A CLASS OF QUADRATIC HAMILTONIAN SYSTEMS UNDER QUADRATIC PERTURBATION
Institute of Scientific and Technical Information of China (English)
丰建文; 陈士华
2001-01-01
This paper deals with a class of quadratic Hamiltonian systems with quadratic perturbation. The authors prove that if the first order Melnikov function M1(h) = 0 and the second order Melnikov function M2(h) ≡ 0, then the origin of the Hamiltonian system with small perturbation is a center.
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.
Symmetric quadratic Hamiltonians with pseudo-Hermitian matrix representation
Energy Technology Data Exchange (ETDEWEB)
Fernández, Francisco M., E-mail: fernande@quimica.unlp.edu.ar
2016-06-15
We prove that any symmetric Hamiltonian that is a quadratic function of the coordinates and momenta has a pseudo-Hermitian adjoint or regular matrix representation. The eigenvalues of the latter matrix are the natural frequencies of the Hamiltonian operator. When all the eigenvalues of the matrix are real, then the spectrum of the symmetric Hamiltonian is real and the operator is Hermitian. As illustrative examples we choose the quadratic Hamiltonians that model a pair of coupled resonators with balanced gain and loss, the electromagnetic self-force on an oscillating charged particle and an active LRC circuit. -- Highlights: •Symmetric quadratic operators are useful models for many physical applications. •Any such operator exhibits a pseudo-Hermitian matrix representation. •Its eigenvalues are the natural frequencies of the Hamiltonian operator. •The eigenvalues may be real or complex and describe a phase transition.
Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations
DEFF Research Database (Denmark)
Nam, Phan Thanh; Napiorkowski, Marcin; Solovej, Jan Philip
2016-01-01
We provide general conditions for which bosonic quadratic Hamiltonians on Fock spaces can be diagonalized by Bogoliubov transformations. Our results cover the case when quantum systems have infinite degrees of freedom and the associated one-body kinetic and paring operators are unbounded. Our...
Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations
DEFF Research Database (Denmark)
Nam, Phan Thanh; Napiorkowski, Marcin; Solovej, Jan Philip
2016-01-01
We provide general conditions for which bosonic quadratic Hamiltonians on Fock spaces can be diagonalized by Bogoliubov transformations. Our results cover the case when quantum systems have infinite degrees of freedom and the associated one-body kinetic and paring operators are unbounded. Our...
Twistless Version of Thirring's Approach to the KAM Theorem for Quadratic Hamiltonians
Chandre, C
1998-01-01
We give a proof of the KAM theorem on the existence of invariant tori for weakly perturbed Hamiltonian systems, based on Thirring's approach for Hamiltonians that are quadratic in the action variables. The main point of this approach is that the iteration of canonical transformations on which the proof is based stays within the space of quadratic Hamiltonians. We show that Thirring's proof for nondegenerate Hamiltonians can be adapted to twistless Hamiltonians. This twistless assumption, in fact, drastically simplifies Thirring's proof.
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.
Global stability and quadratic Hamiltonian structure in Lotka-Volterra and quasi-polynomial systems
Energy Technology Data Exchange (ETDEWEB)
Szederkenyi, Gabor; Hangos, Katalin M
2004-04-26
We show that the global stability of quasi-polynomial (QP) and Lotka-Volterra (LV) systems with the well-known logarithmic Lyapunov function is equivalent to the existence of a local generalized dissipative Hamiltonian description of the LV system with a diagonal quadratic form as a Hamiltonian function. The Hamiltonian function can be calculated and the quadratic dissipativity neighborhood of the origin can be estimated by solving linear matrix inequalities.
The quadratic-form identity for constructing Hamiltonian structures of the Guo hierarchy
Institute of Scientific and Technical Information of China (English)
Dong Huan-He; Zhang Ning
2006-01-01
The trace identity is extended to the quadratic-form identity. The Hamiltonian structures of the multi-component Guo hierarchy, integrable coupling of Guo hierarchy and (2+1)-dimensional Guo hierarchy are obtained by the quadraticform identity. The method can be used to produce the Hamiltonian structures of the other integrable couplings or multi-component hierarchies.
Vladimirov, Igor G
2012-01-01
This paper extends the energy-based version of the stochastic linearization method, known for classical nonlinear systems, to open quantum systems with canonically commuting dynamic variables governed by quantum stochastic differential equations with non-quadratic Hamiltonians. The linearization proceeds by approximating the actual Hamiltonian of the quantum system by a quadratic function of its observables which corresponds to the Hamiltonian of a quantum harmonic oscillator. This approximation is carried out in a mean square optimal sense with respect to a Gaussian reference quantum state and leads to a self-consistent linearization procedure where the mean vector and quantum covariance matrix of the system observables evolve in time according to the effective linear dynamics. We demonstrate the proposed Hamiltonian-based Gaussian linearization for the quantum Duffing oscillator whose Hamiltonian is a quadro-quartic polynomial of the momentum and position operators. The results of the paper are applicable t...
The wave function and minimum uncertainty function of the bound quadratic Hamiltonian system
Yeon, Kyu Hwang; Um, Chung IN; George, T. F.
1994-01-01
The bound quadratic Hamiltonian system is analyzed explicitly on the basis of quantum mechanics. We have derived the invariant quantity with an auxiliary equation as the classical equation of motion. With the use of this invariant it can be determined whether or not the system is bound. In bound system we have evaluated the exact eigenfunction and minimum uncertainty function through unitary transformation.
Existence for stationary mean-field games with congestion and quadratic Hamiltonians
Gomes, Diogo A.
2015-09-03
Here, we investigate the existence of solutions to a stationary mean-field game model introduced by J.-M. Lasry and P.-L. Lions. This model features a quadratic Hamiltonian and congestion effects. The fundamental difficulty of potential singular behavior is caused by congestion. Thanks to a new class of a priori bounds, combined with the continuation method, we prove the existence of smooth solutions in arbitrary dimensions. © 2015 Springer Basel
On nondecomposable positive definite Hermitian forms over imaginary quadratic fields
Institute of Scientific and Technical Information of China (English)
ZHU; Fuzu
2001-01-01
［1］Mordell, L. J., The representation of a definite quadratic form as a sum of two others, Ann. of Math., 937, 38: 75.［2］Erds, P., Ko Chao, On definite quadratic forms, which are not the sum of two definite or semidefinite forms, Acta Arith., 939, 3: 02.［3］Erds, P., Ko Chao, Some results on definite quadratic forms, J. London Math. Soc., 938, 3: 27.［4］Zhu Fu-zu, Construction of nondecomposable positive definite quadratic forms, Sci. Sinica, Ser. A, 987, 30(): 9.［5］Zhu Fuzu, On nondecomposability and indecomposability of quadratic forms, Sci. Sinica, Ser. A, 988, 3(3): 265.［6］Pleskin, W., Additively indecomposable positive integral quadratic forms, J. Number Theory, 994, 47: 273.［7］Zhu Fuzu, An existence theorem on positive definite unimodular even Hermitian forms, Chinese Ann. of Math., Ser. A, 984, 5: 33.［8］Zhu Fu-Zu, On the construction of positive definite indecomposable unimodular even Hermitian forms, J. Number Theory, 995, 30: 38.［9］O'Meara, O. T., Introduction to Quadratic Forms, Berlin, New York: Springer-Verlag, 973.［10］Zhu Fuzu, Construction of indecomposable definite Hermitian forms, Chinese Ann. of Math., Ser. B, 994, 5: 349.［11］Zhu Fuzu, On nondecomposable Hermitian forms over Gaussian domain, Acta Math. Sinica, New Ser., 998, 4: 447.
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.
On Schroedinger Equation with Time-Dependent Quadratic Hamiltonian in $R^d$
Suazo, Erwin
2009-01-01
We study solutions to the Cauchy problem for the equation i\\frac{\\partial \\psi}{\\partial t}=H(t) \\psi + +h|\\psi|^{p-1}\\psi, with a quadratic Hamiltonian depending on time H(t)\\psi ={1/2}\\Delta \\psi +\\sum_{j=1}^{d}(\\frac{b_{j}(t)}{2}x_{j}^{2}\\psi -f_{j}(t)x_{j}\\psi +ig_{j}(t)\\frac{\\partial \\psi}{\\partial x_{j}}-i\\frac{c_{j}(t)}{2}(2x_{j}\\frac{% \\partial \\psi}{\\partial x_{j}}-\\psi)). For the linear case ($h=0$) the evolution operator $U_{H}(t)$ associated to the Cauchy problem can be expressed as integral operator with an explicit formula for the kernel. Local in time Strichartz estimates are available for $U_{H}(t)$ and conditions are given for global in time Strichartz estimates to hold. We show that for the case $h \
A Hamiltonian-based solution to the linear quadratic consensus control problem
Weiss, M.
2012-01-01
The Linear Quadratic Consensus Control (LQCC) problem is a relaxation of the classical Linear Quadratic Regulation (LQR) problem, that consists of asymptotically driving the state of the system to a "consensus" point in which all coordinates are equal, in such a way that a quadratic cost function on
Institute of Scientific and Technical Information of China (English)
FAN Hong-Yi; LU Hai-Liang
2006-01-01
We show that the time-dependent two-mode Fresnel operator is just the time-evolutional unitary operator governed by the Hamiltonian composed of quadratic combination of canonical operators in the way of exhibiting SU(1,1)algebra. This is an approach for obtaining the time-dependent Hamiltonian from the preassigned time evolution in classical phase space, an approach which is in contrast to Lewis-Riesenfeld's invariant operator theory of treating time-dependent harmonic oscillators.
Iemini, Fernando; da Silva Souza, Leonardo; Debarba, Tiago; Cesário, André T.; Maciel, Thiago O.; Vianna, Reinaldo O.
2017-05-01
We obtain the analytical expression for the Kraus decomposition of the quantum map of an environment modeled by an arbitrary quadratic fermionic Hamiltonian acting on one or two qubits, and derive simple functions to check the non-positivity of the intermediate map. These functions correspond to two different sufficient criteria for non-Markovianity. In the particular case of an environment represented by the Ising Hamiltonian, we discuss the two sources of non-Markovianity in the model, one due to the finite size of the lattice, and another due to the kind of interactions.
A smoothing Newton method for a type of inverse semi-definite quadratic programming problem
Xiao, Xiantao; Zhang, Liwei; Zhang, Jianzhong
2009-01-01
We consider an inverse problem arising from the semi-definite quadratic programming (SDQP) problem. We represent this problem as a cone-constrained minimization problem and its dual (denoted ISDQD) is a semismoothly differentiable (SC1) convex programming problem with fewer variables than the original one. The Karush-Kuhn-Tucker conditions of the dual problem (ISDQD) can be formulated as a system of semismooth equations which involves the projection onto the cone of positive semi-definite matrices. A smoothing Newton method is given for getting a Karush-Kuhn-Tucker point of ISDQD. The proposed method needs to compute the directional derivative of the smoothing projector at the corresponding point and to solve one linear system per iteration. The quadratic convergence of the smoothing Newton method is proved under a suitable condition. Numerical experiments are reported to show that the smoothing Newton method is very effective for solving this type of inverse quadratic programming problems.
Hamiltonian and Lagrangian theory of viscoelasticity
Hanyga, A.; Seredyńska, M.
2008-03-01
The viscoelastic relaxation modulus is a positive-definite function of time. This property alone allows the definition of a conserved energy which is a positive-definite quadratic functional of the stress and strain fields. Using the conserved energy concept a Hamiltonian and a Lagrangian functional are constructed for dynamic viscoelasticity. The Hamiltonian represents an elastic medium interacting with a continuum of oscillators. By allowing for multiphase displacement and introducing memory effects in the kinetic terms of the equations of motion a Hamiltonian is constructed for the visco-poroelasticity.
van Enter, A C; Fernández, R
1999-05-01
For classical lattice systems with finite (Ising) spins, we show that the implementation of momentum-space renormalization at the level of Hamiltonians runs into the same type of difficulties as found for real-space transformations: Renormalized Hamiltonians are ill-defined in certain regions of the phase diagram.
Enter, Aernout C.D. van; Fernández, Roberto
For classical lattice systems with finite (Ising) spins, we show that the implementation of momentum-space renormalization at the level of Hamiltonians runs into the same type of difficulties as found for real-space transformations: Renormalized Hamiltonians are ill-defined in certain regions of the
Amaku, Marcos; Coutinho, Francisco A. B.; Masafumi Toyama, F.
2017-09-01
The usual definition of the time evolution operator e-i H t /ℏ=∑n=0∞1/n ! (-i/ℏHt ) n , where H is the Hamiltonian of the system, as given in almost every book on quantum mechanics, causes problems in some situations. The operators that appear in quantum mechanics are either bounded or unbounded. Unbounded operators are not defined for all the vectors (wave functions) of the Hilbert space of the system; when applied to some states, they give a non-normalizable state. Therefore, if H is an unbounded operator, the definition in terms of the power series expansion does not make sense because it may diverge or result in a non-normalizable wave function. In this article, we explain why this is so and suggest, as an alternative, another definition used by mathematicians.
Path Integrals and Hamiltonians
Baaquie, Belal E.
2014-03-01
1. Synopsis; Part I. Fundamental Principles: 2. The mathematical structure of quantum mechanics; 3. Operators; 4. The Feynman path integral; 5. Hamiltonian mechanics; 6. Path integral quantization; Part II. Stochastic Processes: 7. Stochastic systems; Part III. Discrete Degrees of Freedom: 8. Ising model; 9. Ising model: magnetic field; 10. Fermions; Part IV. Quadratic Path Integrals: 11. Simple harmonic oscillators; 12. Gaussian path integrals; Part V. Action with Acceleration: 13. Acceleration Lagrangian; 14. Pseudo-Hermitian Euclidean Hamiltonian; 15. Non-Hermitian Hamiltonian: Jordan blocks; 16. The quartic potential: instantons; 17. Compact degrees of freedom; Index.
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 ...... results in (energy dependent) criteria for unstable behavior different from the usual Lyapunov criteria. We discuss some examples of unstable Hamiltonian systems in two dimensions....
Integrable Coupling of KN Hierarchy and Its Hamiltonian Structure
Institute of Scientific and Technical Information of China (English)
GUO Fu-Kui; ZHANG Yu-Feng
2006-01-01
The Hamiltonian structure of the integrable couplings obtained by our method has not been solved. In this paper, the Hamiltonian structure of the KN hierarchy is obtained by making use of the quadratic-form identity.
Ryan, M.
1972-01-01
The study of cosmological models by means of equations of motion in Hamiltonian form is considered. Hamiltonian methods applied to gravity seem to go back to Rosenfeld (1930), who constructed a quantum-mechanical Hamiltonian for linearized general relativity theory. The first to notice that cosmologies provided a simple model in which to demonstrate features of Hamiltonian formulation was DeWitt (1967). Applications of the ADM formalism to homogeneous cosmologies are discussed together with applications of the Hamiltonian formulation, giving attention also to Bianchi-type universes. Problems involving the concept of superspace and techniques of quantization are investigated.
Square conservation systems and Hamiltonian systems
Institute of Scientific and Technical Information of China (English)
王斌; 曾庆存; 季仲贞
1995-01-01
The internal and external relationships between the square conservation scheme and the symplectic scheme are revealed by a careful study on the interrelation between the square conservation system and the Hamiltonian system in the linear situation, thus laying a theoretical basis for the application and extension of symplectic schemes to square conservations systems, and of those schemes with quadratic conservation properties to Hamiltonian systems.
Ryckelynck, Philippe
2011-01-01
This paper addresses the classical and discrete Euler-Lagrange equations for systems of $n$ particles interacting quadratically in $\\mathbb{R}^d$. By highlighting the role played by the center of mass of the particles, we solve the previous systems via the classical quadratic eigenvalue problem (QEP) and its discrete transcendental generalization. The roots of classical and discrete QEP being given, we state some conditional convergence results. Next, we focus especially on periodic and choreographic solutions and we provide some numerical experiments which confirm the convergence.
Quantum bouncer with quadratic dissipation
Energy Technology Data Exchange (ETDEWEB)
Gonzalez, G. [NanoScience Technology Center, University of Central Florida, Orlando, FL 32826 (United States)]. e-mail: ggonzalez@physics.ucf.edu
2008-07-01
The energy loss due to a quadratic velocity-dependent force on a quantum particle bouncing off a perfectly reflecting surface is obtained for a full cycle of motion. We approach this problem by means of a new, effective, phenomenological Hamiltonian which corresponds to the actual energy of the system and obtain the correction to the eigenvalues of the energy in first-order quantum perturbation theory for the case of weak dissipation. (Author)
Quantum bouncer with quadratic dissipation
González, G.
2008-02-01
The energy loss due to a quadratic velocity dependent force on a quantum particle bouncing on a perfectly reflecting surface is obtained for a full cycle of motion. We approach this problem by means of a new effective phenomenological Hamiltonian which corresponds to the actual energy of the system and obtained the correction to the eigenvalues of the energy in first order quantum perturbation theory for the case of weak dissipation.
Brugnano, Luigi; Trigiante, Donato
2009-01-01
One main issue, when numerically integrating autonomous Hamiltonian systems, is the long-term conservation of some of its invariants, among which the Hamiltonian function itself. For example, it is well known that standard (even symplectic) methods can only exactly preserve quadratic Hamiltonians. In this paper, a new family of methods, called Hamiltonian Boundary Value Methods (HBVMs), is introduced and analyzed. HBVMs are able to exactly preserve, in the discrete solution, Hamiltonian functions of polynomial type of arbitrarily high degree. These methods turn out to be symmetric, perfectly $A$-stable, and can have arbitrarily high order. A few numerical tests confirm the theoretical results.
Institute of Scientific and Technical Information of China (English)
殷婷; 王杰
2013-01-01
对于传统的电力系统广义Hamilton实现，判定Hamilton函数Hessian矩阵的正定性是保证系统Lyapunov意义下稳定的充分条件，而复杂电力系统中此Hessian矩阵通常为高维分块矩阵，其正定性判定较为困难。基于二次型和块对角占优的思想，推导出判断高阶分块矩阵正定性的一般方法，利用矩阵分块理论并结合矩阵块的行或列的性质来实现。计算过程简单，大大减小了计算量。运用电力系统暂态能量函数方法有助于控制的设计和研究，并使用上述方法判断系统在平衡点处Hessian 矩阵的正定性。在四机系统中进行 Simulink 仿真，证明了所推导判据的准确性和控制策略的有效性，简化了广义Hamilton系统实现的Hessian矩阵正定性的判断过程。%The positive definiteness judgment of Hessian matrix of Hamilton function is a sufficient condition to guarantee the system stability in the Lyapunov sense for the generalized Hamiltonian realization of the traditional power system.However,the Hessian matrices of complex power system are usually high-dimension blocked matrices and the judgments of positive definiteness are very difficult.The general method to judge the positive definiteness of high-order blocked matrix is derived based on the idea of quadratic form and block diagonal dominance,and it can be realized by using the characteristics of the blocked rows or columns of matrix and blocked matrix theory.The calculating process will be simpler,and it greatly reduces the amount of calculations.At the same time, it will be conducive to the research and design of the control by means of the transient energy function method of power system,and the positive definiteness of Hessian matrix at the equilibrium point is judged by the above methods.The simulation example is given for four-machine system to prove the accuracy of the criterion and the effectiveness of the control strategy,which simplifies the
Energy Technology Data Exchange (ETDEWEB)
Orsucci, Davide [Scuola Normale Superiore, I-56126 Pisa (Italy); Burgarth, Daniel [Department of Mathematics, Aberystwyth University, Aberystwyth SY23 3BZ (United Kingdom); Facchi, Paolo; Pascazio, Saverio [Dipartimento di Fisica and MECENAS, Università di Bari, I-70126 Bari (Italy); INFN, Sezione di Bari, I-70126 Bari (Italy); Nakazato, Hiromichi; Yuasa, Kazuya [Department of Physics, Waseda University, Tokyo 169-8555 (Japan); Giovannetti, Vittorio [NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56126 Pisa (Italy)
2015-12-15
The problem of Hamiltonian purification introduced by Burgarth et al. [Nat. Commun. 5, 5173 (2014)] is formalized and discussed. Specifically, given a set of non-commuting Hamiltonians (h{sub 1}, …, h{sub m}) operating on a d-dimensional quantum system ℋ{sub d}, the problem consists in identifying a set of commuting Hamiltonians (H{sub 1}, …, H{sub m}) operating on a larger d{sub E}-dimensional system ℋ{sub d{sub E}} which embeds ℋ{sub d} as a proper subspace, such that h{sub j} = PH{sub j}P with P being the projection which allows one to recover ℋ{sub d} from ℋ{sub d{sub E}}. The notions of spanning-set purification and generator purification of an algebra are also introduced and optimal solutions for u(d) are provided.
Continuous finite element methods for Hamiltonian systems
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
By applying the continuous finite element methods of ordinary differential equations, the linear element methods are proved having second-order pseudo-symplectic scheme and the quadratic element methods are proved having third-order pseudosymplectic scheme respectively for general Hamiltonian systems, and they both keep energy conservative. The finite element methods are proved to be symplectic as well as energy conservative for linear Hamiltonian systems. The numerical results are in agreement with theory.
Semidefinite programming for quadratically constrained quadratic programs
Olkin, Julia A.; Titterton, Paul J., Jr.
1995-06-01
We consider the linear least squares problem subject to multiple quadratic constraints, which is motivated by a practical application in controller design. We use the techniques of convex optimization, in particluar, interior-point methods for semi-definite programming. We reduce a quasi-convex potential function. Each iteration requires calculating a primal and dual search direction and minimizing along the plane defined by these search directions. The primal search direction requires solving a least squares problem whose matrix is composed of a block- Toeplitz portion plus other structured matrices. We make use of Kronecker products and FFTs to greatly reduce the calculation. In addition, the matrix updates and matrix inverses in the plane search are actually low-rank updates to structured matrices so we are able to further reduce the flops required. Consequently, we can design controllers for problems of considerable size.
INTEGRABLE COUPLINGS OF THE TB HIERARCHY AND ITS HAMILTONIAN STRUCTURE
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
In this paper,we obtain integrable couplings of the TB hierarchy using the new subalgebra of the loop algebra A_3.Then the Hamiltonian structure of the above system is given by the quadratic-form identity.
