Tiecheng; You Fucai; Chen Dengyuan
2005-01-01
First we construct a new isospectral problem with 8 potentials in the present paper. And then a new Lax pair is presented. By making use of Tu scheme, a class of new soliton hierarchy of equations is derived, which is integrable in the sense of Liouville and possesses bi-Hamiltonian structures. After making some reductions, the well-known AKNS hierarchy and other hierarchies of evolution equations are obtained. Finally, in order to illustrate that soliton hierarchy obtained in the paper possesses bi-Hamiltonian structures exactly, we prove that the linear combination of two-Hamiltonian operators admitted are also a Hamiltonian operator constantly. We point out that two Hamiltonian operators obtained of the system are directly derived from a recurrence relations, not from a recurrence operator
Local modular Hamiltonians from the quantum null energy condition
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 .
Periodic solutions of asymptotically linear Hamiltonian systems without twist conditions
Energy Technology Data Exchange (ETDEWEB)
Cheng Rong [Coll. of Mathematics and Physics, Nanjing Univ. of Information Science and Tech., Nanjing (China); Dept. of Mathematics, Southeast Univ., Nanjing (China); Zhang Dongfeng [Dept. of Mathematics, Southeast Univ., Nanjing (China)
2010-05-15
In dynamical system theory, especially in many fields of applications from mechanics, Hamiltonian systems play an important role, since many related equations in mechanics can be written in an Hamiltonian form. In this paper, we study the existence of periodic solutions for a class of Hamiltonian systems. By applying the Galerkin approximation method together with a result of critical point theory, we establish the existence of periodic solutions of asymptotically linear Hamiltonian systems without twist conditions. Twist conditions play crucial roles in the study of periodic solutions for asymptotically linear Hamiltonian systems. The lack of twist conditions brings some difficulty to the study. To the authors' knowledge, very little is known about the case, where twist conditions do not hold. (orig.)
Sdg interacting boson hamiltonian in the seniority scheme
Energy Technology Data Exchange (ETDEWEB)
Yoshinaga, N.
1989-03-06
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 diagnoalizing the exact shell model hamiltonian. In particular the sdg interacting boson model reproduces well-developed rotational bands.
sdg Interacting boson hamiltonian in the seniority scheme
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.
Frustration-free Hamiltonians supporting Majorana zero edge modes
International Nuclear Information System (INIS)
Jevtic, Sania; Barnett, Ryan
2017-01-01
A one-dimensional fermionic system, such as a superconducting wire, may host Majorana zero-energy edge modes (MZMs) at its edges when it is in the topological phase. MZMs provide a path to realising fault-tolerant quantum computation, and so are the focus of intense experimental and theoretical studies. However, given a Hamiltonian, determining whether MZMs exist is a daunting task as it relies on knowing the spectral properties of the Hamiltonian in the thermodynamic limit. The Kitaev chain is a paradigmatic non-interacting model that supports MZMs and the Hamiltonian can be fully diagonalised. However, for interacting models, the situation is far more complex. Here we consider a different classification of models, namely, ones with frustration-free Hamiltonians. Within this class of models, interacting and non-interacting systems are treated on an equal footing, and we identify exactly which Hamiltonians can realise MZMs. (paper)
Frustration-free Hamiltonians supporting Majorana zero edge modes
Jevtic, Sania; Barnett, Ryan
2017-10-01
A one-dimensional fermionic system, such as a superconducting wire, may host Majorana zero-energy edge modes (MZMs) at its edges when it is in the topological phase. MZMs provide a path to realising fault-tolerant quantum computation, and so are the focus of intense experimental and theoretical studies. However, given a Hamiltonian, determining whether MZMs exist is a daunting task as it relies on knowing the spectral properties of the Hamiltonian in the thermodynamic limit. The Kitaev chain is a paradigmatic non-interacting model that supports MZMs and the Hamiltonian can be fully diagonalised. However, for interacting models, the situation is far more complex. Here we consider a different classification of models, namely, ones with frustration-free Hamiltonians. Within this class of models, interacting and non-interacting systems are treated on an equal footing, and we identify exactly which Hamiltonians can realise MZMs.
Glucose control and cardiovascular outcomes: Reorienting approach
Directory of Open Access Journals (Sweden)
Romesh eKhardori
2012-08-01
Full Text Available Cardiovascular disease accounts for nearly 70 % of morbidity and mortality in patients with diabetes mellitus. Strides made in diabetes care have indeed helped prevent or reduce the burden of microvascular complications in both type-1 and type-2 diabetes. However, the same can’t be said about macrovascular disease in diabetes. Several prospective trials so far have failed to provide conclusive evidence of glycemic control superiority in reducing macrovascular complications or death rate in people with advanced disease or those with long duration of diabetes. There are trends that suggest that benefits are restricted to those with lesser burden and shorter duration of disease. Furthermore, it is also suggested that benefits might accrue but it would take longer time to manifest. Clinicians are fraught with challenge to decide how to triage patients for intensified care versus less intense care. This review focusses on evidence and attempts to provide a balanced view of literature that has radically affected how physicians treat patients with macrovascular disease. It also takes cognizance of the fact that natural course of disease may be changing as well possibly related to better overall awareness and possibly improved access to information about better individual healthcare. The review further takes note of some hard held notions about pathobiology of disease that must be interpreted with caution in light of new emerging data. In light of recent developments ADA and EASD have taken step to provide some guidance to clinicians through a joint position statement. A lot more research would be required to figure out how best to manage macrovascular disease in diabetes mellitus. Glucocentric stance would have to yield to evidence based, and possibly, concurrent multifactorial intervention to enhance quality of care that is safe and effective.
Glucose control and cardiovascular outcomes: reorienting approach.
Khardori, Romesh; Nguyen, Diep D
2012-01-01
Cardiovascular disease accounts for nearly 70% of morbidity and mortality in patients with diabetes mellitus. Strides made in diabetes care have indeed helped prevent or reduce the burden of microvascular complications in both type 1 and type 2 diabetes. However, the same cannot be said about macrovascular disease in diabetes. Several prospective trials so far have failed to provide conclusive evidence of the superiority of glycemic control in reducing macrovascular complications or death rates in people with advanced disease or those with long duration of diabetes. There are trends that suggest that benefits are restricted to those with lesser burden and shorter duration of disease. Furthermore, it is also suggested that benefits might accrue but it would take a longer time to manifest. Clinicians are faced with the challenge to decide how to triage patients for intensified care vs less intense care. This review focuses on evidence and attempts to provide a balanced view of the literature that has radically affected how physicians treat patients with macrovascular disease. It also takes cognizance of the fact that the natural course of the disease may be changing as well, possibly related to better overall awareness and possibly improved access to information about better individual healthcare. The review further takes note of some hard held notions about the pathobiology of the disease that must be interpreted with caution in light of new and emerging data. In light of recent developments ADA and EASD have taken step to provide some guidance to clinicians through a joint position statement. A lot more research would be required to figure out how best to manage macrovascular disease in diabetes mellitus. Glucocentric stance would need to be reconsidered, and attention paid to concurrent multifactorial interventions that seem to be effective in reducing vascular outcomes.