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 lik
Mochon, C
2006-01-01
Hamiltonian oracles are the continuum limit of the standard unitary quantum oracles. In this limit, the problem of finding the optimal query algorithm can be mapped into the problem of finding shortest paths on a manifold. The study of these shortest paths leads to lower bounds of the original unitary oracle problem. A number of example Hamiltonian oracles are studied in this paper, including oracle interrogation and the problem of computing the XOR of the hidden bits. Both of these problems are related to the study of geodesics on spheres with non-round metrics. For the case of two hidden bits a complete description of the geodesics is given. For n hidden bits a simple lower bound is proven that shows the problems require a query time proportional to n, even in the continuum limit. Finally, the problem of continuous Grover search is reexamined leading to a modest improvement to the protocol of Farhi and Gutmann.
Institute of Scientific and Technical Information of China (English)
李鑫; 季萍; 张明望
2015-01-01
In this paper, we propose a new full-Newton step primal-dual interior-point algorithm for solving convex quadratic semi-definite programming. By establishing and using new technical results, we show that the iteration complexity of algorithm asO(nlogn)ε is as good as the currently best iteration complexity for small-update interior-point algorithms of convex quadratic semi-definite programming.%对凸二次半定规划提出了一种新的全-Newton步原始-对偶内点算法.通过建立和应用一些新的技术性结果,证明了算法的迭代复杂性为O( n log n )ε ,这与目前凸二次半定规划的小步校正内点算法最好的迭代复杂性一致.
A Class of Hamiltonians for a Three-Particle Fermionic System at Unitarity
Energy Technology Data Exchange (ETDEWEB)
Correggi, M., E-mail: michele.correggi@gmail.com [Università degli Studi Roma Tre, Largo San Leonardo Murialdo 1, Dipartimento di Matematica e Fisica (Italy); Dell’Antonio, G. [“Sapienza” Università di Roma, P.le A. Moro 5, Dipartimento di Matematica (Italy); Finco, D. [Università Telematica Internazionale Uninettuno, Corso V. Emanuele II 39, Facoltà di Ingegneria (Italy); Michelangeli, A. [Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea 265 (Italy); Teta, A. [“Sapienza” Università di Roma, P.le A. Moro 5, Dipartimento di Matematica (Italy)
2015-12-15
We consider a quantum mechanical three-particle system made of two identical fermions of mass one and a different particle of mass m, where each fermion interacts via a zero-range force with the different particle. In particular we study the unitary regime, i.e., the case of infinite two-body scattering length. The Hamiltonians describing the system are, by definition, self-adjoint extensions of the free Hamiltonian restricted on smooth functions vanishing at the two-body coincidence planes, i.e., where the positions of two interacting particles coincide. It is known that for m larger than a critical value m{sup ∗} ≃ (13.607){sup −1} a self-adjoint and lower bounded Hamiltonian H{sub 0} can be constructed, whose domain is characterized in terms of the standard point-interaction boundary condition at each coincidence plane. Here we prove that for m ∈ (m{sup ∗},m{sup ∗∗}), where m{sup ∗∗} ≃ (8.62){sup −1}, there is a further family of self-adjoint and lower bounded Hamiltonians H{sub 0,β}, β ∈ ℝ, describing the system. Using a quadratic form method, we give a rigorous construction of such Hamiltonians and we show that the elements of their domains satisfy a further boundary condition, characterizing the singular behavior when the positions of all the three particles coincide.
Linear Hamiltonian Behaviors and Bilinear Differential Forms
Rapisarda, P.; Trentelman, H.L.
2004-01-01
We study linear Hamiltonian systems using bilinear and quadratic differential forms. Such a representation-free approach allows us to use the same concepts and techniques to deal with systems isolated from their environment and with systems subject to external influences and allows us to study
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
Endicott, Julia S; Izmaylov, Artur F
2014-01-01
We consider a fully quadratic vibronic model Hamiltonian for studying photoinduced electronic transitions through conical intersections. Using a second order perturbative approximation for diabatic couplings we derive an analytical expression for the time evolution of electronic populations at a given temperature. This formalism extends upon a previously developed perturbative technique for a linear vibronic coupling Hamiltonian. The advantage of the quadratic model Hamiltonian is that it allows one to use separate quadratic representations for potential energy surfaces of different electronic states and a more flexible representation of interstate couplings. We explore features introduced by the quadratic Hamiltonian in a series of 2D models, and then apply our formalism to the 2,6-bis(methylene) adamantyl cation, and its dimethyl derivative. The Hamiltonian parameters for the molecular systems have been obtained from electronic structure calculations followed by a diabatization procedure. The evolution of e...
Solvable quadratic Lie algebras
Institute of Scientific and Technical Information of China (English)
ZHU; Linsheng
2006-01-01
A Lie algebra endowed with a nondegenerate, symmetric, invariant bilinear form is called a quadratic Lie algebra. In this paper, the author investigates the structure of solvable quadratic Lie algebras, in particular, the solvable quadratic Lie algebras whose Cartan subalgebras consist of semi-simple elements, the author presents a procedure to construct a class of quadratic Lie algebras from the point of view of cohomology and shows that all solvable quadratic Lie algebras can be obtained in this way.
Finite dimensional quadratic Lie superalgebras
Jarvis, Peter; Yates, Luke
2010-01-01
We consider a special class of Z_2-graded, polynomial algebras of degree 2, which we call quadratic Lie superalgebras. Starting from the formal definition, we discuss the generalised Jacobi relations in the context of the Koszul property, and give a proof of the PBW basis theorem. We give several concrete examples of quadratic Lie superalgebras for low dimensional cases, and discuss aspects of their structure constants for the `type I' class. Based on the factorisation of the enveloping algebra, we derive the Kac module construction for typical and atypical modules, and a related direct construction of irreducible modules due to Gould. We investigate the method for one specific case, the quadratic generalisation gl_2(n/1) of the Lie superalgebra sl(n/1). We formulate the general atypicality conditions at level 1, and present an analysis of zero-and one-step atypical modules for a certain family of Kac modules.
Hamiltonian formulation of teleparallel gravity
Ferraro, Rafael; Guzmán, María José
2016-11-01
The Hamiltonian formulation of the teleparallel equivalent of general relativity is developed from an ordinary second-order Lagrangian, which is written as a quadratic form of the coefficients of anholonomy of the orthonormal frames (vielbeins). We analyze the structure of eigenvalues of the multi-index matrix entering the (linear) relation between canonical velocities and momenta to obtain the set of primary constraints. The canonical Hamiltonian is then built with the Moore-Penrose pseudoinverse of that matrix. The set of constraints, including the subsequent secondary constraints, completes a first-class algebra. This means that all of them generate gauge transformations. The gauge freedoms are basically the diffeomorphisms and the (local) Lorentz transformations of the vielbein. In particular, the Arnowitt, Deser, and Misner algebra of general relativity is recovered as a subalgebra.
Hamiltonian formulation of teleparallel gravity
Ferraro, Rafael
2016-01-01
The Hamiltonian formulation of the teleparallel equivalent of general relativity (TEGR) is developed from an ordinary second-order Lagrangian, which is written as a quadratic form of the coefficients of anholonomy of the orthonormal frames (vielbeins). We analyze the structure of eigenvalues of the multi-index matrix entering the (linear) relation between canonical velocities and momenta to obtain the set of primary constraints. The canonical Hamiltonian is then built with the Moore-Penrose pseudo-inverse of that matrix. The set of constraints, including the subsequent secondary constraints, completes a first class algebra. This means that all of them generate gauge transformations. The gauge freedoms are basically the diffeomorphisms, and the (local) Lorentz transformations of the vielbein. In particular, the ADM algebra of general relativity is recovered as a sub-algebra.
Homogeneous systems with quadratic integrals, Lie-Poisson quasibrackets, and Kovalevskaya's method
Bizyaev, I. A.; Kozlov, V. V.
2015-12-01
We consider differential equations with quadratic right-hand sides that admit two quadratic first integrals, one of which is a positive-definite quadratic form. We indicate conditions of general nature under which a linear change of variables reduces this system to a certain 'canonical' form. Under these conditions, the system turns out to be divergenceless and can be reduced to a Hamiltonian form, but the corresponding linear Lie-Poisson bracket does not always satisfy the Jacobi identity. In the three-dimensional case, the equations can be reduced to the classical equations of the Euler top, and in four-dimensional space, the system turns out to be superintegrable and coincides with the Euler-Poincaré equations on some Lie algebra. In the five-dimensional case we find a reducing multiplier after multiplying by which the Poisson bracket satisfies the Jacobi identity. In the general case for n>5 we prove the absence of a reducing multiplier. As an example we consider a system of Lotka-Volterra type with quadratic right-hand sides that was studied by Kovalevskaya from the viewpoint of conditions of uniqueness of its solutions as functions of complex time. Bibliography: 38 titles.
Darboux transformations of the Jaynes-Cummings Hamiltonian
Samsonov, B F; Samsonov, Boris F; Negro, Javier
2004-01-01
A detailed analysis of matrix Darboux transformations under the condition that the derivative of the superpotential be self-adjoint is given. As a onsequence, a class of the symmetries associated to Schr\\"odinger matrix Hamiltonians is characterized. The applications are oriented towards the Jaynes-Cummings eigenvalue problem, so that exactly solvable $2\\times 2$ matrix Hamiltonians of the Jaynes-Cummings type are obtained. It is also established that the Jaynes-Cummings Hamiltonian is a quadratic function of a Dirac-type Hamiltonian.
Energy Technology Data Exchange (ETDEWEB)
Catoni, F.; Cannata, R.; Nichelatti, E.; Zampetti, P. [ENEA, Divisione Sistemi Energetici per la Mobilita' e l' Habitat, Centro Ricerche Casaccia, S. Maria di Galeria, Rome (Italy)
2001-07-01
Gauss showed the link between the definite quadratic differential forms and the complex functions. Beltrami, following Gauss' idea, linked the complex functions to elliptic partial differential equations. In this report it was shown how the use of hyperbolic numbers and hyperbolic functions allows to extend the same results to non definite quadratic differential forms. Using this kind of approach, one can tackle the hyperbolic partial differential equations by a different point of view. [Italian] In un famoso lavoro per la rappresentazione conforme di due superfici, Gauss scompose le forme differenziali quadratiche in due fattori complessi coniugati. In questo modo ridusse la soluzione del problema a quella di una forma differnziale lineare. Beltrami, partendo dalla stessa decomposizione, collego' le f.d.q. alle equazioni differenziali a derivate parziali di tipo ellittico aprendo cosi' nuove strade per la loro soluzione. Dalla relativita' ristretta hanno pero' assunto importanza fisica anche le forme differenziali quadratiche non definite. Viene qui mostrato come con i numeri ipercomplessi iperbolici si possono seguire i procedimenti di Gauss e Beltrami e collegare queste forme alle equazioni differenziali a derivate parziali di tipo iperbolico. Questo pero' permettere di vedere sotto nuovi aspetti questo tipo di equazioni.
The Koszul-Tate Cohomology in Covariant Hamiltonian Formalism
Mangiarotti, L
1999-01-01
We show that, in the framework of covariant Hamiltonian field theory, a degenerate almost regular quadratic Lagrangian $L$ admits a complete set of non-degenerate Hamiltonian forms such that solutions of the corresponding Hamilton equations, which live in the Lagrangian constraint space, exhaust solutions of the Euler--Lagrange equations for $L$. We obtain the characteristic splittings of the configuration and momentum phase bundles. Due to the corresponding projection operators, the Koszul-Tate resolution of the Lagrangian constraints for a generic almost regular quadratic Lagrangian is constructed in an explicit form.
Twisted Hamiltonian Lie Algebras and Their Multiplicity-Free Representations
Institute of Scientific and Technical Information of China (English)
Ling CHEN
2011-01-01
We construct a class of new Lie algebras by generalizing the one-variable Lie algebras generated by the quadratic conformal algebras (or corresponding Hamiltonian operators) associated with Poisson algebras and a quasi-derivation found by Xu. These algebras can be viewed as certain twists of Xu's generalized Hamiltonian Lie algebras. The simplicity of these algebras is completely determined. Moreover, we construct a family of multiplicity-free representations of these Lie algebras and prove their irreducibility.
Path integrals for actions that are not quadratic in their time derivatives
Cahill, Kevin
2015-01-01
The standard way to construct a path integral is to use a Legendre transformation to find the hamiltonian, to repeatedly insert complete sets of states into the time-evolution operator, and then to integrate over the momenta. This procedure is simple when the action is quadratic in its time derivatives, but in most other cases Legendre's transformation is intractable, and the hamiltonian is unknown. This paper shows how to make path integrals without using the hamiltonian.
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.
Accardi, Luigi
2009-01-01
We construct the quadratic analogue of the boson Fock functor. While in the first order case all contractions on the 1--particle space can be second quantized, the semigroup of contractions that admit a quadratic second quantization is much smaller due to the nonlinearity. Within this semigroup we characterize the unitary and the isometric elements.
Quadratic eigenvalue problems.
Energy Technology Data Exchange (ETDEWEB)
Walsh, Timothy Francis; Day, David Minot
2007-04-01
In this report we will describe some nonlinear eigenvalue problems that arise in the areas of solid mechanics, acoustics, and coupled structural acoustics. We will focus mostly on quadratic eigenvalue problems, which are a special case of nonlinear eigenvalue problems. Algorithms for solving the quadratic eigenvalue problem will be presented, along with some example calculations.
Hamiltonian analysis of higher derivative scalar-tensor theories
Langlois, David
2015-01-01
We perform a Hamiltonian analysis of a large class of scalar-tensor Lagrangians which depend quadratically on the second derivatives of a scalar field. By resorting to a convenient choice of dynamical variables, we show that the Hamiltonian can be written in a very simple form, where the Hamiltonian and the momentum constraints are easily identified. In the case of degenerate Lagrangians, which include the Horndeski and beyond Horndeski quartic Lagrangians, our analysis confirms that the dimension of the physical phase space is reduced by the primary and secondary constraints due to the degeneracy, thus leading to the elimination of the dangerous Ostrogradski ghost. We also present the Hamiltonian formulation for nondegenerate theories and find that they contain four degrees of freedom, as expected. We finally discuss the status of the unitary gauge from the Hamiltonian perspective.
Hamiltonian analysis of higher derivative scalar-tensor theories
Langlois, David; Noui, Karim
2016-07-01
We perform a Hamiltonian analysis of a large class of scalar-tensor Lagrangians which depend quadratically on the second derivatives of a scalar field. By resorting to a convenient choice of dynamical variables, we show that the Hamiltonian can be written in a very simple form, where the Hamiltonian and the momentum constraints are easily identified. In the case of degenerate Lagrangians, which include the Horndeski and beyond Horndeski quartic Lagrangians, our analysis confirms that the dimension of the physical phase space is reduced by the primary and secondary constraints due to the degeneracy, thus leading to the elimination of the dangerous Ostrogradsky ghost. We also present the Hamiltonian formulation for nondegenerate theories and find that they contain four degrees of freedom, including a ghost, as expected. We finally discuss the status of the unitary gauge from the Hamiltonian perspective.
Integration of the Quadratic Function and Generalization
Mitsuma, Kunio
2011-01-01
We will first recall useful formulas in integration that simplify the calculation of certain definite integrals with the quadratic function. A main formula relies only on the coefficients of the function. We will then explore a geometric proof of one of these formulas. Finally, we will extend the formulas to more general cases. (Contains 3…
Quadratic Twists of Rigid Calabi–Yau Threefolds Over
DEFF Research Database (Denmark)
Gouvêa, Fernando Q.; Kiming, Ian; Yui, Noriko
2013-01-01
We consider rigid Calabi–Yau threefolds defined over Q and the question of whether they admit quadratic twists. We give a precise geometric definition of the notion of a quadratic twists in this setting. Every rigid Calabi–Yau threefold over Q is modular so there is attached to it a certain newfo...
Multistage quadratic stochastic programming
Lau, Karen K.; Womersley, Robert S.
2001-04-01
Quadratic stochastic programming (QSP) in which each subproblem is a convex piecewise quadratic program with stochastic data, is a natural extension of stochastic linear programming. This allows the use of quadratic or piecewise quadratic objective functions which are essential for controlling risk in financial and project planning. Two-stage QSP is a special case of extended linear-quadratic programming (ELQP). The recourse functions in QSP are piecewise quadratic convex and Lipschitz continuous. Moreover, they have Lipschitz gradients if each QP subproblem is strictly convex and differentiable. Using these properties, a generalized Newton algorithm exhibiting global and superlinear convergence has been proposed recently for the two stage case. We extend the generalized Newton algorithm to multistage QSP and show that it is globally and finitely convergent under suitable conditions. We present numerical results on randomly generated data and modified publicly available stochastic linear programming test sets. Efficiency schemes on different scenario tree structures are discussed. The large-scale deterministic equivalent of the multistage QSP is also generated and their accuracy compared.
Debergh, N M; Samsonov, B F; Van den Bossche, B
2002-01-01
A matricial Darboux operator intertwining two one-dimensional stationary Dirac Hamiltonians is constructed. This operator is such that the potential of the second Dirac Hamiltonian as well as the corresponding eigenfunctions are determined through the knowledge of only two eigenfunctions of the first Dirac Hamiltonian. Moreover this operator together with its adjoint and the two Hamiltonians generate a quadratic deformation of the superalgebra subtending the usual supersymmetric quantum mechanics. Our developments are illustrated on the free particle case and the generalized Coulomb interaction. In the latter case, a relativistic counterpart of shape-invariance is observed.
Discrete fractional Radon transforms and quadratic forms
Pierce, Lillian B
2010-01-01
We consider discrete analogues of fractional Radon transforms involving integration over paraboloids defined by positive definite quadratic forms. We prove sharp results for this class of discrete operators in all dimensions, providing necessary and sufficient conditions for them to extend to bounded operators from $\\ell^p$ to $\\ell^q$. The method involves an intricate spectral decomposition according to major and minor arcs, motivated by ideas from the circle method of Hardy and Littlewood. Techniques from harmonic analysis, in particular Fourier transform methods and oscillatory integrals, as well as the number theoretic structure of quadratic forms, exponential sums, and theta functions, play key roles in the proof.
Institute of Scientific and Technical Information of China (English)
谭亚茹
2016-01-01
The quadratic Higher Algebra is an important part of this paper, the definition of quadratic forms, introduces the second type of representation, and then describes how to use the allocation method, elementary transformation, orthogonal transformation method, etc. II second type into the standard form, and the second type of normal form, finally introduced posi-tive definite quadratic form and method for determining positive definite quadratic form.%二次型是高等代数的重要组成部分，本文从二次型的定义出发，介绍了二次型的表示方法，然后介绍了如何用配方法、初等变换法、正交变换法等将二次型化为标准形，以及二次型的规范形，最后介绍了正定二次型和判定正定二次型的方法。
Maxwell's Optics Symplectic Hamiltonian
Kulyabov, D S; Sevastyanov, L A
2015-01-01
The Hamiltonian formalism is extremely elegant and convenient to mechanics problems. However, its application to the classical field theories is a difficult task. In fact, you can set one to one correspondence between the Lagrangian and Hamiltonian in the case of hyperregular Lagrangian. It is impossible to do the same in gauge-invariant field theories. In the case of irregular Lagrangian the Dirac Hamiltonian formalism with constraints is usually used, and this leads to a number of certain difficulties. The paper proposes a reformulation of the problem to the case of a field without sources. This allows to use a symplectic Hamiltonian formalism. The proposed formalism will be used by the authors in the future to justify the methods of vector bundles (Hamiltonian bundles) in transformation optics.
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.
Singh, Parampreet
2015-01-01
The problem of obtaining canonical Hamiltonian structures from the equations of motion is studied in the context of the spatially flat Friedmann-Robertson-Walker models. Modifications to Raychaudhuri equation are implemented independently as quadratic and cubic terms of energy density without introducing additional degrees of freedom. Depending on its sign, modifications make gravity repulsive above a curvature scale for matter satisfying strong energy condition, or more attractive than in the classical theory. Canonical structure of the modified theories is determined demanding that the total Hamiltonian be a linear combination of gravity and matter Hamiltonians. Both of the repulsive modifications are found to yield singularity avoidance. In the quadratic repulsive case, the modified canonical phase space of gravity is a polymerized phase space with canonical momentum as inverse trigonometric function of Hubble rate; the canonical Hamiltonian can be identified with the effective Hamiltonian in loop quantum ...
A Hamiltonian Algorithm for Singular Optimal LQ Control Systems
Delgado-Tellez, M
2012-01-01
A Hamiltonian algorithm, both theoretical and numerical, to obtain the reduced equations implementing Pontryagine's Maximum Principle for singular linear-quadratic optimal control problems is presented. This algorithm is inspired on the well-known Rabier-Rheinhboldt constraints algorithm used to solve differential-algebraic equations. Its geometrical content is exploited fully by implementing a Hamiltonian extension of it which is closer to Gotay-Nester presymplectic constraint algorithm used to solve singular Hamiltonian systems. Thus, given an optimal control problem whose optimal feedback is given in implicit form, a consistent set of equations is obtained describing the first order differential conditions of Pontryaguine's Maximum Principle. Such equations are shown to be Hamiltonian and the set of first class constraints corresponding to controls that are not determined, are obtained explicitly. The strength of the algorithm is shown by exhibiting a numerical implementation with partial feedback on the c...
Hamiltonian Description of Multi-fluid Streaming
Valls, C.; de La Llave, R.; Morrison, P. J.
2001-10-01
The general noncanonical Hamiltonian description of interpenetrating fluids coupled by electrostatic, gravitational, or other forces is presented. This formalism is used to describe equilibrium and nonlinear stability using techniques of Hamiltonian dynamics theory. For example, we study the stability of two warm counter-streaming electron beams in a neutralizing ion background. The normal modes are obtained from an energy functional by computing the lowest-order expression for the perturbed energy about an equilibrium, and transforming the corresponding system into action-angle variables. Higher-order terms in the Hamiltonian provide coupling between normal modes and can lead to instability because of the presence of negative energy modes (NEM's). (The signature of the NEM's is determined by the signature of the Hamiltonian, Moser's bracket definition, or the conventional plasma definition in terms of the dielectric function, all of which are shown to be equivalent.) The possible nonlinear behavior is discovered by constructing the Birkhoff normal form. Accounting for resonances, we transform away terms in the Hamiltonian to address the question of long-time stability for such systems.
On Convex Quadratic Approximation
den Hertog, D.; de Klerk, E.; Roos, J.
2000-01-01
In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field of
On Convex Quadratic Approximation
den Hertog, D.; de Klerk, E.; Roos, J.
2000-01-01
In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field of
On Quadratic Differential Forms
Willems, J.C.; Trentelman, H.L.
1998-01-01
This paper develops a theory around the notion of quadratic differential forms in the context of linear differential systems. In many applications, we need to not only understand the behavior of the system variables but also the behavior of certain functionals of these variables. The obvious cases w
Alvarez-Gaume, Luis; Kounnas, Costas; Lust, Dieter; Riotto, Antonio
2016-01-01
We discuss quadratic gravity where terms quadratic in the curvature tensor are included in the action. After reviewing the corresponding field equations, we analyze in detail the physical propagating modes in some specific backgrounds. First we confirm that the pure $R^2$ theory is indeed ghost free. Then we point out that for flat backgrounds the pure $R^2$ theory propagates only a scalar massless mode and no spin-two tensor mode. However, the latter emerges either by expanding the theory around curved backgrounds like de Sitter or anti-de Sitter, or by changing the long-distance dynamics by introducing the standard Einstein term. In both cases, the theory is modified in the infrared and a propagating graviton is recovered. Hence we recognize a subtle interplay between the UV and IR properties of higher order gravity. We also calculate the corresponding Newton's law for general quadratic curvature theories. Finally, we discuss how quadratic actions may be obtained from a fundamental theory like string- or M-...
Hidden conic quadratic representation of some nonconvex quadratic optimization problems
Ben-Tal, A.; den Hertog, D.
2014-01-01
The problem of minimizing a quadratic objective function subject to one or two quadratic constraints is known to have a hidden convexity property, even when the quadratic forms are indefinite. The equivalent convex problem is a semidefinite one, and the equivalence is based on the celebrated S-lemma
Running Couplings in Hamiltonians
Glazek, S D
2000-01-01
We describe key elements of the perturbative similarity renormalization group procedure for Hamiltonians using two, third-order examples: phi^3 interaction term in the Hamiltonian of scalar field theory in 6 dimensions and triple-gluon vertex counterterm in the Hamiltonian of QCD in 4 dimensions. These examples provide insight into asymptotic freedom in Hamiltonian approach to quantum field theory. The renormalization group procedure also suggests how one may obtain ultraviolet-finite effective Schrödinger equations that correspond to the asymptotically free theories, including transition from quark and gluon to hadronic degrees of freedom in case of strong interactions. The dynamics is invariant under boosts and allows simultaneous analysis of bound state structure in the rest and infinite momentum frames.
Extended gcd of quadratic integers
Miled, Abdelwaheb
2010-01-01
Computation of the extended gcd of two quadratic integers. The ring of integers considered is principal but could be euclidean or not euclidean ring. This method rely on principal ideal ring and reduction of binary quadratic forms.
On Characterization of Quadratic Splines
DEFF Research Database (Denmark)
Chen, B. T.; Madsen, Kaj; Zhang, Shuzhong
2005-01-01
A quadratic spline is a differentiable piecewise quadratic function. Many problems in numerical analysis and optimization literature can be reformulated as unconstrained minimizations of quadratic splines. However, only special cases of quadratic splines are studied in the existing literature...... between the convexity of a quadratic spline function and the monotonicity of the corresponding LCP problem. It is shown that, although both conditions lead to easy solvability of the problem, they are different in general......., and algorithms are developed on a case by case basis. There lacks an analytical representation of a general or even a convex quadratic spline. The current paper fills this gap by providing an analytical representation of a general quadratic spline. Furthermore, for convex quadratic spline, it is shown...
Covariant Hamiltonian field theory
Giachetta, G; Sardanashvily, G
1999-01-01
We study the relationship between the equations of first order Lagrangian field theory on fiber bundles and the covariant Hamilton equations on the finite-dimensional polysymplectic phase space of covariant Hamiltonian field theory. The main peculiarity of these Hamilton equations lies in the fact that, for degenerate systems, they contain additional gauge fixing conditions. We develop the BRST extension of the covariant Hamiltonian formalism, characterized by a Lie superalgebra of BRST and anti-BRST symmetries.
Endicott, Julia S; Joubert-Doriol, Loïc; Izmaylov, Artur F
2014-07-21
We consider a fully quadratic vibronic model Hamiltonian for studying photoinduced electronic transitions through conical intersections. Using a second order perturbative approximation for diabatic couplings, we derive an analytical expression for the time evolution of electronic populations at a given temperature. This formalism extends upon a previously developed perturbative technique for a linear vibronic coupling Hamiltonian. The advantage of the quadratic model Hamiltonian is that it allows one to use separate quadratic representations for potential energy surfaces of different electronic states and a more flexible representation of interstate couplings. We explore features introduced by the quadratic Hamiltonian in a series of 2D models, and then apply our formalism to the 2,6-bis(methylene) adamantyl cation and its dimethyl derivative. The Hamiltonian parameters for the molecular systems have been obtained from electronic structure calculations followed by a diabatization procedure. The evolution of electronic populations in the molecular systems using the perturbative formalism shows a good agreement with that from variational quantum dynamics.
Quadratic dynamical decoupling with nonuniform error suppression
Energy Technology Data Exchange (ETDEWEB)
Quiroz, Gregory; Lidar, Daniel A. [Department of Physics and Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089 (United States); Departments of Electrical Engineering, Chemistry, and Physics, and Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089 (United States)
2011-10-15
We analyze numerically the performance of the near-optimal quadratic dynamical decoupling (QDD) single-qubit decoherence errors suppression method [J. West et al., Phys. Rev. Lett. 104, 130501 (2010)]. The QDD sequence is formed by nesting two optimal Uhrig dynamical decoupling sequences for two orthogonal axes, comprising N{sub 1} and N{sub 2} pulses, respectively. Varying these numbers, we study the decoherence suppression properties of QDD directly by isolating the errors associated with each system basis operator present in the system-bath interaction Hamiltonian. Each individual error scales with the lowest order of the Dyson series, therefore immediately yielding the order of decoherence suppression. We show that the error suppression properties of QDD are dependent upon the parities of N{sub 1} and N{sub 2}, and near-optimal performance is achieved for general single-qubit interactions when N{sub 1}=N{sub 2}.
Modified Dirac Hamiltonian for efficient quantum mechanical simulations of micron sized devices
Habib, K. M. Masum; Sajjad, Redwan N.; Ghosh, Avik W.
2016-03-01
Representing massless Dirac fermions on a spatial lattice poses a potential challenge known as the Fermion Doubling problem. Addition of a quadratic term to the Dirac Hamiltonian provides a possible way to circumvent this problem. We show that the modified Hamiltonian with the additional term results in a very small Hamiltonian matrix when discretized on a real space square lattice. The resulting Hamiltonian matrix is considerably more efficient for numerical simulations without sacrificing on accuracy and is several orders of magnitude faster than the atomistic tight binding model. Using this Hamiltonian and the non-equilibrium Green's function formalism, we show several transport phenomena in graphene, such as magnetic focusing, chiral tunneling in the ballistic limit, and conductivity in the diffusive limit in micron sized graphene devices. The modified Hamiltonian can be used for any system with massless Dirac fermions such as Topological Insulators, opening up a simulation domain that is not readily accessible otherwise.
The Symmetry of Singular Hamiltonian Differential Operators and Properties of Deficiency Indices
Institute of Scientific and Technical Information of China (English)
Jian Gang QI
2006-01-01
The symmetry of singular Hamiltonian differential operators is proved under the standard "definiteness condition", which is strictly weaker than the densely definite condition used by A. M.Krall. Meanwhile, some properties of deficiency indices are given.
Quadratic forms representing all odd positive integers
Rouse, Jeremy
2011-01-01
We consider the problem of classifying all positive-definite integer-valued quadratic forms that represent all positive odd integers. Kaplansky considered this problem for ternary forms, giving a list of 23 candidates, and proving that 19 of those represent all positive odds. (Jagy later dealt with a 20th candidate.) Assuming that the remaining three forms represent all positive odds, we prove that an arbitrary, positive-definite quadratic form represents all positive odds if and only if it represents the odd numbers from 1 up to 451. This result is analogous to Bhargava and Hanke's celebrated 290-theorem. In addition, we prove that these three remaining ternaries represent all positive odd integers, assuming the generalized Riemann hypothesis. This result is made possible by a new analytic method for bounding the cusp constants of integer-valued quaternary quadratic forms $Q$ with fundamental discriminant. This method is based on the analytic properties of Rankin-Selberg $L$-functions, and we use it to prove...
FEEDBACK REALIZATION OF HAMILTONIAN SYSTEMS
Institute of Scientific and Technical Information of China (English)
CHENG Daizhan; XI Zairong
2002-01-01
This paper investigates the relationship between state feedback and Hamiltonian realizatiou. First, it is proved that a completely controllable linear system always has a state feedback state equation Hamiltonian realization. Necessary and sufficient conditions are obtained for it to have a Hamiltonian realization with natural outpnt. Then some conditions for an affine nonlinear system to have a Hamiltonian realization arc given.For generalized outputs, the conditions of the feedback, keeping Hamiltonian, are discussed. Finally, the admissible feedback controls for generalized Hamiltonian systems are considered.
FEEDBACK REALIZATION OF HAMILTONIAN SYSTEMS
Institute of Scientific and Technical Information of China (English)
CHENGDaizhan; XIZairong
2002-01-01
This paper investigates the relationship between state feedback and Hamiltonican realization.Firest,it is proved that a completely controllable linear system always has a state feedback state equation Hamiltonian realization.Necessary and sufficient conditions are obtained for it to have a Hamiltonian realization with natural output.Then some conditions for an affine nonlinear system to have a Hamiltonian realization are given.some conditions for an affine nonlinear system to have a Hamiltonian realization are given.For generalized outputs,the conditions of the feedback,keeping Hamiltonian,are discussed.Finally,the admissible feedback controls for generalized Hamiltonian systems are considered.
The Liouville integrable coupling system of the m-AKNS hierarchy and its Hamiltonian structure
Institute of Scientific and Technical Information of China (English)
Yue Chao; Yang Geng-Wen; Xu Yue-Cai
2007-01-01
In this paper a type of 9-dimensional vector loop algebra (F) is constructed,which is devoted to establish an isospectral problem.It follows that a Liouville integrable coupling system of the m-AKNS hierarchy is obtained by employing the Tu scheme,whose Hamiltonian structure is worked out by making use of constructed quadratic identity.The method given in the paper can be used to obtain many other integrable couplings and their Hamiltonian structures.
Minimal period estimates for brake orbits of nonlinear symmetric Hamiltonian systems
Liu, Chungen
2009-01-01
In this paper, we consider the minimal period estimates for brake orbits of nonlinear symmetric Hamiltonian systems. We prove that if the Hamiltonian function $H\\in C^2(\\Bbb R^{2n}, \\Bbb R)$ is super-quadratic and convex, for every number $\\tau>0$, there exists at least one $\\tau$-periodic brake orbit $(\\tau,x)$ with minimal period $\\tau$ or $\\tau/2$ provided $H(Nx)=H(x)$.
Orbit structure of Hamiltonian systems arising from Lie transformation group actions
Garzia, M. R.; Loparo, K. A.; Martin, C. F.
1983-01-01
This paper associates the Riccati group and its group action on linear-quadratic optimal control problems to the action of a Lie transformation group on a set of Hamiltonian matrices. In this Lie theoretic setting results are presented concerning the associated orbit structure and the structure of the group itself. These results are of importance in understanding the solution structure of matrix Riccati differential equations, and thus also of importance in linear-quadratic optimal control.
Orbit structure of Hamiltonian systems arising from Lie transformation group actions
Garzia, M. R.; Loparo, K. A.; Martin, C. F.
This paper associates the Riccati group and its group action on linear-quadratic optimal control problems to the action of a Lie transformation group on a set of Hamiltonian matrices. In this Lie theoretic setting results are presented concerning the associated orbit structure and the structure of the group itself. These results are of importance in understanding the solution structure of matrix Riccati differential equations, and thus also of importance in linear-quadratic optimal control.
Remarks on hamiltonian digraphs
DEFF Research Database (Denmark)
Gutin, Gregory; Yeo, Anders
2001-01-01
This note is motivated by A.Kemnitz and B.Greger, Congr. Numer. 130 (1998)127-131. We show that the main result of the paper by Kemnitz and Greger is an easy consequence of the characterization of hamiltonian out-locally semicomplete digraphs by Bang-Jensen, Huang, and Prisner, J. Combin. Theory...... of Fan's su#cient condition [5] for an undirected graph to be hamiltonian. In this note we give another, more striking, example of this kind, which disproves a conjecture from [6]. We also show that the main result of [6] 1 is an easy consequence of the characterization of hamiltonian out......-tournaments by Bang-Jensen, Huang and Prisner [4]. For further information and references on hamiltonian digraphs, see e.g. the chapter on hamiltonicity in [1] as well as recent survey papers [2, 8]. We use the standard terminology and notation on digraphs as described in [1]. A digraph D has vertex set V (D) and arc...
Microscopic plasma Hamiltonian
Peng, Y.-K. M.
1974-01-01
A Hamiltonian for the microscopic plasma model is derived from the Low Lagrangian after the dual roles of the generalized variables are taken into account. The resulting Hamilton equations are shown to agree with the Euler-Lagrange equations of the Low Lagrangian.
Indian Academy of Sciences (India)
R S Kaushal; Ranjit Kumar; Awadhesh Prasad
2006-08-01
Attempts have been made to look for the soliton content in the solutions of the recently studied nonlinear diffusion-reaction equations [R S Kaushal, J. Phys. 38, 3897 (2005)] involving quadratic or cubic nonlinearities in addition to the convective flux term which renders the system nonconservative and the corresponding Hamiltonian non-Hermitian.
Quantization of a particle with a force quadratic in the velocity
Energy Technology Data Exchange (ETDEWEB)
Sa Borges, J.; Epele, L.N.; Fanchiotti, H.; Garcia Canal, C.A.; Sima-tildeo, F.R.A.
1988-09-15
The quantization of a system subject to a force quadratic in the velocity and position dependence is carried out in the phase-space path-integral framework. The resulting Hamiltonian coincides with that obtained by using the Weyl-ordering canonical prescription.
Mei Symmetry and Lie Symmetry of Relativistic Hamiltonian System
Institute of Scientific and Technical Information of China (English)
FANG Jian-Hui; YAN Xiang-Hong; LI Hong; CHEN Pei-Sheng
2004-01-01
The Mei symmetry and the Lie symmetry of the relativistic Hamiltonian system are studied. The definition and criterion of the Mei symmetry and the Lie symmetry of the relativistic Hamiltonian system are given. The relationship between them is found. The conserved quantities which the Mei symmetry and the Lie symmetry lead to are obtained.An example is given to illustrate the application of the result.
Transformation design and nonlinear Hamiltonians
Brougham, Thomas; Jex, Igor
2009-01-01
We study a class of nonlinear Hamiltonians, with applications in quantum optics. The interaction terms of these Hamiltonians are generated by taking a linear combination of powers of a simple `beam splitter' Hamiltonian. The entanglement properties of the eigenstates are studied. Finally, we show how to use this class of Hamiltonians to perform special tasks such as conditional state swapping, which can be used to generate optical cat states and to sort photons.
Universal localizing bounds for compact invariant sets of natural polynomial Hamiltonian systems
Energy Technology Data Exchange (ETDEWEB)
Starkov, Konstantin E. [CITEDI-IPN, Av. del Parque 1310, Mesa de Otay, Tijuana, BC (Mexico)], E-mail: konst@citedi.mx
2008-10-06
In this Letter we study the localization problem of compact invariant sets of natural Hamiltonian systems with a polynomial Hamiltonian. Our results are based on applying the first order extremum conditions. We compute universal localizing bounds for some domain containing all compact invariant sets of a Hamiltonian system by using one quadratic function of a simple form. These bounds depend on the value of the total energy of the system, degree and some coefficients of a potential and, in addition, some positive number got as a result of a solution of one maximization problem. Besides, under some quasihomogeneity condition(s) we generalize our construction of the localization set.
Quadratic solitons as nonlocal solitons
DEFF Research Database (Denmark)
Nikolov, Nikola Ivanov; Neshev, D.; Bang, Ole
2003-01-01
We show that quadratic solitons are equivalent to solitons of a nonlocal Kerr medium. This provides new physical insight into the properties of quadratic solitons, often believed to be equivalent to solitons of an effective saturable Kerr medium. The nonlocal analogy also allows for analytical...
On Characterization of Quadratic Splines
DEFF Research Database (Denmark)
Chen, B. T.; Madsen, Kaj; Zhang, Shuzhong
2005-01-01
that the representation can be refined in a neighborhood of a non-degenerate point and a set of non-degenerate minimizers. Based on these characterizations, many existing algorithms for specific convex quadratic splines are also finite convergent for a general convex quadratic spline. Finally, we study the relationship...
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...
Wieland, Wolfgang M
2013-01-01
This paper presents a Hamiltonian formulation of spinfoam-gravity, which leads to a straight-forward canonical quantisation. To begin with, we derive a continuum action adapted to the simplicial decomposition. The equations of motion admit a Hamiltonian formulation, allowing us to perform the constraint analysis. We do not find any secondary constraints, but only get restrictions on the Lagrange multipliers enforcing the reality conditions. This comes as a surprise. In the continuum theory, the reality conditions are preserved in time, only if the torsionless condition (a secondary constraint) holds true. Studying an additional conservation law for each spinfoam vertex, we discuss the issue of torsion and argue that spinfoam gravity may indeed miss an additional constraint. Next, we canonically quantise. Transition amplitudes match the EPRL (Engle--Pereira--Rovelli--Livine) model, the only difference being the additional torsional constraint affecting the vertex amplitude.
Quantum Hamiltonian Complexity
2014-01-01
Constraint satisfaction problems are a central pillar of modern computational complexity theory. This survey provides an introduction to the rapidly growing field of Quantum Hamiltonian Complexity, which includes the study of quantum constraint satisfaction problems. Over the past decade and a half, this field has witnessed fundamental breakthroughs, ranging from the establishment of a "Quantum Cook-Levin Theorem" to deep insights into the structure of 1D low-temperature quantum systems via s...
Exploring the Hamiltonian inversion landscape.
Donovan, Ashley; Rabitz, Herschel
2014-08-07
The identification of quantum system Hamiltonians through the use of experimental data remains an important research goal. Seeking a Hamiltonian that is consistent with experimental measurements constitutes an excursion over a Hamiltonian inversion landscape, which is the quality of reproducing the data as a function of the Hamiltonian parameters. Recent theoretical work showed that with sufficient experimental data there should be local convexity about the true Hamiltonian on the landscape. The present paper builds on this result and performs simulations to test whether such convexity is observed. A gradient-based Hamiltonian search algorithm is incorporated into an inversion routine as a means to explore the local inversion landscape. The simulations consider idealized noise-free as well as noise-ridden experimental data. The results suggest that a sizable convex domain exists about the true Hamiltonian, even with a modest amount of experimental data and in the presence of a reasonable level of noise.
QUADRATIC INVARIANTS AND SYMPLECTIC STRUCTURE OF GENERAL LINEAR METHODS
Institute of Scientific and Technical Information of China (English)
Ai-guo Xiao; Shou-fu Li; Min Yang
2001-01-01
In this paper, we present some invariants and conservation laws of general linear methods applied to differential equation systems. We show that the quadratic invariants and symplecticity of the systems can be extended to general linear methods by a tensor product, and show that general linear methods with the matrix M=0 inherit in an extended sense the quadratic invariants possessed by the differential equation systems being integrated and preserve in an extended sense the symplectic structure of the phase space in the integration of Hamiltonian systems. These unify and extend existing relevant results on Runge-Kutta methods, linear multistep methods and one-leg methods. Finally, as special cases of general linear methods, we examine multistep Runge-Kutta methods, one-leg methods and linear two-step methods in detail.
Rigorous Performance Bounds for Quadratic and Nested Dynamical Decoupling
Xia, Yuhou; Lidar, Daniel A
2011-01-01
We present rigorous performance bounds for the quadratic dynamical decoupling (QDD) pulse sequence which protects a qubit from general decoherence, and for its nested generalization to an arbitrary number of qubits. Our bounds apply under the assumption of instantaneous pulses and of bounded perturbing environment and qubit-environment Hamiltonians such as those realized by baths of nuclear spins in quantum dots. We prove that if the total sequence time is fixed then the trace-norm distance between the unperturbed and protected system states can be made arbitrarily small by increasing the number of applied pulses.
The cyclicity of the period annulus of a quadratic reversible system with one center of genus one
PENG, Linping; Sun, Yannan
2014-01-01
This paper is concerned with a quadratic reversible and non-Hamiltonian system with one center of genus one. By using the properties of related elliptic integrals and the geometry of some planar curves defined by them, we prove that the cyclicity of the period annulus of the considered system under small quadratic perturbations is two. This verifies Gautier's conjecture about the cyclicity of the related period annulus.
The cyclicity of the period annulus of a quadratic reversible system with one center of genus one
PENG, Linping; Sun, Yannan
2011-01-01
This paper is concerned with a quadratic reversible and non-Hamiltonian system with one center of genus one. By using the properties of related elliptic integrals and the geometry of some planar curves defined by them, we prove that the cyclicity of the period annulus of the considered system under small quadratic perturbations is two. This verifies Gautier's conjecture about the cyclicity of the related period annulus.
Singh, Parampreet; Soni, S. K.