Mechanical systems a unified approach to vibrations and controls
Gans, Roger F
2015-01-01
This essential textbook covers analysis and control of engineering mechanisms, which include almost any apparatus with moving parts used in daily life, from musical instruments to robots. The text presents both vibrations and controls with considerable breadth and depth using a unified notation. It strikes a nice balance between the analytical and the practical. This text contains enough material for a two semester sequence, but it can also be used in a single semester course combining the two topics. Mechanical Systems: A Unified Approach to Vibrations and Controls presents a common notation and approach to these closely related areas. Examples from the both vibrations and controls components are integrated throughout this text. This book also: · Presents a unified approach to vibrations and controls, including an excellent diagram that simultaneously discusses embedding classical vibrations (mechanical systems) in a discussion of models, inverse models, and open and closed loop control ...
A multiparameter chaos control method based on OGY approach
International Nuclear Information System (INIS)
Souza de Paula, Aline; Amorim Savi, Marcelo
2009-01-01
Chaos control is based on the richness of responses of chaotic behavior and may be understood as the use of tiny perturbations for the stabilization of a UPO embedded in a chaotic attractor. Since one of these UPO can provide better performance than others in a particular situation the use of chaos control can make this kind of behavior to be desirable in a variety of applications. The OGY method is a discrete technique that considers small perturbations promoted in the neighborhood of the desired orbit when the trajectory crosses a specific surface, such as a Poincare section. This contribution proposes a multiparameter semi-continuous method based on OGY approach in order to control chaotic behavior. Two different approaches are possible with this method: coupled approach, where all control parameters influences system dynamics although they are not active; and uncoupled approach that is a particular case where control parameters return to the reference value when they become passive parameters. As an application of the general formulation, it is investigated a two-parameter actuation of a nonlinear pendulum control employing coupled and uncoupled approaches. Analyses are carried out considering signals that are generated by numerical integration of the mathematical model using experimentally identified parameters. Results show that the procedure can be a good alternative for chaos control since it provides a more effective UPO stabilization than the classical single-parameter approach.
Dynamics and control of quadcopter using linear model predictive control approach
Islam, M.; Okasha, M.; Idres, M. M.
2017-12-01
This paper investigates the dynamics and control of a quadcopter using the Model Predictive Control (MPC) approach. The dynamic model is of high fidelity and nonlinear, with six degrees of freedom that include disturbances and model uncertainties. The control approach is developed based on MPC to track different reference trajectories ranging from simple ones such as circular to complex helical trajectories. In this control technique, a linearized model is derived and the receding horizon method is applied to generate the optimal control sequence. Although MPC is computer expensive, it is highly effective to deal with the different types of nonlinearities and constraints such as actuators’ saturation and model uncertainties. The MPC parameters (control and prediction horizons) are selected by trial-and-error approach. Several simulation scenarios are performed to examine and evaluate the performance of the proposed control approach using MATLAB and Simulink environment. Simulation results show that this control approach is highly effective to track a given reference trajectory.
The control-of-consumption approach to alcohol abuse prevention
DEFF Research Database (Denmark)
Ravn, Ib
1987-01-01
The single-distribution theory of alcohol consumption and the derived prevention strategy, the control-of-consumption approach, are conceptualized as three probabilistic relationships between four variables, collectively called "the Ledermann string": availability, average consumption, proportion...
Two-process approach to electron beam welding control
International Nuclear Information System (INIS)
Lastovirya, V.N.
1987-01-01
The analysis and synthesis of multi-dimensional welding control systems, which require the usage of computers, should be conducted within the temporal range. From the general control theory point two approaches - one-process and two-process - are possible to electron beam welding. In case of two-process approach, subprocesses of heat source formation and direct metal melting are separated. Two-process approach leads to two-profile control system and provides the complete controlability of electron beam welding within the frameworks of systems with concentrated, as well as, with distributed parameters. Approach choice for the given problem solution is determined, first of all, by stability degree of heat source during welding
A theoretical approach on controlling agricultural pest by biological controls.
Mondal, Prasanta Kumar; Jana, Soovoojeet; Kar, T K
2014-03-01
In this paper we propose and analyze a prey-predator type dynamical system for pest control where prey population is treated as the pest. We consider two classes for the pest namely susceptible pest and infected pest and the predator population is the natural enemy of the pest. We also consider average delay for both the predation rate i.e. predation to the susceptible pest and infected pest. Considering a subsystem of original system in the absence of infection, we analyze the existence of all possible non-negative equilibria and their stability criteria for both the subsystem as well as the original system. We present the conditions for transcritical bifurcation and Hopf bifurcation in the disease free system. The theoretical evaluations are demonstrated through numerical simulations.
A "Hybrid" Approach for Synthesizing Optimal Controllers of Hybrid Systems
DEFF Research Database (Denmark)
Zhao, Hengjun; Zhan, Naijun; Kapur, Deepak
2012-01-01
to discretization manageable and within bounds. A major advantage of our approach is not only that it avoids errors due to numerical computation, but it also gives a better optimal controller. In order to illustrate our approach, we use the real industrial example of an oil pump provided by the German company HYDAC...
An approach of partial control design for system control and synchronization
International Nuclear Information System (INIS)
Hu Wuhua; Wang Jiang; Li Xiumin
2009-01-01
In this paper, a general approach of partial control design for system control and synchronization is proposed. It turns control problems into simpler ones by reducing their control variables. This is realized by utilizing the dynamical relations between variables, which are described by the dynamical relation matrix and the dependence-influence matrix. By adopting partial control theory, the presented approach provides a simple and general way to stabilize systems to their partial or whole equilibriums, or to synchronize systems with their partial or whole states. Further, based on this approach, the controllers can be simplified. Two examples of synchronizing chaotic systems are given to illustrate its effectiveness.
Quantization of a Hamiltonian system with an infinite number of degrees of freedom
International Nuclear Information System (INIS)
Zhidkov, P.E.
1994-01-01
We propose a method of quantization of a discrete Hamiltonian system with an infinite number of degrees of freedom. Our approach is analogous to the usual finite-dimensional quantum mechanics. We construct an infinite-dimensional Schroedinger equation. We show that it is possible to pass from the finite-dimensional quantum mechanics to our construction in the limit when the number of particles tends to infinity. In the paper rigorous mathematical methods are used. 9 refs. (author)
Assessing the Approaches to Classification of the State Financial Control
Directory of Open Access Journals (Sweden)
Baraniuk Yurii R.