2016-06-01
The problem of obtaining canonical Hamiltonian structures from the equations of motion, without any knowledge of the action, is studied in the context of the spatially flat Friedmann, ‘Robertson’, and Walker models. Modifications to the Raychaudhuri equation are implemented independently as quadratic and cubic terms of energy density without introducing additional degrees of freedom. Depending on their sign, modifications make gravity repulsive above a curvature scale for matter satisfying strong energy conditions, or more attractive than in the classical theory. The canonical structure of the modified theories is determined by demanding that the total Hamiltonian be a linear combination of gravity and matter Hamiltonians. In the quadratic repulsive case, the modified canonical phase space of gravity is a polymerized phase space with canonical momentum as inverse a trigonometric function of the Hubble rate; the canonical Hamiltonian can be identified with the effective Hamiltonian in loop quantum cosmology. The repulsive cubic modification results in a ‘generalized polymerized’ canonical phase space. Both the repulsive modifications are found to yield singularity avoidance. In contrast, the quadratic and cubic attractive modifications result in a canonical phase space in which canonical momentum is nontrigonometric and singularities persist. Our results hint at connections between the repulsive/attractive nature of modifications to gravity arising from the gravitational sector and polymerized/non polymerized gravitational phase space.
Lie transform Hamiltonian perturbation theory for limit cycle systems
Shah, Tirth; Chakraborty, Sagar
2016-01-01
Usage of a Hamiltonian perturbation theory for nonconservative system is counterintuitive and in general, a technical impossibility by definition. However, the dual (time independent) Hamiltonian formalism for nonconservative systems have opened the door for using various Hamiltonian (and hence, Lagrangian) perturbation theories for investigating the dynamics of such systems. Following the recent extension of the canonical perturbation theory that brings Li\\'enard systems possessing limit cycles under its scope, here we show that the Lie transform Hamiltonian perturbation theory can also be generalized to find perturbative solutions for similar systems. The Lie transform perturbation theories are comparatively easier while seeking higher order corrections in the perturbative series for the solutions and they are also numerically implementable using any symbolic algebra package. For the sake of concreteness, we have illustrated the methodology using the important example of the van der Pol oscillator. While th...
Keshtkar, F.; Erjaee, G.; Boutefnouchet, M.
2014-01-01
In this article, a brief stability analysis of equilibrium points in nonlinear fractional order dynamical systems is given. Then, based on the first integral concept, a definition of planar Hamiltonian systems with fractional order introduced. Some interesting properties of these fractional Hamiltonian systems are also presented. Finally, we illustrate two examples to see the differences between fractional Hamiltonian systems with their classical order counterparts. NPRP . Grant Number: NP...
SMOOTHING BY CONVEX QUADRATIC PROGRAMMING
Institute of Scientific and Technical Information of China (English)
Bing-sheng He; Yu-mei Wang
2005-01-01
In this paper, we study the relaxed smoothing problems with general closed convex constraints. It is pointed out that such problems can be converted to a convex quadratic minimization problem for which there are good programs in software libraries.
Quantum quadratic operators and processes
Mukhamedov, Farrukh
2015-01-01
Covering both classical and quantum approaches, this unique and self-contained book presents the most recent developments in the theory of quadratic stochastic operators and their Markov and related processes. The asymptotic behavior of dynamical systems generated by classical and quantum quadratic operators is investigated and various properties of quantum quadratic operators are studied, providing an insight into the construction of quantum channels. This book is suitable as a textbook for an advanced undergraduate/graduate level course or summer school in quantum dynamical systems. It can also be used as a reference book by researchers looking for interesting problems to work on, or useful techniques and discussions of particular problems. Since it includes the latest developments in the fields of quadratic dynamical systems, Markov processes and quantum stochastic processes, researchers at all levels are likely to find the book inspiring and useful.
Quadratic Tangles in Planar Algebras
Jones, Vaughan F R
2010-01-01
In planar algebras, we show how to project certain simple "quadratic" tangles onto the linear space spanned by "linear" and "constant" tangles. We obtain some corollaries about the principal graphs and annular structure of subfactors.
Schaft, Arjan van der
1981-01-01
The definitions of symmetries and conservation laws for autonomous (i.e. without external forces) Hamiltonian systems are generalized to Hamiltonian systems with inputs and outputs. It is shown that a symmetry implies the existence of a conservation law and vice versa; thereby generalizing Noether's
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...
Hamiltonian Formulation of Jackiw-Pi 3-Dimensional Gauge Theories
Dayi, O F
1998-01-01
A 3-dimensional non-abelian gauge theory was proposed by Jackiw and Pi to create mass for the gauge fields. However, the set of gauge invariances of the quadratic action obtained by switching off the non-abelian interactions is larger than the original one. This inconsistency in the gauge invariances causes some problems in quantization. Jackiw and Pi proposed another action by enlarging the space of states whose gauge invariances are consistent with the quadratic part. It is shown that all of these theories yield the same number of physical degrees of freedom in the hamiltonian framework. Hence, as far as the physical states are considered there is no inconsistency. Nevertheless, perturbation expansion is still problamatic.
Quantization of noncommutative completely integrable Hamiltonian systems
Giachetta, G; Sardanashvily, G
2007-01-01
Integrals of motion of a Hamiltonian system need not be commutative. The classical Mishchenko-Fomenko theorem enables one to quantize a noncommutative completely integrable Hamiltonian system around its invariant submanifold as an abelian completely integrable Hamiltonian system.
On a theorem by Mather and Aubry-Mather sets for planar Hamiltonian systems
Institute of Scientific and Technical Information of China (English)
蒋美跃
1999-01-01
A result due to Mather on the existence of Aubry-Mather sets for superlinear positive definite Lagrangian systems is generalized in one-dimensional case. Applications to existence of Aubry-Mather sets of planar Hamiltonian systems are given.
Students' understanding of quadratic equations
López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael
2016-05-01
Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help students achieve an understanding of quadratic equations with improved interrelation of ideas and more flexible application of solution methods. Semi-structured interviews with eight beginning undergraduate students explored which of the mental constructions conjectured in the genetic decomposition students could do, and which they had difficulty doing. Two of the mental constructions that form part of the genetic decomposition are highlighted and corresponding further data were obtained from the written work of 121 undergraduate science and engineering students taking a multivariable calculus course. The results suggest the importance of explicitly considering these two highlighted mental constructions.
Successive quadratic programming multiuser detector
Institute of Scientific and Technical Information of China (English)
Mu Xuewen; Zhang Yaling; Liu Sanyang
2007-01-01
Based on the semidefinite programming relaxation of the CDMA maximum likelihood multiuser detection problem,a detection strategy by the successive quadratic programming algorithm is presented. Coupled with the randomized cut generation scheme, the suboptimal solution of the multiuser detection problem in obtained. Compared to the interior point methods previously reported based on semidefinite programming, simulations demonstrate that the successive quadratic programming algorithm often yields the similar BER performances of the multiuser detection problem. But the average CPU time of this approach is significantly reduced.
Integer Quadratic Quasi-polyhedra
Letchford, Adam N.
This paper introduces two fundamental families of 'quasi-polyhedra' - polyhedra with a countably infinite number of facets - that arise in the context of integer quadratic programming. It is shown that any integer quadratic program can be reduced to the minimisation of a linear function over a quasi-polyhedron in the first family. Some fundamental properties of the quasi-polyhedra are derived, along with connections to some other well-studied convex sets. Several classes of facet-inducing inequalities are also derived. Finally, extensions to the mixed-integer case are briefly examined.
On the Reaction Path Hamiltonian
Institute of Scientific and Technical Information of China (English)
孙家钟; 李泽生
1994-01-01
A vector-fiber bundle structure of the reaction path Hamiltonian, which has been introduced by Miller, Handy and Adams, is explored with respect to molecular vibrations orthogonal to the reaction path. The symmetry of the fiber bundle is characterized by the real orthogonal group O(3N- 7) for the dynamical system with N atoms. Under the action of group O(3N- 7). the kinetic energy of the reaction path Hamiltonian is left invariant. Furthermore , the invariant behaviour of the Hamiltonian vector fields is investigated.
Impurity solitons with quadratic nonlinearities
DEFF Research Database (Denmark)
Clausen, Carl A. Balslev; Torres, Juan P-; Torner, Lluis
1998-01-01
We fmd families of solitary waves mediated by parametric mixing in quadratic nonlinear media that are localized at point-defect impurities. Solitons localized at attractive impurities are found to be dynamically stable. It is shown that localization at the impurity modifies strongly the soliton p...
Unramified extensions of quadratic fields
Institute of Scientific and Technical Information of China (English)
Wei Li; Dong Yang; Xianke Zhang
2008-01-01
Let K be a global quadratic field, then every unramified abelian extension of K is proved to be absolutely Galois when K is a number field or under some natural conditions when K is a function field. The absolute Galois group is also determined explicitly.
Quadratic prediction of factor scores
Wansbeek, T
1999-01-01
Factor scores are naturally predicted by means of their conditional expectation given the indicators y. Under normality this expectation is linear in y but in general it is an unknown function of y. II is discussed that under nonnormality factor scores can be more precisely predicted by a quadratic
Quadratic Variation by Markov Chains
DEFF Research Database (Denmark)
Hansen, Peter Reinhard; Horel, Guillaume
We introduce a novel estimator of the quadratic variation that is based on the the- ory of Markov chains. The estimator is motivated by some general results concerning filtering contaminated semimartingales. Specifically, we show that filtering can in prin- ciple remove the effects of market...
Kuramoto dynamics in Hamiltonian systems.
Witthaut, Dirk; Timme, Marc
2014-09-01
The Kuramoto model constitutes a paradigmatic model for the dissipative collective dynamics of coupled oscillators, characterizing in particular the emergence of synchrony (phase locking). Here we present a classical Hamiltonian (and thus conservative) system with 2N state variables that in its action-angle representation exactly yields Kuramoto dynamics on N-dimensional invariant manifolds. We show that locking of the phase of one oscillator on a Kuramoto manifold to the average phase emerges where the transverse Hamiltonian action dynamics of that specific oscillator becomes unstable. Moreover, the inverse participation ratio of the Hamiltonian dynamics perturbed off the manifold indicates the global synchronization transition point for finite N more precisely than the standard Kuramoto order parameter. The uncovered Kuramoto dynamics in Hamiltonian systems thus distinctly links dissipative to conservative dynamics.
Continuum Hamiltonian Hopf Bifurcation II
Hagstrom, G I
2013-01-01
Building on the development of [MOR13], bifurcation of unstable modes that emerge from continuous spectra in a class of infinite-dimensional noncanonical Hamiltonian systems is investigated. Of main interest is a bifurcation termed the continuum Hamiltonian Hopf (CHH) bifurcation, which is an infinite-dimensional analog of the usual Hamiltonian Hopf (HH) bifurcation. Necessary notions pertaining to spectra, structural stability, signature of the continuous spectra, and normal forms are described. The theory developed is applicable to a wide class of 2+1 noncanonical Hamiltonian matter models, but the specific example of the Vlasov-Poisson system linearized about homogeneous (spatially independent) equilibria is treated in detail. For this example, structural (in)stability is established in an appropriate functional analytic setting, and two kinds of bifurcations are considered, one at infinite and one at finite wavenumber. After defining and describing the notion of dynamical accessibility, Kre\\u{i}n-like the...
Hamiltonian Structure of PI Hierarchy
Directory of Open Access Journals (Sweden)
Kanehisa Takasaki
2007-03-01
Full Text Available The string equation of type (2,2g+1 may be thought of as a higher order analogue of the first Painlevé equation that corresponds to the case of g = 1. For g > 1, this equation is accompanied with a finite set of commuting isomonodromic deformations, and they altogether form a hierarchy called the PI hierarchy. This hierarchy gives an isomonodromic analogue of the well known Mumford system. The Hamiltonian structure of the Lax equations can be formulated by the same Poisson structure as the Mumford system. A set of Darboux coordinates, which have been used for the Mumford system, can be introduced in this hierarchy as well. The equations of motion in these Darboux coordinates turn out to take a Hamiltonian form, but the Hamiltonians are different from the Hamiltonians of the Lax equations (except for the lowest one that corresponds to the string equation itself.
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.
Hamiltonian analysis of interacting fluids
Energy Technology Data Exchange (ETDEWEB)
Banerjee, Rabin; Mitra, Arpan Krishna [S. N. Bose National Centre for Basic Sciences, Kolkata (India); Ghosh, Subir [Indian Statistical Institute, Kolkata (India)
2015-05-15
Ideal fluid dynamics is studied as a relativistic field theory with particular stress on its hamiltonian structure. The Schwinger condition, whose integrated version yields the stress tensor conservation, is explicitly verified both in equal-time and light-cone coordinate systems. We also consider the hamiltonian formulation of fluids interacting with an external gauge field. The complementary roles of the canonical (Noether) stress tensor and the symmetric one obtained by metric variation are discussed. (orig.)
When are vector fields hamiltonian?
Crehan, P
1994-01-01
Dynamical systems can be quantised only if they are Hamiltonian. This prompts the question from which our talk gets its title. We show how the simple predator-prey equation and the damped harmonic oscillator can be considered to be Hamiltonian with respect to an infinite number of non-standard Poisson brackets. This raises some interesting questions about the nature of quantisation. Questions which are valid even for flows which possess a canonical structure.
The Quadratic Graver Cone, Quadratic Integer Minimization, and Extensions
Lee, Jon; Romanchuk, Lyubov; Weismantel, Robert
2010-01-01
We consider the nonlinear integer programming problem of minimizing a quadratic function over the integer points in variable dimension satisfying a system of linear inequalities. We show that when the Graver basis of the matrix defining the system is given, and the quadratic function lies in a suitable {\\em dual Graver cone}, the problem can be solved in polynomial time. We discuss the relation between this cone and the cone of positive semidefinite matrices, and show that none contains the other. So we can minimize in polynomial time some non-convex and some (including all separable) convex quadrics. We conclude by extending our results to efficient integer minimization of multivariate polynomial functions of arbitrary degree lying in suitable cones.
Consensus-ADMM for General Quadratically Constrained Quadratic Programming
Huang, Kejun; Sidiropoulos, Nicholas D.
2016-10-01
Non-convex quadratically constrained quadratic programming (QCQP) problems have numerous applications in signal processing, machine learning, and wireless communications, albeit the general QCQP is NP-hard, and several interesting special cases are NP-hard as well. This paper proposes a new algorithm for general QCQP. The problem is first reformulated in consensus optimization form, to which the alternating direction method of multipliers (ADMM) can be applied. The reformulation is done in such a way that each of the sub-problems is a QCQP with only one constraint (QCQP-1), which is efficiently solvable irrespective of (non-)convexity. The core components are carefully designed to make the overall algorithm more scalable, including efficient methods for solving QCQP-1, memory efficient implementation, parallel/distributed implementation, and smart initialization. The proposed algorithm is then tested in two applications: multicast beamforming and phase retrieval. The results indicate superior performance over prior state-of-the-art methods.
Falomir, H.; Pisani, P. A. G.; Vega, F.; Cárcamo, D.; Méndez, F.; Loewe, M.
2016-02-01
We study two-dimensional Hamiltonians in phase space with noncommutativity both in coordinates and momenta. We consider the generator of rotations on the noncommutative plane and the Lie algebra generated by Hermitian rotationally invariant quadratic forms of noncommutative dynamical variables. We show that two quantum phases are possible, characterized by the Lie algebras {sl}(2,{{R}}) or su(2) according to the relation between the noncommutativity parameters, with the rotation generator related with the Casimir operator. From this algebraic perspective, we analyze the spectrum of some simple models with nonrelativistic rotationally invariant Hamiltonians in this noncommutative phase space, such as the isotropic harmonic oscillator, the Landau problem and the cylindrical well potential.
Falomir, H; Vega, F; Cárcamo, D; Méndez, F; Loewe, M
2015-01-01
We study two-dimensional Hamiltonians in phase space with noncommutativity both in coordinates and momenta. We consider the generator of rotations on the noncommutative plane and the Lie algebra generated by Hermitian rotationally invariant quadratic forms of noncommutative dynamical variables. We show that two quantum phases are possible, characterized by the Lie algebras $sl(2,\\mathbb{R})$ or $su(2)$ according to the relation between the noncommutativity parameters. From this perspective, we analyze the spectrum of some simple models with nonrelativistic rotationally invariant Hamiltonians in this noncommutative phase space, as the isotropic harmonic oscillator, the Landau problem and the cylindrical well potential.
Integrability of Quadratic Non-autonomous Quantum Linear Systems
Lopez, Raquel
The Quantum Harmonic Oscillator is one of the most important models in Quantum Mechanics. Analogous to the classical mass vibrating back and forth on a spring, the quantum oscillator system has attracted substantial attention over the years because of its importance in many advanced and difficult quantum problems. This dissertation deals with solving generalized models of the time-dependent Schrodinger equation which are called generalized quantum harmonic oscillators, and these are characterized by an arbitrary quadratic Hamiltonian of linear momentum and position operators. The primary challenge in this work is that most quantum models with timedependence are not solvable explicitly, yet this challenge became the driving motivation for this work. In this dissertation, the methods used to solve the time-dependent Schrodinger equation are the fundamental singularity (or Green's function) and the Fourier (eigenfunction expansion) methods. Certain Riccati- and Ermakov-type systems arise, and these systems are highlighted and investigated. The overall aims of this dissertation are to show that quadratic Hamiltonian systems are completely integrable systems, and to provide explicit approaches to solving the time-dependent Schr¨odinger equation governed by an arbitrary quadratic Hamiltonian operator. The methods and results established in the dissertation are not yet well recognized in the literature, yet hold for high promise for further future research. Finally, the most recent results in the dissertation correspond to the harmonic oscillator group and its symmetries. A simple derivation of the maximum kinematical invariance groups of the free particle and quantum harmonic oscillator is constructed from the view point of the Riccati- and Ermakov-type systems, which shows an alternative to the traditional Lie Algebra approach. To conclude, a missing class of solutions of the time-dependent Schrodinger equation for the simple harmonic oscillator in one dimension is
Interchange graphs and the Hamiltonian cycle polytope
Sierksma, G
1998-01-01
This paper answers the (non)adjacency question for the whole spectrum of Hamiltonian cycles on the Hamiltonian cycle polytope (HC-polytope), also called the symmetric traveling salesman polytope, namely from Hamiltonian cycles that differ in only two edges through Hamiltonian cycles that are edge di
Hamiltonian description of the ideal fluid
Energy Technology Data Exchange (ETDEWEB)
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.
Quadratic and 2-Crossed Modules of Algebras
Institute of Scientific and Technical Information of China (English)
Z. Arvasi; E. Ulualan
2007-01-01
In this work, we define the quadratic modules for commutative algebras and give relations among 2-crossed modules, crossed squares, quadratic modules and simplicial commutative algebras with Moore complex of length 2.
Energy Technology Data Exchange (ETDEWEB)
Cruz, Hans, E-mail: hans@ciencias.unam.mx [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, 04510 México DF (Mexico); Schuch, Dieter [Institut für Theoretische Physik, JW Goethe-Universität Frankfurt am Main, Max-von-Laue-Str. 1, D-60438 Frankfurt am Main (Germany); Castaños, Octavio, E-mail: ocasta@nucleares.unam.mx [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, 04510 México DF (Mexico); Rosas-Ortiz, Oscar [Physics Department, Cinvestav, A. P. 14-740, 07000 México D. F. (Mexico)
2015-09-15
The sensitivity of the evolution of quantum uncertainties to the choice of the initial conditions is shown via a complex nonlinear Riccati equation leading to a reformulation of quantum dynamics. This sensitivity is demonstrated for systems with exact analytic solutions with the form of Gaussian wave packets. In particular, one-dimensional conservative systems with at most quadratic Hamiltonians are studied.
Team Decision Problems with Convex Quadratic Constraints
Gattami, Ather
2015-01-01
In this paper, we consider linear quadratic team problems with an arbitrary number of quadratic constraints in both stochastic and deterministic settings. The team consists of players with different measurements about the state of nature. The objective of the team is to minimize a quadratic cost subject to additional finite number of quadratic constraints. We first consider the problem of countably infinite number of players in the team for a bounded state of nature with a Gaussian distributi...
A polyhedral approach to quadratic assignment problem
Köksaldı, Ahmet Sertaç Murat
1994-01-01
Ankara : Department of Industrial Engineering and the Institute of Engineering and Sciences of Bilkent University, 1994. Thesis (Master's) -- Bilkent University, 1994. Includes bibliographical references. In this thesis, Quadratic Assignment Problem is considered. Since Quadratic Assignment Problem is JVP-bard, no polynomial time exact solution method exists. Proving optimality of solutions to Quadratic Assignment Problems has been limited to instances of small dimension. In...
Orthogonality preserving infinite dimensional quadratic stochastic operators
Energy Technology Data Exchange (ETDEWEB)
Akın, Hasan [Department of Mathematics, Faculty of Education, Zirve University, Gaziantep, 27260 (Turkey); Mukhamedov, Farrukh [Department of Computational & Theoretical Sciences Faculty of Science, International Islamic University Malaysia P.O. Box, 141, 25710, Kuantan Pahang (Malaysia)
2015-09-18
In the present paper, we consider a notion of orthogonal preserving nonlinear operators. We introduce π-Volterra quadratic operators finite and infinite dimensional settings. It is proved that any orthogonal preserving quadratic operator on finite dimensional simplex is π-Volterra quadratic operator. In infinite dimensional setting, we describe all π-Volterra operators in terms orthogonal preserving operators.
Extending the Scope of Robust Quadratic Optimization
Marandi, Ahmadreza; Ben-Tal, A.; den Hertog, Dick; Melenberg, Bertrand
2017-01-01
In this paper, we derive tractable reformulations of the robust counterparts of convex quadratic and conic quadratic constraints with concave uncertainties for a broad range of uncertainty sets. For quadratic constraints with convex uncertainty, it is well-known that the robust counterpart is, in ge
Global Optimization of a Class of Nonconvex Quadratically Constrained Quadratic Programming Problems
Institute of Scientific and Technical Information of China (English)
Yong XIA
2011-01-01
In this paper we study a class of nonconvex quadratically constrained quadratic programming problems generalized from relaxations of quadratic assignment problems.We show that each problem is polynomially solved.Strong duality holds if a redundant constraint is introduced.As an application,a new lower bound is proposed for the quadratic assignment problem.
Runtime of unstructured search with a faulty Hamiltonian oracle
Temme, Kristan
2014-08-01
We show that it is impossible to obtain a quantum speedup for a faulty Hamiltonian oracle. The effect of dephasing noise to this continuous-time oracle model has first been investigated by Shenvi, Brown, and Whaley [Phys. Rev. A 68, 052313 (2003)., 10.1103/PhysRevA.68.052313]. The authors consider a faulty oracle described by a continuous-time master equation that acts as dephasing noise in the basis determined by the marked item. The analysis focuses on the implementation with a particular driving Hamiltonian. A universal lower bound for this oracle model, which rules out a better performance with a different driving Hamiltonian, has so far been lacking. Here, we derive an adversary-type lower bound which shows that the evolution time T has to be at least in the order of N, i.e., the size of the search space, when the error rate of the oracle is constant. This means that quadratic quantum speedup vanishes and the runtime assumes again the classical scaling. For the standard quantum oracle model this result was first proven by Regev and Schiff [in Automata, Languages and Programming, Lecture Notes in Computer Science Vol. 5125 (Springer, Berlin, 2008), pp. 773-781]. Here, we extend this result to the continuous-time setting.
The molecular asymmetric rigid rotor Hamiltonian as an exactly solvable model
Jarvis, P D
2008-01-01
Representations of the rotation group may be formulated in second-quantised language via Schwinger's transcription of angular momentum states onto states of an effective two-dimensional oscillator. In the case of the molecular asymmetric rigid rotor, by projecting onto the state space of rigid body rotations, the standard Ray Hamiltonian $H(1,\\kappa,-1)$ (with asymmetry parameter $1 \\ge \\kappa \\ge -1$), becomes a quadratic polynomial in the generators of the associated dynamical $su(1,1)$ algebra. We point out that $H(1,\\kappa,-1)$ is in fact quadratic in the Gaudin operators arising from the quasiclassical limit of an associated $su_q(1,1)$ Yang-Baxter algebra. The general asymmetric rigid rotor Hamiltonian is thus an exactly solvable model. This fact has important implications for the structure of the spectrum, as well as for the eigenstates and correlation functions of the model.
Effective Hamiltonian of strained graphene.
Linnik, T L
2012-05-23
Based on the symmetry properties of the graphene lattice, we derive the effective Hamiltonian of graphene under spatially nonuniform acoustic and optical strains. Comparison with the published results of the first-principles calculations allows us to determine the values of some Hamiltonian parameters, and suggests the validity of the derived Hamiltonian for acoustical strain up to 10%. The results are generalized for the case of graphene with broken plane reflection symmetry, which corresponds, for example, to the case of graphene placed on a substrate. Here, essential modifications to the Hamiltonian give rise, in particular, to the gap opening in the spectrum in the presence of the out-of-plane component of optical strain, which is shown to be due to the lifting of the sublattice symmetry. The developed effective Hamiltonian can be used as a convenient tool for analysis of a variety of strain-related effects, including electron-phonon interaction or pseudo-magnetic fields induced by the nonuniform strain.
Hamiltonian Dynamics of Preferential Attachment
Zuev, Konstantin; Krioukov, Dmitri
2015-01-01
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, 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 preferential attachment. 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 preferential attachment is nearly identical to the ensemble of random graphs with scale-free degree d...
The electronic Hamiltonian for cuprates
Annett, James F.; Mcmahan, A. K.; Martin, Richard M.
1991-01-01
A realistic many-body Hamiltonian for the cuprate superconductors should include both copper d and oxygen p states, hopping matrix elements between them, and Coulomb energies, both on-site and inter-site. We have developed a novel computational scheme for deriving the relevant parameters ab initio from a constrained occupation local density functional. The scheme includes numerical calculation of appropriate Wannier functions for the copper and oxygen states. Explicit parameter values are given for La2CuO4. These parameters are generally consistent with other estimates and with the observed superexchange energy. Secondly, we address whether this complicated multi-band Hamiltonian can be reduced to a simpler one with fewer basis states per unit cell. We propose a mapping onto a new two-band effective Hamiltonian with one copper d and one oxygen p derived state per unit cell. This mapping takes into account the large oxygen-oxygen hopping given by the ab initio calculations.
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.
Unified Hamiltonian for conducting polymers
Leitão Botelho, André; Shin, Yongwoo; Li, Minghai; Jiang, Lili; Lin, Xi
2011-11-01
Two transferable physical parameters are incorporated into the Su-Schrieffer-Heeger Hamiltonian to model conducting polymers beyond polyacetylene: the parameter γ scales the electron-phonon coupling strength in aromatic rings and the other parameter ɛ specifies the heterogeneous core charges. This generic Hamiltonian predicts the fundamental band gaps of polythiophene, polypyrrole, polyfuran, poly-(p-phenylene), poly-(p-phenylene vinylene), and polyacenes, and their oligomers of all lengths, with an accuracy exceeding time-dependent density functional theory. Its computational costs for moderate-length polymer chains are more than eight orders of magnitude lower than first-principles approaches.
Hamiltonian systems as selfdual equations
Institute of Scientific and Technical Information of China (English)
2008-01-01
Hamiltonian systems with various time boundary conditions are formulated as absolute minima of newly devised non-negative action func-tionals obtained by a generalization of Bogomolnyi's trick of 'completing squares'. Reminiscent of the selfdual Yang-Mills equations, they are not derived from the fact that they are critical points (i.e., from the correspond- ing Euler-Lagrange equations) but from being zeroes of the corresponding non-negative Lagrangians. A general method for resolving such variational problems is also described and applied to the construction of periodic solutions for Hamiltonian systems, but also to study certain Lagrangian intersections.
"On some definitions in matrix algebra"
Magnus, Jan R.; Karim M. Abadir
2007-01-01
Many definitions in matrix algebra are not standardized. This notediscusses some of thepitfalls associated with undesirable orwrong definitions, anddealswith central conceptslikesymmetry, orthogonality, square root, Hermitian and quadratic forms, and matrix derivatives.
Asymptotic Normality of Quadratic Estimators.
Robins, James; Li, Lingling; Tchetgen, Eric; van der Vaart, Aad
2016-12-01
We prove conditional asymptotic normality of a class of quadratic U-statistics that are dominated by their degenerate second order part and have kernels that change with the number of observations. These statistics arise in the construction of estimators in high-dimensional semi- and non-parametric models, and in the construction of nonparametric confidence sets. This is illustrated by estimation of the integral of a square of a density or regression function, and estimation of the mean response with missing data. We show that estimators are asymptotically normal even in the case that the rate is slower than the square root of the observations.
quadratic spline finite element method
Directory of Open Access Journals (Sweden)
A. R. Bahadir
2002-01-01
Full Text Available The problem of heat transfer in a Positive Temperature Coefficient (PTC thermistor, which may form one element of an electric circuit, is solved numerically by a finite element method. The approach used is based on Galerkin finite element using quadratic splines as shape functions. The resulting system of ordinary differential equations is solved by the finite difference method. Comparison is made with numerical and analytical solutions and the accuracy of the computed solutions indicates that the method is well suited for the solution of the PTC thermistor problem.
Optimal control linear quadratic methods
Anderson, Brian D O
2007-01-01
This augmented edition of a respected text teaches the reader how to use linear quadratic Gaussian methods effectively for the design of control systems. It explores linear optimal control theory from an engineering viewpoint, with step-by-step explanations that show clearly how to make practical use of the material.The three-part treatment begins with the basic theory of the linear regulator/tracker for time-invariant and time-varying systems. The Hamilton-Jacobi equation is introduced using the Principle of Optimality, and the infinite-time problem is considered. The second part outlines the
Factorization method of quadratic template
Kotyrba, Martin
2017-07-01
Multiplication of two numbers is a one-way function in mathematics. Any attempt to distribute the outcome to its roots is called factorization. There are many methods such as Fermat's factorization, Dixońs method or quadratic sieve and GNFS, which use sophisticated techniques fast factorization. All the above methods use the same basic formula differing only in its use. This article discusses a newly designed factorization method. Effective implementation of this method in programs is not important, it only represents and clearly defines its properties.
Quadratic reactivity fuel cycle model
Energy Technology Data Exchange (ETDEWEB)
Lewins, J.D.
1985-11-01
For educational purposes it is highly desirable to provide simple yet realistic models for fuel cycle and fuel economy. In particular, a lumped model without recourse to detailed spatial calculations would be very helpful in providing the student with a proper understanding of the purposes of fuel cycle calculations. A teaching model for fuel cycle studies based on a lumped model assuming the summability of partial reactivities with a linear dependence of reactivity usefully illustrates fuel utilization concepts. The linear burnup model does not satisfactorily represent natural enrichment reactors. A better model, showing the trend of initial plutonium production before subsequent fuel burnup and fission product generation, is a quadratic fit. The study of M-batch cycles, reloading 1/Mth of the core at end of cycle, is now complicated by nonlinear equations. A complete account of the asymptotic cycle for any order of M-batch refueling can be given and compared with the linear model. A complete account of the transient cycle can be obtained readily in the two-batch model and this exact solution would be useful in verifying numerical marching models. It is convenient to treat the parabolic fit rho = 1 - tau/sup 2/ as a special case of the general quadratic fit rho = 1 - C/sub tau/ - (1 - C)tau/sup 2/ in suitably normalized reactivity and cycle time units. The parabolic results are given in this paper.
Skurnick, Ronald; Davi, Charles; Skurnick, Mia
2005-01-01
Since 1952, several well-known graph theorists have proven numerous results regarding Hamiltonian graphs. In fact, many elementary graph theory textbooks contain the theorems of Ore, Bondy and Chvatal, Chvatal and Erdos, Posa, and Dirac, to name a few. In this note, the authors state and prove some propositions of their own concerning Hamiltonian…
Hamiltonian monodromy as lattice defect
Zhilinskii, B.
2003-01-01
The analogy between monodromy in dynamical (Hamiltonian) systems and defects in crystal lattices is used in order to formulate some general conjectures about possible types of qualitative features of quantum systems which can be interpreted as a manifestation of classical monodromy in quantum finite particle (molecular) problems.
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.
Dynamical stability of Hamiltonian systems
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Dynamical stability has become the center of study on Hamiltonian system. In this article we intro-duce the recent development in some areas closely related to this topic, such as the KAM theory, Mather theory, Arnolddiffusion and non-singular collision of n-body problem.
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.
Time-reversible Hamiltonian systems
Schaft, Arjan van der
1982-01-01
It is shown that transfer matrices satisfying G(-s) = G(s) = G^T(-s) have a minimal Hamiltonian realization with an energy which is the sum of potential and kinetic energy, yielding the time reversibility of the equations. Furthermore connections are made with an associated gradient system. The
Hamiltonian analysis of curvature-squared gravity with or without conformal invariance
Klusoň, Josef; Tureanu, Anca
2013-01-01
We analyze gravitational theories with quadratic curvature terms, including the case of conformally invariant Weyl gravity, motivated by the intention to find a renormalizable theory of gravity in the ultraviolet region, yet yielding general relativity at long distances. In the Hamiltonian formulation of Weyl gravity, the number of local constraints is equal to the number of unstable directions in phase space, which in principle could be sufficient for eliminating the unstable degrees of freedom in the full nonlinear theory. All the other theories of quadratic type are unstable -- a problem appearing as ghost modes in the linearized theory. We find that the full projection of the Weyl tensor onto a three-dimensional hypersurface contains an additional fully traceless component, given by a quadratic extrinsic curvature tensor. A certain inconsistency in the literature is found and resolved: when the conformal invariance of Weyl gravity is broken by a cosmological constant term, the theory becomes pathological,...
On third order integrable vector Hamiltonian equations
Meshkov, A. G.; Sokolov, V. V.
2017-03-01
A complete list of third order vector Hamiltonian equations with the Hamiltonian operator Dx having an infinite series of higher conservation laws is presented. A new vector integrable equation on the sphere is found.
Hamiltonian realizations of nonlinear adjoint operators
Fujimoto, Kenji; Scherpen, Jacquelien M.A.; Gray, W. Steven
2002-01-01
This paper addresses the issue of state-space realizations for nonlinear adjoint operators. In particular, the relationships between nonlinear Hilbert adjoint operators, Hamiltonian extensions and port-controlled Hamiltonian systems are established. Then, characterizations of the adjoints of control
Hamiltonian Realizations of Nonlinear Adjoint Operators
Fujimoto, Kenji; Scherpen, Jacquelien M.A.; Gray, W. Steven
2000-01-01
This paper addresses state-space realizations for nonlinear adjoint operators. In particular the relationship among nonlinear Hilbert adjoint operators, Hamiltonian extensions and port-controlled Hamiltonian systems are clarified. The characterization of controllability, observability and Hankel ope
Quantum Jacobi fields in Hamiltonian mechanics
Giachetta, G; Sardanashvily, G
2000-01-01
Jacobi fields of classical solutions of a Hamiltonian mechanical system are quantized in the framework of vertical-extended Hamiltonian formalism. Quantum Jacobi fields characterize quantum transitions between classical solutions.
Quantization of noncommutative completely integrable Hamiltonian systems
Energy Technology Data Exchange (ETDEWEB)
Giachetta, G. [Department of Mathematics and Informatics, University of Camerino, 62032 Camerino (Italy); Mangiarotti, L. [Department of Mathematics and Informatics, University of Camerino, 62032 Camerino (Italy); Sardanashvily, G. [Department of Theoretical Physics, Moscow State University, 117234 Moscow (Russian Federation)]. E-mail: gennadi.sardanashvily@unicam.it
2007-02-26
Integrals of motion of a Hamiltonian system need not commute. The classical Mishchenko-Fomenko theorem enables one to quantize a noncommutative completely integrable Hamiltonian system around its invariant submanifold as the Abelian one.
Tang, Chun-Ming; Jian, Jin-Bao
2008-10-01
Based on an augmented Lagrangian line search function, a sequential quadratically constrained quadratic programming method is proposed for solving nonlinearly constrained optimization problems. Compared to quadratic programming solved in the traditional SQP methods, a convex quadratically constrained quadratic programming is solved here to obtain a search direction, and the Maratos effect does not occur without any other corrections. The "active set" strategy used in this subproblem can avoid recalculating the unnecessary gradients and (approximate) Hessian matrices of the constraints. Under certain assumptions, the proposed method is proved to be globally, superlinearly, and quadratically convergent. As an extension, general problems with inequality and equality constraints as well as nonmonotone line search are also considered.
Mathematical Aspects of Quantum Systems with a Pseudo-Hermitian Hamiltonian
Bebiano, N.; da Providência, J.; da Providência, J. P.
2016-04-01
A non-self-adjoint bosonic Hamiltonian H possessing real eigenvalues is investigated. It is shown that the operator can be diagonalized by making use of pseudo-bosonic operators. The biorthogonal sets of eigenvectors for the Hamiltonian and its adjoint are explicitly constructed. The positive definite operator which connects both sets of eigenvectors is also given. The dynamics of the model is briefly analyzed.
Revised Virial Theorem for Hamiltonians with Coordinates-Momentum Coupling Terms
Institute of Scientific and Technical Information of China (English)
GUO Qin; FAN Hong-Yi
2008-01-01
Usually the Virial thcorem,which can be derived from the Feynman-Hellmann theorem,applies to Hamil-tonians without coordinates-momentum coupling.In this paper we discuss when there are such kind of couplings in Hamiltonians then how the Virial theorem should be modified.We also discuss the energy contribution arising from the coordinates-momentum coupling for a definite energy level.
On Algebraic Approach in Quadratic Systems
Directory of Open Access Journals (Sweden)
Matej Mencinger
2011-01-01
Full Text Available When considering friction or resistance, many physical processes are mathematically simulated by quadratic systems of ODEs or discrete quadratic dynamical systems. Probably the most important problem when such systems are applied in engineering is the stability of critical points and (nonchaotic dynamics. In this paper we consider homogeneous quadratic systems via the so-called Markus approach. We use the one-to-one correspondence between homogeneous quadratic dynamical systems and algebra which was originally introduced by Markus in (1960. We resume some connections between the dynamics of the quadratic systems and (algebraic properties of the corresponding algebras. We consider some general connections and the influence of power-associativity in the corresponding quadratic system.
An Algorithm for Solving Quadratic Programming Problems
Directory of Open Access Journals (Sweden)
V. Moraru
1997-08-01
Full Text Available Herein is investigated the method of solution of quadratic programming problems. The algorithm is based on the effective selection of constraints. Quadratic programming with constraints-equalities are solved with the help of an algorithm, so that matrix inversion is avoided, because of the more convenient organization of the Calculus. Optimal solution is determined in a finite number of iterations. It is discussed the extension of the algorithm over solving quadratic non-convex programming problems.
Port-Hamiltonian systems: an introductory survey
Schaft, van der Arjan; Sanz-Sole, M.; Soria, J.; Varona, J.L.; Verdera, J.
2006-01-01
The theory of port-Hamiltonian systems provides a framework for the geometric description of network models of physical systems. It turns out that port-based network models of physical systems immediately lend themselves to a Hamiltonian description. While the usual geometric approach to Hamiltonian
New sufficient conditions for Hamiltonian paths.
Rahman, M Sohel; Kaykobad, M; Firoz, Jesun Sahariar
2014-01-01
A Hamiltonian path in a graph is a path involving all the vertices of the graph. In this paper, we revisit the famous Hamiltonian path problem and present new sufficient conditions for the existence of a Hamiltonian path in a graph.
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…
Geometric Hamiltonian structures and perturbation theory
Energy Technology Data Exchange (ETDEWEB)
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.
Driving Hamiltonian in a Quantum Search Problem
Oshima, K
2001-01-01
We examine the driving Hamiltonian in the analog analogue of Grover's algorithm by Farhi and Gutmann. For a quantum system with a given Hamiltonian $E|w> $ from an initial state $|s>$, the driving Hamiltonian $E^{\\prime}|s> < s|(E^{\\prime} \
The Random Quadratic Assignment Problem
Paul, Gerald; Shao, Jia; Stanley, H. Eugene
2011-11-01
The quadratic assignment problem, QAP, is one of the most difficult of all combinatorial optimization problems. Here, we use an abbreviated application of the statistical mechanics replica method to study the asymptotic behavior of instances in which the entries of at least one of the two matrices that specify the problem are chosen from a random distribution P. Surprisingly, the QAP has not been studied before using the replica method despite the fact that the QAP was first proposed over 50 years ago and the replica method was developed over 30 years ago. We find simple forms for C min and C max , the costs of the minimal and maximum solutions respectively. Notable features of our results are the symmetry of the results for C min and C max and their dependence on P only through its mean and standard deviation, independent of the details of P.
Renormalized Effective QCD Hamiltonian Gluonic Sector
Robertson, D G; Szczepaniak, A P; Ji, C R; Cotanch, S R
1999-01-01
Extending previous QCD Hamiltonian studies, we present a new renormalization procedure which generates an effective Hamiltonian for the gluon sector. The formulation is in the Coulomb gauge where the QCD Hamiltonian is renormalizable and the Gribov problem can be resolved. We utilize elements of the Glazek and Wilson regularization method but now introduce a continuous cut-off procedure which eliminates non-local counterterms. The effective Hamiltonian is then derived to second order in the strong coupling constant. The resulting renormalized Hamiltonian provides a realistic starting point for approximate many-body calculations of hadronic properties for systems with explicit gluon degrees of freedom.
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.
Lowest Eigenvalues of Random Hamiltonians
Shen, J J; Arima, A; Yoshinaga, N
2008-01-01
In this paper we present results of the lowest eigenvalues of random Hamiltonians for both fermion and boson systems. We show that an empirical formula of evaluating the lowest eigenvalues of random Hamiltonians in terms of energy centroids and widths of eigenvalues are applicable to many different systems (except for $d$ boson systems). We improve the accuracy of the formula by adding moments higher than two. We suggest another new formula to evaluate the lowest eigenvalues for random matrices with large dimensions (20-5000). These empirical formulas are shown to be applicable not only to the evaluation of the lowest energy but also to the evaluation of excited energies of systems under random two-body interactions.
On Hamiltonian formulation of cosmologies
Indian Academy of Sciences (India)
K D Krori; S Dutta
2000-03-01
Novello et al [1,2] have shown that it is possible to ﬁnd a pair of canonically conjugate variables (written in terms of gauge-invariant variables) so as to obtain a Hamiltonian that describes the dynamics of a cosmological system. This opens up the way to the usual technique of quantization. Elbaz et al [4] have applied this method to the Hamiltonian formulation of FRW cosmological equations. This note presents a generalization of this approach to a variety of cosmologies. A general Schrödinger wave equation has been derived and exact solutions have been worked out for the stiff matter era for some cosmological models. It is argued that these solutions appear to hint at their possible relevance in the early phase of cosmological evolution.
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.
Hamiltonian mechanics of stochastic acceleration.
Burby, J W; Zhmoginov, A I; Qin, H
2013-11-08
We show how to find the physical Langevin equation describing the trajectories of particles undergoing collisionless stochastic acceleration. These stochastic differential equations retain not only one-, but two-particle statistics, and inherit the Hamiltonian nature of the underlying microscopic equations. This opens the door to using stochastic variational integrators to perform simulations of stochastic interactions such as Fermi acceleration. We illustrate the theory by applying it to two example problems.
Hamiltonian chaos and fractional dynamics
Zaslavsky, George M
2008-01-01
The dynamics of realistic Hamiltonian systems has unusual microscopic features that are direct consequences of its fractional space-time structure and its phase space topology. The book deals with the fractality of the chaotic dynamics and kinetics, and also includes material on non-ergodic and non-well-mixing Hamiltonian dynamics. The book does not follow the traditional scheme of most of today's literature on chaos. The intention of the author has been to put together some of the most complex and yet open problems on the general theory of chaotic systems. The importance of the discussed issues and an understanding of their origin should inspire students and researchers to touch upon some of the deepest aspects of nonlinear dynamics. The book considers the basic principles of the Hamiltonian theory of chaos and some applications including for example, the cooling of particles and signals, control and erasing of chaos, polynomial complexity, Maxwell's Demon, and others. It presents a new and realistic image ...
Binary Quadratic Forms: A Historical View
Khosravani, Azar N.; Beintema, Mark B.