2017-11-01
Full Text Available The article is aimed at assessing the approaches to classification of the State financial control, as well as disclosing the relationship and differences between its forms, types and methods. The results of comparative analysis of existing classifications of the State financial control have been covered. The substantiation of its identification by forms, types and methods of control was explored. Clarification of the interpretation of the concepts of «form of control», «type of control», «subtype of control», «method of control», «methodical reception of control» has been provided. It has been determined that the form of the State financial control is a manifestation of the internal organization of control and the methods of its carrying out; a model of classification of the State financial control has been substantiated; attributes of the first and second order have been allocated; substantiation of methods and techniques has been improved; their composition and structure have been identified. This approach allows to divide general questions of the State financial control into theoretical and practical and, taking into consideration the expansion of the list of objects of the State financial control, will help to improve its methodology.
A layered and distributed approach to platform systems control
Neef, R.M.; Lieburg, A. van; Gosliga, S.P. van; Gillis, M.P.W.
2003-01-01
With the increasing complexity of platform systems and the ongoing demand for reduced manning comes the need for novel approaches to ship control systems. Current control and management systems fall short on maintainability, robustness and scalability. From the operator's perspective information
Formation control of unicycle robots using virtual structure approach
Sadowska, A.D.; Huijberts, H.J.C.; Kostic, D.; Wouw, van de N.; Nijmeijer, H.
2011-01-01
This paper addresses the problem of formation control of groups of unicycle robots with possibly time-varying formation shapes. To solve the problem, we propose two simple distributed formation control algorithms based on the virtual structure approach. We prove exponential convergence of error
New Hamiltonian constraint operator for loop quantum gravity
Directory of Open Access Journals (Sweden)
Jinsong Yang
2015-12-01
Full Text Available A new symmetric Hamiltonian constraint operator is proposed for loop quantum gravity, which is well defined in the Hilbert space of diffeomorphism invariant states up to non-planar vertices with valence higher than three. It inherits the advantage of the original regularization method to create new vertices to the spin networks. The quantum algebra of this Hamiltonian is anomaly-free on shell, and there is less ambiguity in its construction in comparison with the original method. The regularization procedure for this Hamiltonian constraint operator can also be applied to the symmetric model of loop quantum cosmology, which leads to a new quantum dynamics of the cosmological model.
Greenberger-Horne-Zeilinger States and Few-Body Hamiltonians
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.
Homotopical Dynamics IV: Hopf invariants and hamiltonian flows
Cornea, Octavian
2001-01-01
In a non-compact context the first natural step in the search for periodic orbits of a hamiltonian flow is to detect bounded ones. In this paper we show that, in a non-compact setting, certain algebraic topological constraints imposed to a gradient flow of the hamiltonian function $f$ imply the existence of bounded orbits for the hamiltonian flow of $f$. Once the existence of bounded orbits is established, under favorable circumstances, application of the $C^{1}$-closing lemma leads to period...
New Hamiltonian constraint operator for loop quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Yang, Jinsong, E-mail: yangksong@gmail.com [Department of Physics, Guizhou university, Guiyang 550025 (China); Institute of Physics, Academia Sinica, Taiwan (China); Ma, Yongge, E-mail: mayg@bnu.edu.cn [Department of Physics, Beijing Normal University, Beijing 100875 (China)
2015-12-17
A new symmetric Hamiltonian constraint operator is proposed for loop quantum gravity, which is well defined in the Hilbert space of diffeomorphism invariant states up to non-planar vertices with valence higher than three. It inherits the advantage of the original regularization method to create new vertices to the spin networks. The quantum algebra of this Hamiltonian is anomaly-free on shell, and there is less ambiguity in its construction in comparison with the original method. The regularization procedure for this Hamiltonian constraint operator can also be applied to the symmetric model of loop quantum cosmology, which leads to a new quantum dynamics of the cosmological model.
Remarks on Hamiltonian structures in G2-geometry
International Nuclear Information System (INIS)
Cho, Hyunjoo; Salur, Sema; Todd, A. J.
2013-01-01
In this article, we treat G 2 -geometry as a special case of multisymplectic geometry and make a number of remarks regarding Hamiltonian multivector fields and Hamiltonian differential forms on manifolds with an integrable G 2 -structure; in particular, we discuss existence and make a number of identifications of the spaces of Hamiltonian structures associated to the two multisymplectic structures associated to an integrable G 2 -structure. Along the way, we prove some results in multisymplectic geometry that are generalizations of results from symplectic geometry
Hamiltonian reduction and supersymmetric mechanics with Dirac monopole
International Nuclear Information System (INIS)
Bellucci, Stefano; Nersessian, Armen; Yeranyan, Armen
2006-01-01
We apply the technique of Hamiltonian reduction for the construction of three-dimensional N=4 supersymmetric mechanics specified by the presence of a Dirac monopole. For this purpose we take the conventional N=4 supersymmetric mechanics on the four-dimensional conformally-flat spaces and perform its Hamiltonian reduction to three-dimensional system. We formulate the final system in the canonical coordinates, and present, in these terms, the explicit expressions of the Hamiltonian and supercharges. We show that, besides a magnetic monopole field, the resulting system is specified by the presence of a spin-orbit coupling term. A comparision with previous work is also carried out
Toric codes and quantum doubles from two-body Hamiltonians
Energy Technology Data Exchange (ETDEWEB)
Brell, Courtney G; Bartlett, Stephen D; Doherty, Andrew C [Centre for Engineered Quantum Systems, School of Physics, University of Sydney, Sydney (Australia); Flammia, Steven T, E-mail: cbrell@physics.usyd.edu.au [Perimeter Institute for Theoretical Physics, Waterloo (Canada)
2011-05-15
We present here a procedure to obtain the Hamiltonians of the toric code and Kitaev quantum double models as the low-energy limits of entirely two-body Hamiltonians. Our construction makes use of a new type of perturbation gadget based on error-detecting subsystem codes. The procedure is motivated by a projected entangled pair states (PEPS) description of the target models, and reproduces the target models' behavior using only couplings that are natural in terms of the original Hamiltonians. This allows our construction to capture the symmetries of the target models.
Greenberger-Horne-Zeilinger states and few-body Hamiltonians.
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.
A control approach for plasma density in tokamak machines
Energy Technology Data Exchange (ETDEWEB)
Boncagni, Luca, E-mail: luca.boncagni@enea.it [EURATOM – ENEA Fusion Association, Frascati Research Center, Division of Fusion Physics, Rome, Frascati (Italy); Pucci, Daniele; Piesco, F.; Zarfati, Emanuele [Dipartimento di Ingegneria Informatica, Automatica e Gestionale ' ' Antonio Ruberti' ' , Sapienza Università di Roma (Italy); Mazzitelli, G. [EURATOM – ENEA Fusion Association, Frascati Research Center, Division of Fusion Physics, Rome, Frascati (Italy); Monaco, S. [Dipartimento di Ingegneria Informatica, Automatica e Gestionale ' ' Antonio Ruberti' ' , Sapienza Università di Roma (Italy)
2013-10-15
Highlights: •We show a control approach for line plasma density in tokamak. •We show a control approach for pressure in a tokamak chamber. •We show experimental results using one valve. -- Abstract: In tokamak machines, chamber pre-fill is crucial to attain plasma breakdown, while plasma density control is instrumental for several tasks such as machine protection and achievement of desired plasma performances. This paper sets the principles of a new control strategy for attaining both chamber pre-fill and plasma density regulation. Assuming that the actuation mean is a piezoelectric valve driven by a varying voltage, the proposed control laws ensure convergence to reference values of chamber pressure during pre-fill, and of plasma density during plasma discharge. Experimental results at FTU are presented to discuss weaknesses and strengths of the proposed control strategy. The whole system has been implemented by using the MARTe framework [1].
An Adaptive Speed Control Approach for DC Shunt Motors
Directory of Open Access Journals (Sweden)
Ruben Tapia-Olvera
2016-11-01
Full Text Available A B-spline neural networks-based adaptive control technique for angular speed reference trajectory tracking tasks with highly efficient performance for direct current shunt motors is proposed. A methodology for adaptive control and its proper training procedure are introduced. This algorithm sets the control signal without using a detailed mathematical model nor exact values of the parameters of the nonlinear dynamic system. The proposed robust adaptive tracking control scheme only requires measurements of the velocity output signal. Thus, real-time measurements or estimations of acceleration, current and disturbance signals are avoided. Experimental results confirm the efficient and robust performance of the proposed control approach for highly demanding motor operation conditions exposed to variable-speed reference trajectories and completely unknown load torque. Hence, laboratory experimental tests on a direct current shunt motor prove the viability of the proposed adaptive output feedback trajectory tracking control approach.
Separation of Dirac's Hamiltonian by Van Vleck transformation
Jørgensen, Flemming
2017-01-01
The now classic Foldy-Wouthuysen transformation (FWT) was introduced as successive unitary transformations. This fundamental idea has become the standard in later developments such as the Douglas-Kroll transformation (DKT) - but it is not the only possibility. FWT can be seen as a simple special case of the general Van Vleck transformation (VVT) which besides the successive version has another, known as the canonical because of a series of nice mathematical properties discovered gradually over time. The aim of the present paper is to compare the two approaches - which give identical results in the lower orders, but not in the higher. After having recapitalised both, we apply them to Dirac's Hamiltonian for the electron in a constant electromagnetic field, written with so few assumptions about the operators that the mathematical techniques stand out separated from the terminology of relativistic quantum mechanics. FWT for a free particle is dealt with by a recent geometric approach to VVT. The original FWT is continued through the next non-zero orders. DKT is considered with special weight on equivalent formulations of the generalised and the optimised forms introduced by Wolf, Reiher and Hess.
A Goal-Function Approach to Analysis of Control Situations
DEFF Research Database (Denmark)
Lind, Morten
2010-01-01
The concept of situations plays a central role in all theories of meaning and context. and serve to frame or group events and other occurrences into coherent meaningful wholes. Situations are typed, may be interconnected and organized into higher level structures. In operation of industrial...... processes situations should identify operational aspects relevant for control agent’s decision making in plant supervision and control. Control situations can be understood as recurrent and interconnected patterns of control with important implications for control and HMI design. Goal-Function approaches...
Assessing the Approaches to Classification of the State Financial Control
Baraniuk Yurii R.
2017-01-01
The article is aimed at assessing the approaches to classification of the State financial control, as well as disclosing the relationship and differences between its forms, types and methods. The results of comparative analysis of existing classifications of the State financial control have been covered. The substantiation of its identification by forms, types and methods of control was explored. Clarification of the interpretation of the concepts of «form of control», «type of control», «sub...
Nonlinear identification and control a neural network approach
Liu, G P
2001-01-01
The series Advances in Industrial Control aims to report and encourage technology transfer in control engineering. The rapid development of control technology has an impact on all areas of the control discipline. New theory, new controllers, actuators, sensors, new industrial processes, computer methods, new applications, new philosophies . . . , new challenges. Much of this development work resides in industrial reports, feasibility study papers and the reports of advanced collaborative projects. The series otTers an opportunity for researchers to present an extended exposition of such new work in all aspects of industrial control for wider and rapid dissemination. The time for nonlinear control to enter routine application seems to be approaching. Nonlinear control has had a long gestation period but much ofthe past has been concerned with methods that involve formal nonlinear functional model representations. It seems more likely that the breakthough will come through the use of other more flexible and ame...
Parametric Approach to Trajectory Tracking Control of Robot Manipulators
Directory of Open Access Journals (Sweden)
Shijie Zhang
2013-01-01
Full Text Available The mathematic description of the trajectory of robot manipulators with the optimal trajectory tracking problem is formulated as an optimal control problem, and a parametric approach is proposed for the optimal trajectory tracking control problem. The optimal control problem is first solved as an open loop optimal control problem by using a time scaling transform and the control parameterization method. Then, by virtue of the relationship between the optimal open loop control and the optimal closed loop control along the optimal trajectory, a practical method is presented to calculate an approximate optimal feedback gain matrix, without having to solve an optimal control problem involving the complex Riccati-like matrix differential equation coupled with the original system dynamics. Simulation results of 2-link robot manipulator are presented to show the effectiveness of the proposed method.
Stochastic Control of Energy Efficient Buildings: A Semidefinite Programming Approach
Energy Technology Data Exchange (ETDEWEB)
Ma, Xiao [ORNL; Dong, Jin [ORNL; Djouadi, Seddik M [ORNL; Nutaro, James J [ORNL; Kuruganti, Teja [ORNL
2015-01-01
The key goal in energy efficient buildings is to reduce energy consumption of Heating, Ventilation, and Air- Conditioning (HVAC) systems while maintaining a comfortable temperature and humidity in the building. This paper proposes a novel stochastic control approach for achieving joint performance and power control of HVAC. We employ a constrained Stochastic Linear Quadratic Control (cSLQC) by minimizing a quadratic cost function with a disturbance assumed to be Gaussian. The problem is formulated to minimize the expected cost subject to a linear constraint and a probabilistic constraint. By using cSLQC, the problem is reduced to a semidefinite optimization problem, where the optimal control can be computed efficiently by Semidefinite programming (SDP). Simulation results are provided to demonstrate the effectiveness and power efficiency by utilizing the proposed control approach.