2006-01-01
We present an expository account of the development of the theory of binary quadratic forms. Beginning with the formulation and proof of the Two-Square Theorem, we show how the study of forms of the type x[squared] + ny[squared] led to the discovery of the Quadratic Reciprocity Law, and how this theorem, along with the concept of reduction relates…
Quadratic Boost A-Source Impedance Network
DEFF Research Database (Denmark)
Siwakoti, Yam Prasad; Blaabjerg, Frede; Chub, Andrii
2016-01-01
A novel quadratic boost type A-source impedance network is proposed in this paper for realizing converters that demand a very high voltage gain. To achieve that, the proposed network uses an auto-transformer, whose obtained gain is quadratically dependent on the duty ratio and is presently not ma...
Quadratic Boost A-Source Impedance Network
DEFF Research Database (Denmark)
Siwakoti, Yam Prasad; Blaabjerg, Frede; Chub, Andrii
2016-01-01
A novel quadratic boost A-source impedance network is proposed to realize converters that demand very high voltage gain. To satisfy the requirement, the network uses an autotransformer where the obtained gain is quadratically dependent on the duty ratio and is unmatched by any existing impedance ...
Factorising a Quadratic Expression with Geometric Insights
Joarder, Anwar H.
2015-01-01
An algorithm is presented for factorising a quadratic expression to facilitate instruction and learning. It appeals to elementary geometry which may provide better insights to some students or teachers. There have been many methods for factorising a quadratic expression described in school text books. However, students often seem to struggle with…
An example in linear quadratic optimal control
Weiss, George; Zwart, Heiko J.
1998-01-01
We construct a simple example of a quadratic optimal control problem for an infinite-dimensional linear system based on a shift semigroup. This system has an unbounded control operator. The cost is quadratic in the input and the state, and the weighting operators are bounded. Despite its extreme
An example in linear quadratic optimal control
Weiss, George; Zwart, Heiko J.
1998-01-01
We construct a simple example of a quadratic optimal control problem for an infinite-dimensional linear system based on a shift semigroup. This system has an unbounded control operator. The cost is quadratic in the input and the state, and the weighting operators are bounded. Despite its extreme sim
Quadratic Hedging of Basis Risk
Directory of Open Access Journals (Sweden)
Hardy Hulley
2015-02-01
Full Text Available This paper examines a simple basis risk model based on correlated geometric Brownian motions. We apply quadratic criteria to minimize basis risk and hedge in an optimal manner. Initially, we derive the Föllmer–Schweizer decomposition for a European claim. This allows pricing and hedging under the minimal martingale measure, corresponding to the local risk-minimizing strategy. Furthermore, since the mean-variance tradeoff process is deterministic in our setup, the minimal martingale- and variance-optimal martingale measures coincide. Consequently, the mean-variance optimal strategy is easily constructed. Simple pricing and hedging formulae for put and call options are derived in terms of the Black–Scholes formula. Due to market incompleteness, these formulae depend on the drift parameters of the processes. By making a further equilibrium assumption, we derive an approximate hedging formula, which does not require knowledge of these parameters. The hedging strategies are tested using Monte Carlo experiments, and are compared with results achieved using a utility maximization approach.
On Quadratic Variation of Martingales
Indian Academy of Sciences (India)
Rajeeva L Karandikar; B V Rao
2014-08-01
We give a construction of an explicit mapping $$\\Psi: D([0,∞),\\mathbb{R})→ D([0,∞),\\mathbb{R}),$$ where $D([0,∞), \\mathbb{R})$ denotes the class of real valued r.c.l.l. functions on $[0,∞)$ such that for a locally square integrable martingale $(M_t)$ with r.c.l.l. paths, $$\\Psi(M.())=A.()$$ gives the quadratic variation process (written usually as $[M,M]_t$) of $(M_t)$. We also show that this process $(A_t)$ is the unique increasing process $(B_t)$ such that $M_t^2-B_t$ is a local martingale, $B_0=0$ and $$\\mathbb{P}(( B)_t=[( M)_t]^2, 0 < ∞)=1.$$ Apart from elementary properties of martingales, the only result used is the Doob’s maximal inequality. This result can be the starting point of the development of the stochastic integral with respect to r.c.l.l. martingales.
On the classification of elliptic foliations induced by real quadratic fields with center
Puchuri, Liliana; Bueno, Orestes
2016-12-01
Related to the study of Hilbert's infinitesimal problem, is the problem of determining the existence and estimating the number of limit cycles of the linear perturbation of Hamiltonian fields. A classification of the elliptic foliations in the projective plane induced by the fields obtained by quadratic fields with center was already studied by several authors. In this work, we devise a unified proof of the classification of elliptic foliations induced by quadratic fields with center. This technique involves using a formula due to Cerveau & Lins Neto to calculate the genus of the generic fiber of a first integral of foliations of these kinds. Furthermore, we show that these foliations induce several examples of linear families of foliations which are not bimeromorphically equivalent to certain remarkable examples given by Lins Neto.
Vladimirov, Igor G
2012-01-01
The paper is concerned with open quantum systems whose Heisenberg dynamics are described by quantum stochastic differential equations driven by external boson fields. The system-field coupling operators are assumed to be quadratic polynomials of the system observables, with the latter satisfying canonical commutation relations. In combination with a cubic system Hamiltonian, this leads to a class of quasilinear quantum stochastic systems which retain algebraic closedness in the evolution of mixed moments of the observables. Although such a system is nonlinear and its quantum state is no longer Gaussian, the dynamics of the moments of any order are amenable to exact analysis, including the computation of their steady-state values. In particular, a generalized criterion is developed for quadratic stability of the quasilinear systems. The results of the paper are applicable to the generation of non-Gaussian quantum states with manageable moments and an optimal design of linear quantum controllers for quasilinear...
A possible method for non-Hermitian and Non-PT-symmetric Hamiltonian systems.
Li, Jun-Qing; Miao, Yan-Gang; Xue, Zhao
2014-01-01
A possible method to investigate non-Hermitian Hamiltonians is suggested through finding a Hermitian operator η+ and defining the annihilation and creation operators to be η+ -pseudo-Hermitian adjoint to each other. The operator η+ represents the η+ -pseudo-Hermiticity of Hamiltonians. As an example, a non-Hermitian and non-PT-symmetric Hamiltonian with imaginary linear coordinate and linear momentum terms is constructed and analyzed in detail. The operator η+ is found, based on which, a real spectrum and a positive-definite inner product, together with the probability explanation of wave functions, the orthogonality of eigenstates, and the unitarity of time evolution, are obtained for the non-Hermitian and non-PT-symmetric Hamiltonian. Moreover, this Hamiltonian turns out to be coupled when it is extended to the canonical noncommutative space with noncommutative spatial coordinate operators and noncommutative momentum operators as well. Our method is applicable to the coupled Hamiltonian. Then the first and second order noncommutative corrections of energy levels are calculated, and in particular the reality of energy spectra, the positive-definiteness of inner products, and the related properties (the probability explanation of wave functions, the orthogonality of eigenstates, and the unitarity of time evolution) are found not to be altered by the noncommutativity.
A possible method for non-Hermitian and Non-PT-symmetric Hamiltonian systems.
Directory of Open Access Journals (Sweden)
Jun-Qing Li
Full Text Available A possible method to investigate non-Hermitian Hamiltonians is suggested through finding a Hermitian operator η+ and defining the annihilation and creation operators to be η+ -pseudo-Hermitian adjoint to each other. The operator η+ represents the η+ -pseudo-Hermiticity of Hamiltonians. As an example, a non-Hermitian and non-PT-symmetric Hamiltonian with imaginary linear coordinate and linear momentum terms is constructed and analyzed in detail. The operator η+ is found, based on which, a real spectrum and a positive-definite inner product, together with the probability explanation of wave functions, the orthogonality of eigenstates, and the unitarity of time evolution, are obtained for the non-Hermitian and non-PT-symmetric Hamiltonian. Moreover, this Hamiltonian turns out to be coupled when it is extended to the canonical noncommutative space with noncommutative spatial coordinate operators and noncommutative momentum operators as well. Our method is applicable to the coupled Hamiltonian. Then the first and second order noncommutative corrections of energy levels are calculated, and in particular the reality of energy spectra, the positive-definiteness of inner products, and the related properties (the probability explanation of wave functions, the orthogonality of eigenstates, and the unitarity of time evolution are found not to be altered by the noncommutativity.
New results for time reversed symplectic dynamic systems and quadratic functionals
Directory of Open Access Journals (Sweden)
Roman Simon Hilscher
2012-05-01
Full Text Available In this paper, we examine time scale symplectic (or Hamiltonian systems and the associated quadratic functionals which contain a forward shift in the time variable. Such systems and functionals have a close connection to Jacobi systems for calculus of variations and optimal control problems on time scales. Our results, among which we consider the Reid roundabout theorem, generalize the corresponding classical theory for time reversed discrete symplectic systems, as well as they complete the recently developed theory of time scale symplectic systems.
Quadratic algebra for superintegrable monopole system in a Taub-NUT space
Hoque, Md Fazlul; Marquette, Ian; Zhang, Yao-Zhong
2016-09-01
We introduce a Hartmann system in the generalized Taub-NUT space with Abelian monopole interaction. This quantum system includes well known Kaluza-Klein monopole and MIC-Zwanziger monopole as special cases. It is shown that the corresponding Schrödinger equation of the Hamiltonian is separable in both spherical and parabolic coordinates. We obtain the integrals of motion of this superintegrable model and construct the quadratic algebra and Casimir operator. This algebra can be realized in terms of a deformed oscillator algebra and has finite dimensional unitary representations (unirreps) which provide energy spectra of the system. This result coincides with the physical spectra obtained from the separation of variables.
Nandi, Debottam
2016-01-01
In this work, we present a consistent Hamiltonian analysis of cosmological perturbations for generalized non-canonical scalar fields. In order to do so, we introduce a new phase-space variable that is uniquely defined for different non-canonical scalar fields. We also show that this is the simplest and efficient way of expressing the Hamiltonian. We extend the Hamiltonian approach of [arXiv:1512.02539] to non-canonical scalar field and obtain a new definition of speed of sound in phase-space. In order to invert generalized phase-space Hamilton's equations to Euler-Lagrange equations of motion, we prescribe a general inversion formulae and show that our approach for non-canonical scalar field is consistent. We also obtain the third and fourth order interaction Hamiltonian for generalized non-canonical scalar fields and briefly discuss the extension of our method to generalized Galilean scalar fields.
The Group of Hamiltonian Homeomorphisms in the L^\\infty-norm
Müller, Stefan C
2007-01-01
The group Hameo (M,\\omega) of Hamiltonian homeomorphisms of a connected symplectic manifold (M,\\omega) was defined and studied in [7] and further in [6]. In these papers, the authors consistently used the L^{(1,\\infty)}-Hofer norm (and not the L^\\infty-Hofer norm) on the space of Hamiltonian paths (see below for the definitions). A justification for this choice was given in [7]. In this article we study the L^\\infty-case. In view of the fact that the Hofer norm on the group Ham (M,\\omega) of Hamiltonian diffeomorphisms does not depend on the choice of the L^{(1,\\infty)}-norm vs. the L^\\infty-norm [9], Y.-G. Oh and D. McDuff (private communications) asked whether the two notions of Hamiltonian homeomorphisms arising from the different norms coincide. We will give an affirmative answer to this question in this paper.
Monte Carlo Hamiltonian: Linear Potentials
Institute of Scientific and Technical Information of China (English)
LUO Xiang-Qian; LIU Jin-Jiang; HUANG Chun-Qing; JIANG Jun-Qin; Helmut KROGER
2002-01-01
We further study the validity of the Monte Carlo Hamiltonian method. The advantage of the method,in comparison with the standard Monte Carlo Lagrangian approach, is its capability to study the excited states. Weconsider two quantum mechanical models: a symmetric one V(x) = |x|/2; and an asymmetric one V(x) = ∞, forx ＜ 0 and V(x) = x, for x ≥ 0. The results for the spectrum, wave functions and thermodynamical observables are inagreement with the analytical or Runge-Kutta calculations.
LOCALIZATION THEOREM ON HAMILTONIAN GRAPHS
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Let G be a 2-connected graph of order n( 3).If I(u,v) S(u,v) or max {d(u),d(v)} n/2 for any two vertices u,v at distance two in an induced subgraph K1,3 or P3 of G,then G is hamiltonian.Here I(u,v) = ｜N(u)∩ N(v)｜,S(u,v) denotes thenumber of edges of maximum star containing u,v as an induced subgraph in G.
Discrete Hamiltonian for General Relativity
Ziprick, Jonathan
2015-01-01
Beginning from canonical general relativity written in terms of Ashtekar variables, we derive a discrete phase space with a physical Hamiltonian for gravity. The key idea is to define the gravitational fields within a complex of three-dimensional cells such that the dynamics is completely described by discrete boundary variables, and the full theory is recovered in the continuum limit. Canonical quantization is attainable within the loop quantum gravity framework, and we believe this will lead to a promising candidate for quantum gravity.
Chasing Hamiltonian structure in gyrokinetic theory
Burby, J W
2015-01-01
Hamiltonian structure is pursued and uncovered in collisional and collisionless gyrokinetic theory. A new Hamiltonian formulation of collisionless electromagnetic theory is presented that is ideally suited to implementation on modern supercomputers. The method used to uncover this structure is described in detail and applied to a number of examples, where several well-known plasma models are endowed with a Hamiltonian structure for the first time. The first energy- and momentum-conserving formulation of full-F collisional gyrokinetics is presented. In an effort to understand the theoretical underpinnings of this result at a deeper level, a \\emph{stochastic} Hamiltonian modeling approach is presented and applied to pitch angle scattering. Interestingly, the collision operator produced by the Hamiltonian approach is equal to the Lorentz operator plus higher-order terms, but does not exactly conserve energy. Conversely, the classical Lorentz collision operator is provably not Hamiltonian in the stochastic sense.
The Pure Virtual Braid Group Is Quadratic
Lee, Peter
2011-01-01
If an augmented algebra K over Q is filtered by powers of its augmentation ideal I, the associated graded algebra gr_I K need not in general be quadratic: although it is generated in degree 1, its relations may not be generated by homogeneous relations of degree 2. In this paper we give a criterion which is equivalent to gr_I K being quadratic. We apply this criterion to the group algebra of the pure virtual braid group (also known as the quasi-triangular group), and show that the corresponding associated graded algebra is quadratic.
Specialization of Quadratic and Symmetric Bilinear Forms
Knebusch, Manfred
2010-01-01
The specialization theory of quadratic and symmetric bilinear forms over fields and the subsequent generic splitting theory of quadratic forms were invented by the author in the mid-1970's. They came to fruition in the ensuing decades and have become an integral part of the geometric methods in quadratic form theory. This book comprehensively covers the specialization and generic splitting theories. These theories, originally developed for fields of characteristic different from 2, are explored here without this restriction. In addition to chapters on specialization theory, generic splitting t
Quadratic stabilization of switched nonlinear systems
Institute of Scientific and Technical Information of China (English)
DONG YaLi; FAN JiaoJiao; MEI ShengWei
2009-01-01
In this paper, the problem of quadratic stabilization of multi-input multi-output switched nonlinear systems under an arbitrary switching law is investigated. When switched nonlinear systems have uniform normal form and the zero dynamics of uniform normal form is asymptotically stable under an arbitrary switching law, state feedbacks are designed and a common quadratic Lyapunov function of all the closed-loop subsystems is constructed to realize quadratic stabilizability of the class of switched nonlinear systems under an arbitrary switching law. The results of this paper are also applied to switched linear systems.
The Optimal Linear Quadratic Feedback State Regulator Problem for Index One Descriptor Systems
Engwerda, J.C.; Salmah, Y.; Wijayanti, I.E.
2008-01-01
In this note we present both necessary and sufficient conditions for the existence of a linear static state feedback controller if the system is described by an index one descriptor system. A priori no definiteness restrictions are made w.r.t. the quadratic performance criterium. It is shown that in
Solution to Projectile Motion with Quadratic Drag and Graphing the Trajectory in Spreadsheets
Benacka, Jan
2010-01-01
This note gives the analytical solution to projectile motion with quadratic drag by decomposing the velocity vector to "x," "y" coordinate directions. The solution is given by definite integrals. First, the impact angle is estimated from above, then the projectile coordinates are computed, and the trajectory is graphed at various launch angles and…
Institute of Scientific and Technical Information of China (English)
FAN Hong-Yi; FAN Yue
2003-01-01
By introducing a convenient complex form of the α-th 2-dimensional fractional Fourier transform (CFFT) operation we find that it possesses new eigenmodes which are two-mode Hermite polynomials. We prove the eigenvalues of propagation in quadratic graded-index medium over a definite distance are the same as the eigenvalues of the α-th CFFT, which means that our definition of the α-th CFFT is physically meaningful.
Stochastic averaging of quasi-Hamiltonian systems
Institute of Scientific and Technical Information of China (English)
朱位秋
1996-01-01
A stochastic averaging method is proposed for quasi-Hamiltonian systems (Hamiltonian systems with light dampings subject to weakly stochastic excitations). Various versions of the method, depending on whether the associated Hamiltonian systems are integrable or nonintegrable, resonant or nonresonant, are discussed. It is pointed out that the standard stochastic averaging method and the stochastic averaging method of energy envelope are special cases of the stochastic averaging method of quasi-Hamiltonian systems and that the results obtained by this method for several examples prove its effectiveness.
Hamiltonian cosmology in bigravity and massive gravity
Soloviev, Vladimir O
2015-01-01
In the Hamiltonian language we provide a study of flat-space cosmology in bigravity and massive gravity constructed mostly with de Rham, Gabadadze, Tolley (dRGT) potential. It is demonstrated that the Hamiltonian methods are powerful not only in proving the absence of the Boulware-Deser ghost, but also in solving other problems. The purpose of this work is to give an introduction both to the Hamiltonian formalism and to the cosmology of bigravity. We sketch three roads to the Hamiltonian of bigravity with the dRGT potential: the metric, the tetrad and the minisuperspace approaches.
Asymptocic Freedom of Gluons in Hamiltonian Dynamics
Gómez-Rocha, María; Głazek, Stanisław D.
2016-07-01
We derive asymptotic freedom of gluons in terms of the renormalized SU(3) Yang-Mills Hamiltonian in the Fock space. Namely, we use the renormalization group procedure for effective particles to calculate the three-gluon interaction term in the front-form Yang-Mills Hamiltonian using a perturbative expansion in powers of g up to third order. The resulting three-gluon vertex is a function of the scale parameter s that has an interpretation of the size of effective gluons. The corresponding Hamiltonian running coupling constant exhibits asymptotic freedom, and the corresponding Hamiltonian {β} -function coincides with the one obtained in an earlier calculation using a different generator.
Hamiltonian tomography of photonic lattices
Ma, Ruichao; Owens, Clai; LaChapelle, Aman; Schuster, David I.; Simon, Jonathan
2017-06-01
In this paper we introduce an approach to Hamiltonian tomography of noninteracting tight-binding photonic lattices. To begin with, we prove that the matrix element of the low-energy effective Hamiltonian between sites α and β may be obtained directly from Sα β(ω ) , the (suitably normalized) two-port measurement between sites α and β at frequency ω . This general result enables complete characterization of both on-site energies and tunneling matrix elements in arbitrary lattice networks by spectroscopy, and suggests that coupling between lattice sites is a topological property of the two-port spectrum. We further provide extensions of this technique for measurement of band projectors in finite, disordered systems with good band flatness ratios, and apply the tool to direct real-space measurement of the Chern number. Our approach demonstrates the extraordinary potential of microwave quantum circuits for exploration of exotic synthetic materials, providing a clear path to characterization and control of single-particle properties of Jaynes-Cummings-Hubbard lattices. More broadly, we provide a robust, unified method of spectroscopic characterization of linear networks from photonic crystals to microwave lattices and everything in between.
A Hamiltonian interpretation of Penrose's quasi-local mass
Mason, L. J.
1989-02-01
A connection is established between Penrose's definition of quasi-local mass and the more conventional notions of mass, momentum etc., arising from the canonical formalism of general relativity (which exist at least asymptotically). It is shown that each component of the 'angular momentum' twistor can be thought of as the value of a Hamiltonian which generates motions of regions of the spacetime which tend towards one of a collection of 'quasi-Killing vectors' on the bounding 2-surface on which the computations take place. The quasi-Killing vectors are obtained from solutions of the twistor equation, and essential use is made of the spinorial version of the gravitational Hamiltonian first employed in Witten's simplified proof of positive energy in general relativity. These ideas are then used to suggest a variation on Penrose's quasi-local mass definition using 'quasi-conformal Killing vectors' rather than quasi-Killing vectors. This has the advantage that there are only sixteen real quantities rather than the twenty real (ten complex) ones from Penrose's original definition.
Structure of Solvable Quadratic Lie Algebras
Institute of Scientific and Technical Information of China (English)
ZHU Lin-sheng
2005-01-01
@@ Killing form plays a key role in the theory of semisimple Lie algebras. It is natural to extend the study to Lie algebras with a nondegenerate symmetric invariant bilinear form. Such a Lie algebra is generally called a quadratic Lie algebra which occur naturally in physics[10,12,13]. Besides semisimple Lie algebras, interesting quadratic Lie algebras include the Kac-Moody algebras and the Extended Affine Lie algebras.
Compression limits in cascaded quadratic soliton compression
DEFF Research Database (Denmark)
Bache, Morten; Bang, Ole; Krolikowski, Wieslaw;
2008-01-01
Cascaded quadratic soliton compressors generate under optimal conditions few-cycle pulses. Using theory and numerical simulations in a nonlinear crystal suitable for high-energy pulse compression, we address the limits to the compression quality and efficiency.......Cascaded quadratic soliton compressors generate under optimal conditions few-cycle pulses. Using theory and numerical simulations in a nonlinear crystal suitable for high-energy pulse compression, we address the limits to the compression quality and efficiency....