A methodological approach to designing sewer system control
DEFF Research Database (Denmark)
Mollerup, Ane Loft
for this thesis was therefore the wish for a methodological approach to sewer system control design. Using a case study the following research hypothesis was tested in this thesis: Using classical and modern control theory, a methodological approach can be derived for designing sewer system control. This can aid....... This was not unexpected, since the true potential of having optimisation arises, when a system has many control loops with limit-ing constraints and/or changing prioritisation between them. The results showed that for small sewer systems, where the complexity is limited, it is not necessarily the best option to implement...... generate control systems of the future that are more robust, more structured, have a better performance and are easi-er to maintain....
g Algebra and two-dimensional quasiexactly solvable Hamiltonian ...
Indian Academy of Sciences (India)
Keywords. g2 algebra; quasiexactly solvable Hamiltonian; hidden algebra; Poschl–Teller potential. ... space of the polynomials, restricting to a linear transformation on this space, the associ- .... The operators L6 and L7 are the positive root.
Integrable Hamiltonian systems and interactions through quadratic constraints
International Nuclear Information System (INIS)
Pohlmeyer, K.
1975-08-01
Osub(n)-invariant classical relativistic field theories in one time and one space dimension with interactions that are entirely due to quadratic constraints are shown to be closely related to integrable Hamiltonian systems. (orig.) [de
Towards practical characterization of quantum systems with quantum Hamiltonian learning
Santagati, R.; Wang, J.; Paesani, S.; Knauer, S.; Gentile, A. A.; Wiebe, N.; Petruzzella, M.; O'Brien, J. L.; Rarity, J. G.; Laing, A.; Thompson, M. G.
2017-01-01
Here we show the first experimental implementation of quantum Hamiltonian Learning, where a silicon-on-insulator quantum photonic simulator is used to learn the dynamics of an electron-spin in an NV center in diamond.
On the quantization of sectorially Hamiltonian dissipative systems
Energy Technology Data Exchange (ETDEWEB)
Castagnino, M. [Instituto de Fisica de Rosario, 2000 Rosario (Argentina); Instituto de Astronomia y Fisica del Espacio, Casilla de Correos 67, Sucursal 28, 1428 Buenos Aires (Argentina); Gadella, M. [Instituto de Fisica de Rosario, 2000 Rosario (Argentina); Departamento de Fisica Teorica, Atomica y Optica, Facultad de Ciencias, Universidad de Valladolid, 47005 Valladolid (Spain)], E-mail: manuelgadella@yahoo.com.ar; Lara, L.P. [Instituto de Fisica de Rosario, 2000 Rosario (Argentina); Facultad Regional Rosario, UTN, 2000 Rosario (Argentina)
2009-10-15
We present a theoretical discussion showing that, although some dissipative systems may have a sectorial Hamiltonian description, this description does not allow for canonical quantization. However, a quantum Liouville counterpart of these systems is possible, although it is not unique.
On the quantization of sectorially Hamiltonian dissipative systems
International Nuclear Information System (INIS)
Castagnino, M.; Gadella, M.; Lara, L.P.
2009-01-01
We present a theoretical discussion showing that, although some dissipative systems may have a sectorial Hamiltonian description, this description does not allow for canonical quantization. However, a quantum Liouville counterpart of these systems is possible, although it is not unique.
A local inverse spectral theorem for Hamiltonian systems
International Nuclear Information System (INIS)
Langer, Matthias; Woracek, Harald
2011-01-01
We consider (2 × 2)-Hamiltonian systems of the form y'(x) = zJH(x)y(x), x in [s − , s + ). If a system of this form is in the limit point case, an analytic function is associated with it, namely its Titchmarsh–Weyl coefficient q H . The (global) uniqueness theorem due to de Branges says that the Hamiltonian H is (up to reparameterization) uniquely determined by the function q H . In this paper we give a local uniqueness theorem; if the Titchmarsh–Weyl coefficients q H 1 and q H 2 corresponding to two Hamiltonian systems are exponentially close, then the Hamiltonians H 1 and H 2 coincide (up to reparameterization) up to a certain point of their domain, which depends on the quantitative degree of exponential closeness of the Titchmarsh–Weyl coefficients
A new approach of active compliance control via fuzzy logic control for multifingered robot hand
Jamil, M. F. A.; Jalani, J.; Ahmad, A.
2016-07-01
Safety is a vital issue in Human-Robot Interaction (HRI). In order to guarantee safety in HRI, a model reference impedance control can be a very useful approach introducing a compliant control. In particular, this paper establishes a fuzzy logic compliance control (i.e. active compliance control) to reduce impact and forces during physical interaction between humans/objects and robots. Exploiting a virtual mass-spring-damper system allows us to determine a desired compliant level by understanding the behavior of the model reference impedance control. The performance of fuzzy logic compliant control is tested in simulation for a robotic hand known as the RED Hand. The results show that the fuzzy logic is a feasible control approach, particularly to control position and to provide compliant control. In addition, the fuzzy logic control allows us to simplify the controller design process (i.e. avoid complex computation) when dealing with nonlinearities and uncertainties.
Time and a physical Hamiltonian for quantum gravity.
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
A hierarchy of Liouville integrable discrete Hamiltonian equations
Energy Technology Data Exchange (ETDEWEB)
Xu Xixiang [College of Science, Shandong University of Science and Technology, Qingdao 266510 (China)], E-mail: xixiang_xu@yahoo.com.cn
2008-05-12
Based on a discrete four-by-four matrix spectral problem, a hierarchy of Lax integrable lattice equations with two potentials is derived. Two Hamiltonian forms are constructed for each lattice equation in the resulting hierarchy by means of the discrete variational identity. A strong symmetry operator of the resulting hierarchy is given. Finally, it is shown that the resulting lattice equations are all Liouville integrable discrete Hamiltonian systems.
On the topological entropy of an optical Hamiltonian flow
Niche, Cesar J.
2000-01-01
In this article we prove two formulas for the topological entropy of an F-optical Hamiltonian flow induced by a C^{\\infty} Hamiltonian, where F is a Lagrangian distribution. In these formulas, we calculate the topological entropy as the exponential growth rate of the average of the determinant of the differential of the flow, restricted to the Lagrangian distribution or to a proper modification.
SOLVING THE HAMILTONIAN CYCLE PROBLEM USING SYMBOLIC DETERMINANTS
Ejov, V.; Filar, J. A.; Lucas, S. K.; Nelson, J. L.
2006-01-01
In this note we show how the Hamiltonian Cycle problem can be reduced to solving a system of polynomial equations related to the adjacency matrix of a graph. This system of equations can be solved using the method of Gröbner bases, but we also show how a symbolic determinant related to the adjacency matrix can be used to directly decide whether a graph has a Hamiltonian cycle.
Noncanonical Hamiltonian density formulation of hydrodynamics and ideal MHD
International Nuclear Information System (INIS)
Morrison, P.J.; Greene, J.M.
1980-04-01
A new Hamiltonian density formulation of a perfect fluid with or without a magnetic field is presented. Contrary to previous work the dynamical variables are the physical variables, rho, v, B, and s, which form a noncanonical set. A Poisson bracket which satisfies the Jacobi identity is defined. This formulation is transformed to a Hamiltonian system where the dynamical variables are the spatial Fourier coefficients of the fluid variables
Families of superintegrable Hamiltonians constructed from exceptional polynomials
International Nuclear Information System (INIS)
Post, Sarah; Tsujimoto, Satoshi; Vinet, Luc
2012-01-01
We introduce a family of exactly-solvable two-dimensional Hamiltonians whose wave functions are given in terms of Laguerre and exceptional Jacobi polynomials. The Hamiltonians contain purely quantum terms which vanish in the classical limit leaving only a previously known family of superintegrable systems. Additional, higher-order integrals of motion are constructed from ladder operators for the considered orthogonal polynomials proving the quantum system to be superintegrable. (paper)
Orbits and variational principles for conservative Hamiltonian systems
International Nuclear Information System (INIS)
Torres del Castillo, G.F.
1989-01-01
It is shown that for any Hamiltonian system whose Hamiltonian is time-independent the equations that determine the orbits followed by the system, without making reference to time, have the form of Hamilton's equations in a phase space of dimension two units smaller than that of the original phase space. By considering the cases of classical mechanics and of geometrical optics, it is shown that this result amounts, respectively, to Maupertuis' least action principle and to Fermat's principle. (Author)
Zając, Magdalena; Rudowicz, Czesław; Ohta, Hitoshi; Sakurai, Takahiro
2018-03-01
Utilizing the package MSH/VBA, based on the microscopic spin Hamiltonian (MSH) approach, spectroscopic and magnetic properties of Fe2+ (3d6; S = 2) ions at (nearly) orthorhombic sites in Fe(NH4)2(SO4)2·6H2O (FASH) are modeled. The zero-field splitting (ZFS) parameters and the Zeeman electronic (Ze) factors are predicted for wide ranges of values of the microscopic parameters, i.e. the spin-orbit (λ), spin-spin (ρ) coupling constants, and the crystal-field (ligand-field) energy levels (Δi) within the 5D multiplet. This enables to consider the dependence of the ZFS parameters bkq (in the Stevens notation), or the conventional ones (e.g., D and E), and the Zeeman factors gi on λ, ρ, and Δi. By matching the theoretical SH parameters and the experimental ones measured by electron magnetic resonance (EMR), the values of λ, ρ, and Δi best describing Fe2+ ions in FASH are determined. The novel aspect is prediction of the fourth-rank ZFS parameters and the ρ(spin-spin)-related contributions, not considered in previous studies. The higher-order contributions to the second- and fourth-rank ZFSPs are found significant. The MSH predictions provide guidance for high-magnetic field and high-frequency EMR (HMF-EMR) measurements and enable assessment of suitability of FASH for application as high-pressure probes for HMF-EMR studies. The method employed here and the present results may be also useful for other structurally related Fe2+ (S = 2) systems.
An ecosystem approach to malaria control in an urban setting
Directory of Open Access Journals (Sweden)
Carrasquilla Gabriel
2001-01-01
Full Text Available We conducted a research project aimed at strengthening local government and the community for a sustainable malaria control strategy. The project began with a baseline diagnosis of malaria prevalence, a KAP survey, entomology, and health services delivery, after which an epidemiological study was performed to identify risk factors associated with malaria, thereafter used to plan intervention measures. A program evaluation was conducted five years later. By using an ecosystem approach to reanalyze data, this paper discusses how malaria arises from a complex interaction of cultural, economic, ecological, social, and individual factors. Intervention measures require an intersectorial and transdisciplinary approach that does not exist at the moment. Health sector leadership is limited, and there is no true community participation. Implications for research, including the use of qualitative and quantitative methods, study design, and complexity of data analysis are discussed. Finally, implications for malaria control are discussed, stressing the differences between the ecosystem and integrated disease control approaches.
Spectral bounds for the PT-breaking Hamiltonian p2 + x4 + iax
International Nuclear Information System (INIS)
Handy, C R; Wang Xiaoqian
2003-01-01
The non-Hermitian Hamiltonian p 2 + x 4 + iax, which spontaneously breaks PT-symmetry, and the subject of a recent study by Bender et al (2001 J. Phys. A: Math. Gen. 34 L31), is amenable to a positivity representation, facilitating the generation of converging bounds to the complex-eigenenergies of the PT-breaking states. This system is much easier (i.e. fewer variational parameters) than the previously studied case of the Hamiltonian p 2 + ix 3 + iax (2001 Handy J. Phys. A: Math. Gen. 34 5065, Handy et al 2001 J. Phys. A: Math. Gen. 34 5593), as first proposed by Delabaere and Trinh (2000 J. Phys. A: Math. Gen. 33 8771), enabling the generation of low order algebraic spectral bounds (i.e. Re(E) > 81/4 (Im(E)/a) 4 + O(a 2 )), in addition to high order, numerically generated, converging bounds to the discrete states. We examine both approaches here
International Nuclear Information System (INIS)
Skachkov, N.; Solovtsov, I.
1979-01-01
Based on the hamiltonian formulation of quantum field theory proposed by Kadyshevsky the three-dimensional relativistic approach is developed for describing the form factors of composite systems. The main features of the diagram technique appearing in the covariant hamiltonian formulation of field theory are discussed. The three-dimensional relativistic equation for the vertex function is derived and its connection with that for the quasipotential wave function is found. The expressions are obtained for the form factor of the system through equal-time two-particle wave functions both in momentum and relativistic configurational representations. An explicit expression for the form factor is found for the case of two-particle interaction through the Coulomb potential
Complexified coherent states and quantum evolution with non-Hermitian Hamiltonians
International Nuclear Information System (INIS)
Graefe, Eva-Maria; Schubert, Roman
2012-01-01
The complex geometry underlying the Schrödinger dynamics of coherent states for non-Hermitian Hamiltonians is investigated. In particular, two seemingly contradictory approaches are compared: (i) a complex WKB formalism, for which the centres of coherent states naturally evolve along complex trajectories, which leads to a class of complexified coherent states; (ii) the investigation of the dynamical equations for the real expectation values of position and momentum, for which an Ehrenfest theorem has been derived in a previous paper, yielding real but non-Hamiltonian classical dynamics on phase space for the real centres of coherent states. Both approaches become exact for quadratic Hamiltonians. The apparent contradiction is resolved building on an observation by Huber, Heller and Littlejohn, that complexified coherent states are equivalent if their centres lie on a specific complex Lagrangian manifold. A rich underlying complex symplectic geometry is unravelled. In particular, a natural complex structure is identified that defines a projection from complex to real phase space, mapping complexified coherent states to their real equivalents. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’. (paper)
Weak form of Stokes-Dirac structures and geometric discretization of port-Hamiltonian systems
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.