Radiotherapy treatment planning linear-quadratic radiobiology
Chapman, J Donald
2015-01-01
Understand Quantitative Radiobiology from a Radiation Biophysics PerspectiveIn the field of radiobiology, the linear-quadratic (LQ) equation has become the standard for defining radiation-induced cell killing. Radiotherapy Treatment Planning: Linear-Quadratic Radiobiology describes tumor cell inactivation from a radiation physics perspective and offers appropriate LQ parameters for modeling tumor and normal tissue responses.Explore the Latest Cell Killing Numbers for Defining Iso-Effective Cancer TreatmentsThe book compil
Quadratic stabilization for uncertain stochastic systems
Institute of Scientific and Technical Information of China (English)
Jun'e FENG; Weihai ZHANG
2005-01-01
This paper discusses the robust quadratic stabilization control problem for stochastic uncertain systems,where the uncertain matrix is norm bounded,and the external disturbance is a stochastic process.Two kinds of controllers are designed,which include state feedback case and output feedback case.The conditions for the robust quadratic stabilization of stochastic uncertain systems are given via linear matrix inequalities.The detailed design methods are presented.Numerical examples show the effectiveness of our results.
Cascaded quadratic soliton compression at 800 nm
DEFF Research Database (Denmark)
Bache, Morten; Bang, Ole; Moses, Jeffrey;
2007-01-01
We study soliton compression in quadratic nonlinear materials at 800 nm, where group-velocity mismatch dominates. We develop a nonlocal theory showing that efficient compression depends strongly on characteristic nonlocal time scales related to pulse dispersion.......We study soliton compression in quadratic nonlinear materials at 800 nm, where group-velocity mismatch dominates. We develop a nonlocal theory showing that efficient compression depends strongly on characteristic nonlocal time scales related to pulse dispersion....
A NEW INEXACT SEQUENTIAL QUADRATIC PROGRAMMING ALGORITHM
Institute of Scientific and Technical Information of China (English)
倪勤
2002-01-01
This paper represents an inexact sequential quadratic programming (SQP ) algorithm which can solve nonlinear programming (NLP ) problems. An inexact solution of the quadratic programming subproblem is determined by a projection and contraction method such that only matrix-vector product is required. Some truncated criteria are chosen such that the algorithm is suitable to large scale NLP problem. The global convergence of the algorithm is proved.
The explicit dependence of quadrat variance on the ratio of clump size to quadrat size.
Ferrandino, Francis J
2005-05-01
ABSTRACT In the past decade, it has become common practice to pool mapped binary epidemic data into quadrats. The resultant "quadrat counts" can then be analyzed by fitting them to a probability distribution (i.e., betabinomial). Often a binary form of Taylor's power law is used to relate the quadrat variance to the quadrat mean. The fact that there is an intrinsic dependence of such analyses on quadrat size and shape is well known. However, a clear-cut exposition of the direct connection between the spatial properties of the two-dimensional pattern of infected plants in terms of the geometry of the quadrat and the results of quadrat-based analyses is lacking. This problem was examined both empirically and analytically. The empirical approach is based on a set of stochastically generated "mock epidemics" using a Neyman-Scott cluster process. The resultant spatial point-patterns of infected plants have a fixed number of disease foci characterized by a known length scale (monodisperse) and saturated to a known disease level. When quadrat samples of these epidemics are fit to a beta-binomial distribution, the resulting measures of aggregation are totally independent of disease incidence and most strongly dependent on the ratio of the length scale of the quadrat to the length scale of spatial aggregation and to a lesser degree on disease saturation within individual foci. For the analytical approach, the mathematical form for the variation in the sum of random variates is coupled to the geometry of a quadrat through an assumed exponential autocorrelation function. The net result is an explicit equation expressing the intraquadrat correlation, quadrat variance, and the index of dispersion in terms of the ratio of the quadrat length scale to the correlative length scale.
Distribution Results for Positive Definite Quadratic Forms with Repeated Roots.
1984-07-10
the distri- bution function of Q for P - 2 and 3 have been given by Grad and Solomon (1955) and Solomon (1960) and Marsaglia (1960). (An abridged...Grad and Solomon, and Marsaglia , and Johnson and Kotz become even more useful. It seems clear that the tables 3 * a = -b = J : * ,’ I ... . *,, - , Z...probabilities by Haynam, Govindarajulu, Leone and Siefert (1983) and these may be used to supplement the tables of Solomon (1960) and Marsaglia (1960
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
Implicit variational principle for contact Hamiltonian systems
Wang, Kaizhi; Wang, Lin; Yan, Jun
2017-02-01
We establish an implicit variational principle for the contact Hamiltonian systems generated by the Hamiltonian H(x, u, p) with respect to the contact 1-form α =\\text{d}u-p\\text{d}x under Tonelli and Lipschitz continuity conditions.
Some Graphs Containing Unique Hamiltonian Cycles
Lynch, Mark A. M.
2002-01-01
In this paper, two classes of graphs of arbitrary order are described which contain unique Hamiltonian cycles. All the graphs have mean vertex degree greater than one quarter the order of the graph. The Hamiltonian cycles are detailed, their uniqueness proved and simple rules for the construction of the adjacency matrix of the graphs are given.…
A parcel formulation for Hamiltonian layer models
Bokhove, O.; Oliver, M.
2009-01-01
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 Hamilton
Equivalence of Conformal Superalgebras to Hamiltonian Superoperators
Institute of Scientific and Technical Information of China (English)
Xiaoping Xu
2001-01-01
In this paper, we present a formal variational calculus of super functions in one real variable and find the conditions for a "matrix differential operator'' to be a Hamiltonian superoperator. Moreover, we prove that conformal superalgebras are equivalent to certain Hamiltonian superoperators.
ON THE STABILITY BOUNDARY OF HAMILTONIAN SYSTEMS
Institute of Scientific and Technical Information of China (English)
QI Zhao-hui(齐朝晖); Alexander P. Seyranian
2002-01-01
The criterion for the points in the parameter space being on the stability boundary of linear Hamiltonian system depending on arbitrary numbers of parameters was given, through the sensitivity analysis of eigenvalues and eigenvectors. The results show that multiple eigenvalues with Jordan chain take a very important role in the stability of Hamiltonian systems.
Hamiltonian for a restricted isoenergetic thermostat
Dettmann, C. P.
1999-01-01
Nonequilibrium molecular dynamics simulations often use mechanisms called thermostats to regulate the temperature. A Hamiltonian is presented for the case of the isoenergetic (constant internal energy) thermostat corresponding to a tunable isokinetic (constant kinetic energy) thermostat, for which a Hamiltonian has recently been given.
Normal Form for Families of Hamiltonian Systems
Institute of Scientific and Technical Information of China (English)
Zhi Guo WANG
2007-01-01
We consider perturbations of integrable Hamiltonian systems in the neighborhood of normally parabolic invariant tori. Using the techniques of KAM-theory we prove that there exists a canonical transformation that puts the Hamiltonian in normal form up to a remainder of weighted order 2d+1. And some dynamical consequences are obtained.
Bohr Hamiltonian with time-dependent potential
Naderi, L.; Hassanabadi, H.; Sobhani, H.
2016-04-01
In this paper, Bohr Hamiltonian has been studied with the time-dependent potential. Using the Lewis-Riesenfeld dynamical invariant method appropriate dynamical invariant for this Hamiltonian has been constructed and the exact time-dependent wave functions of such a system have been derived due to this dynamical invariant.
Infinite-dimensional Hamiltonian Lie superalgebras
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
The natural filtration of the infinite-dimensional Hamiltonian Lie superalgebra over a field of positive characteristic is proved to be invariant under automorphisms by characterizing ad-nilpotent elements.We are thereby able to obtain an intrinsic characterization of the Hamiltonian Lie superalgebra and establish a property of the automorphisms of the Lie superalgebra.
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 Hamiltonian approach to Thermodynamics
Baldiotti, M C; 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 ontop 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.
Towards the Right Hamiltonian for Singular Perturbations via Regularization and Extension Theory
Neidhardt, Hagen; Zagrebnov, Valentin
For singular potentials in quantum mechanics it can happen that the Schrödinger operator is not esssentially self-adjoint on a natural domain, i.e., each self-adjoint extension is a candidate for the right physical Hamiltonian. Traditional way to single out this Hamiltonian is the removing cut-offs for regularizing potential. Connecting regularization and extension theory we develop an abstract operator method to treat the problem of the right Hamiltonian. We show that, using the notion of the maximal (with respect to the perturbation) Friedrichs extension of unperturbed operator, one can classify the above problem as wellposed or ill-posed depending on intersection of the quadratic form domain of perturbation and deficiency subspace corresponding to restriction of unperturbed operator to stability domain. If this intersection is trivial, then the right Hamiltonian is unique: it coincides with the form sum of perturbation and the Friedrich extension of the unperturbed operator restricted to the stability domain. Otherwise it is not unique: the family of “right Hamiltonians” can be described in terms of symmetric extensions reducing the ill-posed problem to the well-posed problem.
Energy Technology Data Exchange (ETDEWEB)
Lopez-Moreno, Enrique; Grether, M; Velazquez, Victor, E-mail: elm@hp.fciencias.unam.mx [Facultad de Ciencias, Departamento de Fisica, Universidad Nacional Autonoma de Mexico, Cd. Universitaria, Circuito Exterior, 04510 Mexico DF (Mexico)
2011-11-25
A general spin system with a nonaxially symmetric Hamiltonian containing J{sub x}, J{sub z}-linear and J{sub z}-quadratic terms, widely used in many-body fermionic and bosonic systems and in molecular magnetism, is considered for the variations of general parameters describing intensity interaction changes of each of its terms. For this model Hamiltonian, a semiclassical energy surface (ES) is obtained by means of the coherent-state formalism. An analysis of this ES function, based on catastrophe theory, determines the separatrix in the control parameter space of the system Hamiltonian: the loci of singularities representing semiclassical phase transitions. Here we show that distinct regions of qualitatively different spectrum structures, as well as a singular behavior of quantum states, are ruled by this separatrix: here we show that the separatrix not only describes ground-state singularities, which have been associated with quantum phase transitions, but also reveals the structure of the excited spectrum, distinguishing different quantum phases within the parameter space. Finally, we consider magnetic susceptibility and heat capacity of the system at finite temperature, in order to study thermal properties and thermodynamical phase transitions in the perspective of the separatrix of this Hamiltonian system. (paper)
Effective Hamiltonians for Complexes of Unstable Particles
Urbanowski, K
2014-01-01
Effective Hamiltonians governing the time evolution in a subspace of unstable states can be found using more or less accurate approximations. A convenient tool for deriving them is the evolution equation for a subspace of state space sometime called the Krolikowski-Rzewuski (KR) equation. KR equation results from the Schr\\"{o}dinger equation for the total system under considerations. We will discuss properties of approximate effective Hamiltonians derived using KR equation for $n$--particle, two particle and for one particle subspaces. In a general case these affective Hamiltonians depend on time $t$. We show that at times much longer than times at which the exponential decay take place the real part of the exact effective Hamiltonian for the one particle subsystem (that is the instantaneous energy) tends to the minimal energy of the total system when $t \\rightarrow \\infty$ whereas the imaginary part of this effective Hamiltonian tends to the zero as $t\\rightarrow \\infty$.
Lagrangian and Hamiltonian two-scale reduction
Giannoulis, Johannes; Mielke, Alexander
2008-01-01
Studying high-dimensional Hamiltonian systems with microstructure, it is an important and challenging problem to identify reduced macroscopic models that describe some effective dynamics on large spatial and temporal scales. This paper concerns the question how reasonable macroscopic Lagrangian and Hamiltonian structures can by derived from the microscopic system. In the first part we develop a general approach to this problem by considering non-canonical Hamiltonian structures on the tangent bundle. This approach can be applied to all Hamiltonian lattices (or Hamiltonian PDEs) and involves three building blocks: (i) the embedding of the microscopic system, (ii) an invertible two-scale transformation that encodes the underlying scaling of space and time, (iii) an elementary model reduction that is based on a Principle of Consistent Expansions. In the second part we exemplify the reduction approach and derive various reduced PDE models for the atomic chain. The reduced equations are either related to long wave...
Simulating sparse Hamiltonians with star decompositions
Childs, Andrew M
2010-01-01
We present an efficient algorithm for simulating the time evolution due to a sparse Hamiltonian. In terms of the maximum degree d and dimension N of the space on which the Hamiltonian H acts, this algorithm uses (d^2(d+log* N)||H||)^{1+o(1)} queries. This improves the complexity of the sparse Hamiltonian simulation algorithm of Berry, Ahokas, Cleve, and Sanders, which scales like (d^4(log* N)||H||)^{1+o(1)}. To achieve this, we decompose a general sparse Hamiltonian into a small sum of Hamiltonians whose graphs of non-zero entries have the property that every connected component is a star, and efficiently simulate each of these pieces.
Hunter, Richard
2010-01-01
It is known that all weakly conformal Hamiltonian stationary Lagrangian immersions of tori in the complex projective plane may be constructed by methods from integrable systems theory. This article describes the precise details of a construction which leads to a form of classification. The immersion is encoded as spectral data in a similar manner to the case of minimal Lagrangian tori in the complex projective plane, but the details require a careful treatment of both the "dressing construction" and the spectral data to deal with a loop of flat connexions which is quadratic in the loop parameter.
Homoclinic orbits for the second-order Hamiltonian systems with obstacle item
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
This paper is concerned with the existence of homoclinic orbits for the second-order Hamiltonian system with obstacle item, ü(t)-A u(t) =▽F (t, u), where F (t, u) is T-periodic in t with ▽F (t, u) = L(t)u + ▽R(t,u). By using a generalized linking theorem for strongly indefinite functionals, we prove the existence of homoclinic orbits for both the super-quadratic case and the asymptotically linear one.
DEFF Research Database (Denmark)
Mak, Vicky; Thomadsen, Tommy
2006-01-01
This paper considers the cardinality constrained quadratic knapsack problem (QKP) and the quadratic selective travelling salesman problem (QSTSP). The QKP is a generalization of the knapsack problem and the QSTSP is a generalization of the travelling salesman problem. Thus, both problems are NP...
Linear-quadratic control and quadratic differential forms for multidimensional behaviors
Napp, D.; Trentelman, H.L.
2011-01-01
This paper deals with systems described by constant coefficient linear partial differential equations (nD-systems) from a behavioral point of view. In this context we treat the linear-quadratic control problem where the performance functional is the integral of a quadratic differential form. We look
Xia, Yong; Han, Ying-Wei
2014-01-01
In this paper, we propose a mixed-binary convex quadratic programming reformulation for the box-constrained nonconvex quadratic integer program and then implement IBM ILOG CPLEX 12.6 to solve the new model. Computational results demonstrate that our approach clearly outperform the very recent state-of-the-art solvers.
Indian Academy of Sciences (India)
DEEPAK KUMAR; A G RAMAKRISHNAN
2016-03-01
Particle swarm optimization (PSO) is used in several combinatorial optimization problems. In this work, particle swarms are used to solve quadratic programming problems with quadratic constraints. The central idea is to use PSO to move in the direction towards optimal solution rather than searching the entire feasibleregion. Binary classification is posed as a quadratically constrained quadratic problem and solved using the proposed method. Each class in the binary classification problem is modeled as a multidimensional ellipsoid to forma quadratic constraint in the problem. Particle swarms help in determining the optimal hyperplane or classification boundary for a data set. Our results on the Iris, Pima, Wine, Thyroid, Balance, Bupa, Haberman, and TAE datasets show that the proposed method works better than a neural network and the performance is close to that of a support vector machine
Nonperturbative embedding for highly nonlocal Hamiltonians
Subaşı, Yiǧit; Jarzynski, Christopher
2016-07-01
The need for Hamiltonians with many-body interactions arises in various applications of quantum computing. However, interactions beyond two-body are difficult to realize experimentally. Perturbative gadgets were introduced to obtain arbitrary many-body effective interactions using Hamiltonians with at most two-body interactions. Although valid for arbitrary k -body interactions, their use is limited to small k because the strength of interaction is k th order in perturbation theory. In this paper we develop a nonperturbative technique for obtaining effective k -body interactions using Hamiltonians consisting of at most l -body interactions with l effect of this procedure is shown to be equivalent to evolving the system with the original nonlocal Hamiltonian. This technique does not suffer from the aforementioned shortcoming of perturbative methods and requires only one ancilla qubit for each k -body interaction irrespective of the value of k . It works best for Hamiltonians with a few many-body interactions involving a large number of qubits and can be used together with perturbative gadgets to embed Hamiltonians of considerable complexity in proper subspaces of two-local Hamiltonians. We describe how our technique can be implemented in a hybrid (gate-based and adiabatic) as well as solely adiabatic quantum computing scheme.
Fast approximate quadratic programming for graph matching.
Directory of Open Access Journals (Sweden)
Joshua T Vogelstein
Full Text Available Quadratic assignment problems arise in a wide variety of domains, spanning operations research, graph theory, computer vision, and neuroscience, to name a few. The graph matching problem is a special case of the quadratic assignment problem, and graph matching is increasingly important as graph-valued data is becoming more prominent. With the aim of efficiently and accurately matching the large graphs common in big data, we present our graph matching algorithm, the Fast Approximate Quadratic assignment algorithm. We empirically demonstrate that our algorithm is faster and achieves a lower objective value on over 80% of the QAPLIB benchmark library, compared with the previous state-of-the-art. Applying our algorithm to our motivating example, matching C. elegans connectomes (brain-graphs, we find that it efficiently achieves performance.
Fast approximate quadratic programming for graph matching.
Vogelstein, Joshua T; Conroy, John M; Lyzinski, Vince; Podrazik, Louis J; Kratzer, Steven G; Harley, Eric T; Fishkind, Donniell E; Vogelstein, R Jacob; Priebe, Carey E
2015-01-01
Quadratic assignment problems arise in a wide variety of domains, spanning operations research, graph theory, computer vision, and neuroscience, to name a few. The graph matching problem is a special case of the quadratic assignment problem, and graph matching is increasingly important as graph-valued data is becoming more prominent. With the aim of efficiently and accurately matching the large graphs common in big data, we present our graph matching algorithm, the Fast Approximate Quadratic assignment algorithm. We empirically demonstrate that our algorithm is faster and achieves a lower objective value on over 80% of the QAPLIB benchmark library, compared with the previous state-of-the-art. Applying our algorithm to our motivating example, matching C. elegans connectomes (brain-graphs), we find that it efficiently achieves performance.
Quadratic Interpolation Algorithm for Minimizing Tabulated Function
Directory of Open Access Journals (Sweden)
E. A. Youness
2008-01-01
Full Text Available Problem statement: The problem of finding the minimum value of objective function, when we know only some values of it, is needed in more practical fields. Quadratic interpolation algorithms are the famous tools deal with this kind of these problems. These algorithms interested with the polynomial space in which the objective function is approximated. Approach: In this study we approximated the objective function by a one dimensional quadratic polynomial. This approach saved the time and the effort to get the best point at which the objective is minimized. Results: The quadratic polynomial in each one of the steps of the proposed algorithm, accelerate the convergent to the best value of the objective function without taking into account all points of the interpolation set. Conclusion: Any n-dimensional problem of finding a minimal value of a function, given by some values, can be converted to one dimensional problem easier in deal.
Quadratic gravity: from weak to strong
Holdom, Bob
2016-01-01
More than three decades ago quadratic gravity was found to present a perturbative, renormalizable and asymptotically free theory of quantum gravity. Unfortunately the theory appeared to have problems with a spin-2 ghost. In this essay we revisit quadratic gravity in a different light by considering the case that the asymptotically free interaction flows to a strongly interacting regime. This occurs when the coefficient of the Einstein-Hilbert term is smaller than the scale $\\Lambda_{\\mathrm{QG}}$ where the quadratic couplings grow strong. Here QCD provides some useful insights. By pushing the analogy with QCD, we conjecture that the nonperturbative effects can remove the naive spin-2 ghost and lead to the emergence of general relativity in the IR.
Pavlov, V. P.
2014-03-01
Faddeev and Vershik proposed the Hamiltonian and Lagrangian formulations of constrained mechanical systems that are invariant from the differential geometry standpoint. In both formulations, the description is based on a nondegenerate symplectic 2-form defined on a cotangent bundle T*Q (in the Hamiltonian formulation) or on a tangent bundle TQ (in the Lagrangian formulation), and constraints are sets of functions in involution on these manifolds. We demonstrate that this technique does not allow "invariantization" of the Dirac procedure of constraint "proliferation." We show this in an example of a typical quantum field model in which the original Lagrange function is a quadratic form in velocities with a degenerate coefficient matrix. We postulate that the initial phase space is a manifold where all arguments of the action functional including the Lagrange multipliers are defined. The Lagrange multipliers can then be naturally interpreted physically as velocities (in the Hamiltonian formulation) or momenta (in the Lagrangian formulation) related to "nonphysical" degrees of freedom. A quasisymplectic 2-form invariantly defined on such a manifold is degenerate. We propose new differential-geometric structures that allow formulating the Dirac procedure invariantly.
Lectures on Hamiltonian Dynamics : Theory and Applications
Benettin, Giancarlo; Kuksin, Sergei
2005-01-01
This volume collects three series of lectures on applications of the theory of Hamiltonian systems, contributed by some of the specialists in the field. The aim is to describe the state of the art for some interesting problems, such as the Hamiltonian theory for infinite-dimensional Hamiltonian systems, including KAM theory, the recent extensions of the theory of adiabatic invariants and the phenomena related to stability over exponentially long times of Nekhoroshev's theory. The books may serve as an excellent basis for young researchers, who will find here a complete and accurate exposition of recent original results and many hints for further investigation.
Extended Hamiltonian approach to continuous tempering.
Gobbo, Gianpaolo; Leimkuhler, Benedict J
2015-06-01
We introduce an enhanced sampling simulation technique based on continuous tempering, i.e., on continuously varying the temperature of the system under investigation. Our approach is mathematically straightforward, being based on an extended Hamiltonian formulation in which an auxiliary degree of freedom, determining the effective temperature, is coupled to the physical system. The physical system and its temperature evolve continuously in time according to the equations of motion derived from the extended Hamiltonian. Due to the Hamiltonian structure, it is easy to show that a particular subset of the configurations of the extended system is distributed according to the canonical ensemble for the physical system at the correct physical temperature.