Controller synthesis for negative imaginary systems: a data driven approach
Mabrok, Mohamed
2016-02-17
The negative imaginary (NI) property occurs in many important applications. For instance, flexible structure systems with collocated force actuators and position sensors can be modelled as negative imaginary systems. In this study, a data-driven controller synthesis methodology for NI systems is presented. In this approach, measured frequency response data of the plant is used to construct the controller frequency response at every frequency by minimising a cost function. Then, this controller response is used to identify the controller transfer function using system identification methods. © The Institution of Engineering and Technology 2016.
Episodic reinforcement learning control approach for biped walking
Directory of Open Access Journals (Sweden)
Katić Duško
2012-01-01
Full Text Available This paper presents a hybrid dynamic control approach to the realization of humanoid biped robotic walk, focusing on the policy gradient episodic reinforcement learning with fuzzy evaluative feedback. The proposed structure of controller involves two feedback loops: a conventional computed torque controller and an episodic reinforcement learning controller. The reinforcement learning part includes fuzzy information about Zero-Moment- Point errors. Simulation tests using a medium-size 36-DOF humanoid robot MEXONE were performed to demonstrate the effectiveness of our method.
APE (state-oriented approach) centralized control procedures
International Nuclear Information System (INIS)
Astier, D.; Depont, G.; Van Dermarliere, Y.
2004-01-01
This article presents the progressive implementation of the state-oriented approach (APE) for centralized control procedures in French nuclear power plants. The implementation began in the years 1982-83 and it concerned only the circuits involved in engineered safeguard systems such IS (safety injection), EAS (containment spray system) and GMPP (reactor coolant pump set). In 2003 the last PWR unit switched from the event oriented approach to APE for post-accidental situations
A new approach to adaptive control of manipulators
Seraji, H.
1987-01-01
An approach in which the manipulator inverse is used as a feedforward controller is employed in the adaptive control of manipulators in order to achieve trajectory tracking by the joint angles. The desired trajectory is applied as an input to the feedforward controller, and the controller output is used as the driving torque for the manipulator. An adaptive algorithm obtained from MRAC theory is used to update the controller gains to cope with variations in the manipulator inverse due to changes of the operating point. An adaptive feedback controller and an auxiliary signal enhance closed-loop stability and achieve faster adaptation. Simulation results demonstrate the effectiveness of the proposed control scheme for different reference trajectories, and despite large variations in the payload.
Oscillator representations for self-adjoint Calogero Hamiltonians
Energy Technology Data Exchange (ETDEWEB)
Gitman, D M [Institute of Physics, University of Sao Paulo (Brazil); Tyutin, I V; Voronov, B L, E-mail: gitman@dfn.if.usp.br, E-mail: tyutin@lpi.ru, E-mail: voronov@lpi.ru [Lebedev Physical Institute, Moscow (Russian Federation)
2011-10-21
In Gitman et al (2010 J. Phys. A: Math. Theor. 43 145205), we presented a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential V(x) = {alpha}x{sup -2}. We described all possible self-adjoint (s.a.) operators (s.a. Hamiltonians) associated with the differential operation H=-d{sub x}{sup 2}+{alpha}x{sup -2} for the Calogero Hamiltonian. Here, we discuss a new aspect of the problem, the so-called oscillator representations for the Calogero Hamiltonians. As is known, operators of the form N-hat = a-hat{sup +} a-hat and A-hat = a-hat a-hat{sup +} are called operators of oscillator type. Oscillator-type operators possess a number of useful properties in the case when the elementary operators a-hat are closed. It turns out that some s.a. Calogero Hamiltonians allow oscillator-type representations. We describe such Hamiltonians and find the corresponding mutually adjoint elementary operators a-hat and a-hat{sup +}. An oscillator-type representation for a given Hamiltonian is generally not unique. (paper)
Oscillator representations for self-adjoint Calogero Hamiltonians
International Nuclear Information System (INIS)
Gitman, D M; Tyutin, I V; Voronov, B L
2011-01-01
In Gitman et al (2010 J. Phys. A: Math. Theor. 43 145205), we presented a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential V(x) = αx -2 . We described all possible self-adjoint (s.a.) operators (s.a. Hamiltonians) associated with the differential operation H=-d x 2 +αx -2 for the Calogero Hamiltonian. Here, we discuss a new aspect of the problem, the so-called oscillator representations for the Calogero Hamiltonians. As is known, operators of the form N-hat = a-hat + a-hat and A-hat = a-hat a-hat + are called operators of oscillator type. Oscillator-type operators possess a number of useful properties in the case when the elementary operators a-hat are closed. It turns out that some s.a. Calogero Hamiltonians allow oscillator-type representations. We describe such Hamiltonians and find the corresponding mutually adjoint elementary operators a-hat and a-hat + . An oscillator-type representation for a given Hamiltonian is generally not unique. (paper)
International Nuclear Information System (INIS)
Brandow, B.H.
1977-01-01
The Brueckner--Goldstone form of linked-cluster perturbation theory is derived, together with its open-shell analog, by an elementary time-independent approach. This serves to focus attention on the physical interpretation of the results. The open-shell expansion is used to provide a straightforward justification for the effective π-electron Hamiltonians of planar organic molecules
Accreting fluids onto regular black holes via Hamiltonian approach
Energy Technology Data Exchange (ETDEWEB)
Jawad, Abdul [COMSATS Institute of Information Technology, Department of Mathematics, Lahore (Pakistan); Shahzad, M.U. [COMSATS Institute of Information Technology, Department of Mathematics, Lahore (Pakistan); University of Central Punjab, CAMS, UCP Business School, Lahore (Pakistan)
2017-08-15
We investigate the accretion of test fluids onto regular black holes such as Kehagias-Sfetsos black holes and regular black holes with Dagum distribution function. We analyze the accretion process when different test fluids are falling onto these regular black holes. The accreting fluid is being classified through the equation of state according to the features of regular black holes. The behavior of fluid flow and the existence of sonic points is being checked for these regular black holes. It is noted that the three-velocity depends on critical points and the equation of state parameter on phase space. (orig.)
A Hamiltonian approach to model and analyse networks of ...
Indian Academy of Sciences (India)
and a microwave signal generator at the nanoscale. ..... The AC signal is then fed into a rectifier and a related power converter circuit that stores the ..... [17] R Rogers, Applied mathematics in integrated navigation systems (American Institute of.
An Approach to Robust Control of the Hopf Bifurcation
Directory of Open Access Journals (Sweden)
Giacomo Innocenti
2011-01-01
Full Text Available The paper illustrates a novel approach to modify the Hopf bifurcation nature via a nonlinear state feedback control, which leaves the equilibrium properties unchanged. This result is achieved by recurring to linear and nonlinear transformations, which lead the system to locally assume the ordinary differential equation representation. Third-order models are considered, since they can be seen as proper representatives of a larger class of systems. The explicit relationship between the control input and the Hopf bifurcation nature is obtained via a frequency approach, that does not need the computation of the center manifold.
The control-of-consumption approach to alcohol abuse prevention
DEFF Research Database (Denmark)
Ravn, Ib
1987-01-01
Key empirical studies of the postulates of the single-distribution theory and the associated control-of-consumption approach are reviewed. The review is organized in terms of the six links possible between the four variables of the "Ledermann string" (availability, average consumption, proportion...... of heavy consumers, and prevalence of damage) presented in Part I. It is concluded that, on the whole, the available evidence is too inconsistent to support the control-of-consumption approach and that a more comprehensive understanding of alcohol abuse and prevention is needed....
Optimization of nonlinear controller with an enhanced biogeography approach
Directory of Open Access Journals (Sweden)
Mohammed Salem
2014-07-01
Full Text Available This paper is dedicated to the optimization of nonlinear controllers basing of an enhanced Biogeography Based Optimization (BBO approach. Indeed, The BBO is combined to a predator and prey model where several predators are used with introduction of a modified migration operator to increase the diversification along the optimization process so as to avoid local optima and reach the optimal solution quickly. The proposed approach is used in tuning the gains of PID controller for nonlinear systems. Simulations are carried out over a Mass spring damper and an inverted pendulum and has given remarkable results when compared to genetic algorithm and BBO.
Combinatorial quantization of the Hamiltonian Chern-Simons theory
International Nuclear Information System (INIS)
Alekseev, A.Yu.; Grosse, H.; Schomerus, V.
1996-01-01
This paper further develops the combinatorial approach to quantization of the Hamiltonian Chern Simons theory. Using the theory of quantum Wilson lines, we show how the Verlinde algebra appears within the context of quantum group gauge theory. This allows to discuss flatness of quantum connections so that we can give a mathematically rigorous definition of the algebra of observables A CS of the Chern Simons model. It is a *-algebra of ''functions on the quantum moduli space of flat connections'' and comes equipped with a positive functional ω (''integration''). We prove that this data does not depend on the particular choices which have been made in the construction. The algebra A CS provides a deformation quantization of the algebra of functions on the moduli space along the natural Poisson bracket induced by the Chern Simons action. We evaluate a volume of the quantized moduli space and prove that it coincides with the Verlinde number. This answer is also interpreted as a partition partition function of the lattice Yang-Mills theory corresponding to a quantum gauge group. (orig.). With 1 fig
Hamiltonian analysis for linearly acceleration-dependent Lagrangians
Energy Technology Data Exchange (ETDEWEB)
Cruz, Miguel, E-mail: miguelcruz02@uv.mx, E-mail: roussjgc@gmail.com, E-mail: molgado@fc.uaslp.mx, E-mail: efrojas@uv.mx; Gómez-Cortés, Rosario, E-mail: miguelcruz02@uv.mx, E-mail: roussjgc@gmail.com, E-mail: molgado@fc.uaslp.mx, E-mail: efrojas@uv.mx; Rojas, Efraín, E-mail: miguelcruz02@uv.mx, E-mail: roussjgc@gmail.com, E-mail: molgado@fc.uaslp.mx, E-mail: efrojas@uv.mx [Facultad de Física, Universidad Veracruzana, 91000 Xalapa, Veracruz, México (Mexico); Molgado, Alberto, E-mail: miguelcruz02@uv.mx, E-mail: roussjgc@gmail.com, E-mail: molgado@fc.uaslp.mx, E-mail: efrojas@uv.mx [Facultad de Ciencias, Universidad Autónoma de San Luis Potosí, Avenida Salvador Nava S/N Zona Universitaria, CP 78290 San Luis Potosí, SLP, México (Mexico)
2016-06-15
We study the constrained Ostrogradski-Hamilton framework for the equations of motion provided by mechanical systems described by second-order derivative actions with a linear dependence in the accelerations. We stress out the peculiar features provided by the surface terms arising for this type of theories and we discuss some important properties for this kind of actions in order to pave the way for the construction of a well defined quantum counterpart by means of canonical methods. In particular, we analyse in detail the constraint structure for these theories and its relation to the inherent conserved quantities where the associated energies together with a Noether charge may be identified. The constraint structure is fully analyzed without the introduction of auxiliary variables, as proposed in recent works involving higher order Lagrangians. Finally, we also provide some examples where our approach is explicitly applied and emphasize the way in which our original arrangement results in propitious for the Hamiltonian formulation of covariant field theories.
Model predictive control approach for a CPAP-device
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Scheel Mathias
2017-09-01
Full Text Available The obstructive sleep apnoea syndrome (OSAS is characterized by a collapse of the upper respiratory tract, resulting in a reduction of the blood oxygen- and an increase of the carbon dioxide (CO2 - concentration, which causes repeated sleep disruptions. The gold standard to treat the OSAS is the continuous positive airway pressure (CPAP therapy. The continuous pressure keeps the upper airway open and prevents the collapse of the upper respiratory tract and the pharynx. Most of the available CPAP-devices cannot maintain the pressure reference [1]. In this work a model predictive control approach is provided. This control approach has the possibility to include the patient’s breathing effort into the calculation of the control variable. Therefore a patient-individualized control strategy can be developed.
New approaches in intelligent control techniques, methodologies and applications
Kountchev, Roumen
2016-01-01
This volume introduces new approaches in intelligent control area from both the viewpoints of theory and application. It consists of eleven contributions by prominent authors from all over the world and an introductory chapter. This volume is strongly connected to another volume entitled "New Approaches in Intelligent Image Analysis" (Eds. Roumen Kountchev and Kazumi Nakamatsu). The chapters of this volume are self-contained and include summary, conclusion and future works. Some of the chapters introduce specific case studies of various intelligent control systems and others focus on intelligent theory based control techniques with applications. A remarkable specificity of this volume is that three chapters are dealing with intelligent control based on paraconsistent logics.