EXISTENCE OF HAMILTONIAN κ-FACTOR
Institute of Scientific and Technical Information of China (English)
CAI Maocheng; FANG Qizhi; LI Yanjun
2004-01-01
A Hamiltonian k-factor is a k-factor containing a Hamiltonian cycle. An n/2-critical graph G is a simple graph of order n which satisfies δ(G) ≥ n/2 and δ(G - e) ＜ n/2for any edge e ∈ E(G). Let κ≥ 2 be an integer and G be an n/2-critical graph of even order n ≥ 8κ - 14. It is shown in this paper that for any given Hamiltonian cycle Cexcept that G - C consists of two components of odd orders when κ is odd, G has a k-factor containing C.
Orthogonal separable Hamiltonian systems on T2
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
In this paper we characterize the Liouvillian integrable orthogonal separable Hamiltonian systems on T2 for a given metric, and prove that the Hamiltonian flow on any compact level hypersurface has zero topological entropy. Furthermore, by examples we show that the integrable Hamiltonian systems on T2 can have complicated dynamical phenomena. For instance they can have several families of invariant tori, each family is bounded by the homoclinic-loop-like cylinders and heteroclinic-loop-like cylinders. As we know, it is the first concrete example to present the families of invariant tori at the same time appearing in such a complicated way.
EXTENDED CASIMIR APPROACH TO CONTROLLED HAMILTONIAN SYSTEMS
Institute of Scientific and Technical Information of China (English)
Yuqian GUO; Daizhan CHENG
2006-01-01
In this paper, we first propose an extended Casimir method for energy-shaping. Then it is used to solve some control problems of Hamiltonian systems. To solve the H∞ control problem, the energy function of a Hamiltonian system is shaped to such a form that could be a candidate solution of HJI inequality. Next, the energy function is shaped as a candidate of control ISS-Lyapunov function, and then the input-to-state stabilization of port-controlled Hamiltonian systems is achieved. Some easily verifiable sufficient conditions are presented.
Minimal Realizations of Supersymmetry for Matrix Hamiltonians
Andrianov, Alexandr A
2014-01-01
The notions of weak and strong minimizability of a matrix intertwining operator are introduced. Criterion of strong minimizability of a matrix intertwining operator is revealed. Criterion and sufficient condition of existence of a constant symmetry matrix for a matrix Hamiltonian are presented. A method of constructing of a matrix Hamiltonian with a given constant symmetry matrix in terms of a set of arbitrary scalar functions and eigen- and associated vectors of this matrix is offered. Examples of constructing of $2\\times2$ matrix Hamiltonians with given symmetry matrices for the cases of different structure of Jordan form of these matrices are elucidated.
On a general Heisenberg exchange effective Hamiltonian
Energy Technology Data Exchange (ETDEWEB)
Blanco, J.A.; Prida Pidal, V.M. [Dept. de Fisica, Oviedo Univ. (Spain)
1995-07-01
A general Heisenberg exchange effective Hamiltonian is deduced in a straightforward way from the elemental quantum mechanical principles for the case of magnetic ions with non-orbital degeneracy in a crystalline lattice. Expressions for the high order direct exchange coupling constants or parameters are presented. The meaning of this effective Hamiltonian is important because extracting information from the Heisenberg Hamiltonian is a difficult task and is however taken as the starting point for many quite profound investigations of magnetism in solids and therefore could play an important role in an introductory course to solid state physics. (author)
Algebraic Hamiltonian for Vibrational Spectra of Stibine
Institute of Scientific and Technical Information of China (English)
HOU Xi-Wen
2004-01-01
@@ An algebraic Hamiltonian, which in a limit can be reduced to an extended local mode model by Law and Duncan,is proposed to describe both stretching and bending vibrational energy levels of polyatomic molecules, where Fermi resonances between the stretches and the bends are considered. The Hamiltonian is used to study the vibrational spectra of stibine (SbH3). A comparison with the extended local mode model is made. Results of fitting the experimental data show that the algebraic Hamiltonian reproduces the observed values better than the extended local mode model.
Dicycle Cover of Hamiltonian Oriented Graphs
Directory of Open Access Journals (Sweden)
Khalid A. Alsatami
2016-01-01
Full Text Available A dicycle cover of a digraph D is a family F of dicycles of D such that each arc of D lies in at least one dicycle in F. We investigate the problem of determining the upper bounds for the minimum number of dicycles which cover all arcs in a strong digraph. Best possible upper bounds of dicycle covers are obtained in a number of classes of digraphs including strong tournaments, Hamiltonian oriented graphs, Hamiltonian oriented complete bipartite graphs, and families of possibly non-Hamiltonian digraphs obtained from these digraphs via a sequence of 2-sum operations.
Improved Sufficient Conditions for Hamiltonian Properties
Directory of Open Access Journals (Sweden)
Bode Jens-P.
2015-05-01
Full Text Available In 1980 Bondy [2] proved that a (k+s-connected graph of order n ≥ 3 is traceable (s = −1 or Hamiltonian (s = 0 or Hamiltonian-connected (s = 1 if the degree sum of every set of k+1 pairwise nonadjacent vertices is at least ((k+1(n+s−1+1/2. It is shown in [1] that one can allow exceptional (k+ 1-sets violating this condition and still implying the considered Hamiltonian property. In this note we generalize this result for s = −1 and s = 0 and graphs that fulfill a certain connectivity condition.
The Wiener maximum quadratic assignment problem
Cela, Eranda; Woeginger, Gerhard J
2011-01-01
We investigate a special case of the maximum quadratic assignment problem where one matrix is a product matrix and the other matrix is the distance matrix of a one-dimensional point set. We show that this special case, which we call the Wiener maximum quadratic assignment problem, is NP-hard in the ordinary sense and solvable in pseudo-polynomial time. Our approach also yields a polynomial time solution for the following problem from chemical graph theory: Find a tree that maximizes the Wiener index among all trees with a prescribed degree sequence. This settles an open problem from the literature.
A CART extention using Quadratic Decision Borders
DEFF Research Database (Denmark)
Hartelius, Karsten
1999-01-01
In this article we put forward an extention to the hierarchical CART classification method which uses quadratic decision borders. The original CART applies univariate splits on individual variables as well as splits on combinations of variables to recursively partition the feature......-space into subsets which are successively more class-homogeneous. Guided by the fact that class-distributions in feature-space are very often hyper-elliptical shaped, we give an extension to the original CART which also uses quadratic shaped decision borders which can be modelled by a mean-vector and a dispersion...
A CART extension using Quadratic Decision Borders
DEFF Research Database (Denmark)
Hartelius, Karsten
1999-01-01
In this article we put forward an extention to the hierarchical CART classification method which uses quadratic decision borders. The original CART applies univariate splits on individual variables as well as splits on combinations of variables to recursively partition the feature......-space into subsets which are successively more class-homogeneous. Guided by the fact that class-distributions in feature-space are very often hyper-elliptical shaped, we give an extension to the original CART which also uses quadratic shaped decision borders which can be modelled by a mean-vector and a dispersion...
PSQP: Puzzle Solving by Quadratic Programming.
Andalo, Fernanda A; Taubin, Gabriel; Goldenstein, Siome
2017-02-01
In this article we present the first effective method based on global optimization for the reconstruction of image puzzles comprising rectangle pieces-Puzzle Solving by Quadratic Programming (PSQP). The proposed novel mathematical formulation reduces the problem to the maximization of a constrained quadratic function, which is solved via a gradient ascent approach. The proposed method is deterministic and can deal with arbitrary identical rectangular pieces. We provide experimental results showing its effectiveness when compared to state-of-the-art approaches. Although the method was developed to solve image puzzles, we also show how to apply it to the reconstruction of simulated strip-shredded documents, broadening its applicability.
Quintessence with quadratic coupling to dark matter
Boehmer, Christian G; Chan, Nyein; Lazkoz, Ruth; Maartens, Roy
2009-01-01
We introduce a new form of coupling between dark energy and dark matter that is quadratic in their energy densities. Then we investigate the background dynamics when dark energy is in the form of exponential quintessence. The three types of quadratic coupling all admit late-time accelerating critical points, but these are not scaling solutions. We also show that two types of coupling allow for a suitable matter era at early times and acceleration at late times, while the third type of coupling does not admit a suitable matter era.
Guises and disguises of quadratic divergences
Energy Technology Data Exchange (ETDEWEB)
Cherchiglia, A.L., E-mail: adriano@fisica.ufmg.br [Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P.O. BOX 702, 30.161-970, Belo Horizonte, MG (Brazil); Vieira, A.R., E-mail: arvieira@fisica.ufmg.br [Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P.O. BOX 702, 30.161-970, Belo Horizonte, MG (Brazil); Hiller, Brigitte, E-mail: brigitte@teor.fis.uc.pt [Departamento de Física, Faculdade de Ciências e Tecnologia, Universidade de Coimbra, 3004-516 Coimbra (Portugal); Baêta Scarpelli, A.P., E-mail: scarpelli.apbs@dpf.gov.br [Setor Técnico-Científico, Departamento de Polícia Federal, Rua Hugo D’Antola, 95 - Lapa, São Paulo (Brazil); Sampaio, Marcos, E-mail: marcos.sampaio@durham.ac.uk [Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P.O. BOX 702, 30.161-970, Belo Horizonte, MG (Brazil); Centre for Particle Theory, Department of Mathematical Sciences, Durham University, South Road Durham DH1 3LE (United Kingdom)
2014-12-15
In this contribution, we present a new perspective on the control of quadratic divergences in quantum field theory, in general, and in the Higgs naturalness problem, in particular. Our discussion is essentially based on an approach where UV divergences are parameterized, after being reduced to basic divergent integrals (BDI) in one internal momentum, as functions of a cutoff and a renormalization group scale λ. We illustrate our proposal with well-known examples, such as the gluon vacuum self energy of QCD and the Higgs decay in two photons within this approach. We also discuss frameworks in effective low-energy QCD models, where quadratic divergences are indeed fundamental.
Lambda-Lifting in Quadratic Time
DEFF Research Database (Denmark)
Danvy, Olivier; Schultz, Ulrik Pagh
2004-01-01
Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda...... on the simple observation that all functions in each component need the same extra parameters and thus a transitive closure is not needed. We therefore simplify the search for extra parameters by treating each strongly connected component instead of each function as a unit, thereby reducing the time complexity...
Lambda-lifting in Quadratic Time
DEFF Research Database (Denmark)
Danvy, O.; Schultz, U.P.
2004-01-01
Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda...... on the simple observation that all functions in each component need the same extra parameters and thus a transitive closure is not needed. We therefore simplify the search for extra parameters by treating each strongly connected component instead of each function as a unit, thereby reducing the time complexity...
On orthogonality preserving quadratic stochastic operators
Energy Technology Data Exchange (ETDEWEB)
Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd [Department of Computational and Theoretical Sciences, Faculty of Science International Islamic University Malaysia, P.O. Box 141, 25710 Kuantan, Pahang Malaysia (Malaysia)
2015-05-15
A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too.
From physical principles to relativistic classical Hamiltonian and Lagrangian particle mechanics
Carcassi, Gabriele
2015-01-01
We show that classical particle mechanics (Hamiltonian and Lagrangian consistent with relativistic electromagnetism) can be derived from three fundamental assumptions: infinite reducibility, deterministic and reversible evolution, and kinematic equivalence. The core idea is that deterministic and reversible systems preserve the cardinality of a set of states, which puts considerable constraints on the equations of motion. This perspective links different concepts from different branches of math and physics (e.g. cardinality of a set, cotangent bundle for phase space, Hamiltonian flow, locally Minkowskian space-time manifold), providing new insights. The derivation strives to use definitions and mathematical concepts compatible with future extensions to field theories and quantum mechanics.
DEALING WITH INCONSISTENT QUADRATIC PROGRAMS IN A SQP BASED ALGORITHM
Directory of Open Access Journals (Sweden)
M.T. de Gouvêa
1997-03-01
Full Text Available In this paper we present a new sequential quadratic programming SQP algorithm that does not need any preprocessing phase. Its main features consist of not enforcing the Hessian to be positive definite and of dealing with infeasible QP problems in a novel way. The linearized constraints are analyzed and all those that do not belong to the minimal representation of the feasible region are eliminated. In the approach used the convergence rate of the algorithm may be adjusted by the user by properly selecting some tuning parameters that are also used to improve the robustness of the algorithm. The SQP code presented here is also able to deal with bound constraints that may be linearly dependent on the linearized equality or original constraints. The algorithm is shown to be robust and to perform well for small to medium-sized problems
Effective stability for generalized Hamiltonian systems
Institute of Scientific and Technical Information of China (English)
CONG; Fuzhong; LI; Yong
2004-01-01
An effective stability result for generalized Hamiltonian systems is obtained by applying the simultaneous approximation technique due to Lochak. Among these systems,dimensions of action variables and angle variables might be distinct.
Spinor-Like Hamiltonian for Maxwellian Optics
Directory of Open Access Journals (Sweden)
Kulyabov D.S.
2016-01-01
Conclusions. For Maxwell equations in the Dirac-like form we can expand research methods by means of quantum field theory. In this form, the connection between the Hamiltonians of geometric, beam and Maxwellian optics is clearly visible.
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.
Compressed quantum metrology for the Ising Hamiltonian
Boyajian, W. L.; Skotiniotis, M.; Dür, W.; Kraus, B.
2016-12-01
We show how quantum metrology protocols that seek to estimate the parameters of a Hamiltonian that exhibits a quantum phase transition can be efficiently simulated on an exponentially smaller quantum computer. Specifically, by exploiting the fact that the ground state of such a Hamiltonian changes drastically around its phase-transition point, we construct a suitable observable from which one can estimate the relevant parameters of the Hamiltonian with Heisenberg scaling precision. We then show how, for the one-dimensional Ising Hamiltonian with transverse magnetic field acting on N spins, such a metrology protocol can be efficiently simulated on an exponentially smaller quantum computer while maintaining the same Heisenberg scaling for the squared error, i.e., O (N-2) precision, and derive the explicit circuit that accomplishes the simulation.
Momentum and Hamiltonian in Complex Action Theory
Nagao, Keiichi; Nielsen, Holger Bech
In the complex action theory (CAT) we explicitly examine how the momentum and Hamiltonian are defined from the Feynman path integral (FPI) point of view based on the complex coordinate formalism of our foregoing paper. After reviewing the formalism briefly, we describe in FPI with a Lagrangian the time development of a ξ-parametrized wave function, which is a solution to an eigenvalue problem of a momentum operator. Solving this eigenvalue problem, we derive the momentum and Hamiltonian. Oppositely, starting from the Hamiltonian we derive the Lagrangian in FPI, and we are led to the momentum relation again via the saddle point for p. This study confirms that the momentum and Hamiltonian in the CAT have the same forms as those in the real action theory. We also show the third derivation of the momentum relation via the saddle point for q.
A Student's Guide to Lagrangians and Hamiltonians
Hamill, Patrick
2013-11-01
Part I. Lagrangian Mechanics: 1. Fundamental concepts; 2. The calculus of variations; 3. Lagrangian dynamics; Part II. Hamiltonian Mechanics: 4. Hamilton's equations; 5. Canonical transformations: Poisson brackets; 6. Hamilton-Jacobi theory; 7. Continuous systems; Further reading; Index.
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.
Jacobi fields of completely integrable Hamiltonian systems
Energy Technology Data Exchange (ETDEWEB)
Giachetta, G.; Mangiarotti, L.; Sardanashvily, G
2003-03-31
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.
Polysymplectic Hamiltonian formalism and some quantum outcomes
Giachetta, G; Sardanashvily, G
2004-01-01
Covariant (polysymplectic) Hamiltonian field theory is formulated as a particular Lagrangian theory on a polysymplectic phase space that enables one to quantize it in the framework of familiar quantum field theory.
Asymptocic Freedom of Gluons in Hamiltonian Dynamics
Gómez-Rocha, María
2016-01-01
We derive asymptotic freedom of gluons in terms of the renormalized $SU(3)$ Yang-Mills Hamiltonian in the Fock space. Namely, we use the renormalization group procedure for effective particles (RGPEP) to calculate the three-gluon interaction term in the front-form Yang-Mills Hamiltonian using a perturbative expansion in powers of $g$ up to third order. The resulting three-gluon vertex is a function of the scale parameter $s$ that has an interpretation of the size of effective gluons. The corresponding Hamiltonian running coupling constant exhibits asymptotic freedom, and the corresponding Hamiltonian $\\beta$-function coincides with the one obtained in an earlier calculation using a different generator.
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.
Test-assignment: a quadratic coloring problem
Duives, Jelle; Lodi, Andrea; Malaguti, Enrico
2013-01-01
We consider the problem of assigning the test variants of a written exam to the desks of a classroom in such a way that desks that are close-by receive different variants. The problem is a generalization of the Vertex Coloring and we model it as a binary quadratic problem. Exact solution methods bas
Experimental results on quadratic assignment problem
Directory of Open Access Journals (Sweden)
N.P. Nikolov
1999-08-01
Full Text Available The paper presents experimental results on quadratic assignment problem. The "scanning area" method formulated for radioelectronic equipment design is applied. For all more complex tests ours results are better or coincident with the ones known in literature. Conclusion concerning the effectiveness of method are given.
On Quadratic Programming with a Ratio Objective
Bhaskara, Aditya; Manokaran, Rajsekar; Vijayaraghavan, Aravindan
2011-01-01
Quadratic Programming (QP) is the well-studied problem of maximizing over {-1,1} values the quadratic form \\sum_ij a_ij x_i x_j. QP captures many known combinatorial optimization problems and SDP techniques have given optimal approximation algorithms for many of these problems. We extend this body of work by initiating the study of Quadratic Programming problems where the variables take values in the domain {-1,0,1}. The specific problem we study is: QP-Ratio: max_{-1,0,1}^n (x^T A x) / (x^T x). This objective function is a natural relative of several well studied problems. Yet, it is a good testbed for both algorithms and complexity because the techniques used for quadratic problems for the {-1,1} and {0,1} domains do not seem to carry over to the {-1,0,1} domain. We give approximation algorithms and evidence for the hardness of approximating the QP-Ratio problem. We consider an SDP relaxation obtained by adding constraints to the natural SDP relaxation for this problem and obtain an O(n^{2/7}) algorithm for...
Distortion control of conjugacies between quadratic polynomials
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
We use a new type of distortion control of univalent functions to give an alternative proof of Douady-Hubbard’s ray-landing theorem for quadratic Misiurewicz polynomials. The univalent maps arise from Thurston’s iterated algorithm on perturbation of such polynomials.
Target manifold formation using a quadratic SDF
Hester, Charles F.; Risko, Kelly K. D.
2013-05-01
Synthetic Discriminant Function (SDF) formulation of correlation filters provides constraints for forming target subspaces for a target set. In this paper we extend the SDF formulation to include quadratic constraints and use this solution to form nonlinear manifolds in the target space. The theory for forming these manifolds will be developed and demonstrated with data.
The GCD property and irreduciable quadratic polynomials
Directory of Open Access Journals (Sweden)
Saroj Malik
1986-01-01
Full Text Available The proof of the following theorem is presented: If D is, respectively, a Krull domain, a Dedekind domain, or a Prüfer domain, then D is correspondingly a UFD, a PID, or a Bezout domain if and only if every irreducible quadratic polynomial in D[X] is a prime element.
Modulational instability in periodic quadratic nonlinear materials
DEFF Research Database (Denmark)
Corney, Joel Frederick; Bang, Ole
2001-01-01
We investigate the modulational instability of plane waves in quadratic nonlinear materials with linear and nonlinear quasi-phase-matching gratings. Exact Floquet calculations, confirmed by numerical simulations, show that the periodicity can drastically alter the gain spectrum but never complete...
Solitons in quadratic nonlinear photonic crystals
DEFF Research Database (Denmark)
Corney, Joel Frederick; Bang, Ole
2001-01-01
We study solitons in one-dimensional quadratic nonlinear photonic crystals with modulation of both the linear and nonlinear susceptibilities. We derive averaged equations that include induced cubic nonlinearities, which can be defocusing, and we numerically find previously unknown soliton families...
Range-based estimation of quadratic variation
DEFF Research Database (Denmark)
Christensen, Kim; Podolskij, Mark
In this paper, we propose using realized range-based estimation to draw inference about the quadratic variation of jump-diffusion processes. We also construct a new test of the hypothesis that an asset price has a continuous sample path. Simulated data shows that our approach is efficient, the test...
Range-based estimation of quadratic variation
DEFF Research Database (Denmark)
Christensen, Kim; Podolskij, Mark
This paper proposes using realized range-based estimators to draw inference about the quadratic variation of jump-diffusion processes. We also construct a range-based test of the hypothesis that an asset price has a continuous sample path. Simulated data shows that our approach is efficient...
Hamiltonian formulation of guiding center motion
Stern, D. P.
1971-01-01
The nonrelativistic guiding center motion of a charged particle in a static magnetic field is derived using the Hamiltonian formalism. By repeated application of first-order canonical perturbation theory, the first two adiabatic invariants and their averaged Hamiltonians are obtained, including the first-order correction terms. Other features of guiding center theory are also given, including lowest order drifts and the flux invariant.
On Hamiltonians Generating Optimal-Speed Evolutions
2008-01-01
We present a simple derivation of the formula for the Hamiltonian operator(s) that achieve the fastest possible unitary evolution between given initial and final states. We discuss how this formula is modified in pseudo-Hermitian quantum mechanics and provide an explicit expression for the most general optimal-speed quasi-Hermitian Hamiltonian. Our approach allows for an explicit description of the metric- (inner product-) dependence of the lower bound on the travel time and the universality ...
Hamiltonian Quantum Cellular Automata in 1D
Nagaj, Daniel; Wocjan, Pawel
2008-01-01
We construct a simple translationally invariant, nearest-neighbor Hamiltonian on a chain of 10-dimensional qudits that makes it possible to realize universal quantum computing without any external control during the computational process. We only require the ability to prepare an initial computational basis state which encodes both the quantum circuit and its input. The computational process is then carried out by the autonomous Hamiltonian time evolution. After a time polynomially long in th...
Minimal realizations of supersymmetry for matrix Hamiltonians
Energy Technology Data Exchange (ETDEWEB)
Andrianov, Alexander A., E-mail: andrianov@icc.ub.edu; Sokolov, Andrey V., E-mail: avs_avs@rambler.ru
2015-02-06
The notions of weak and strong minimizability of a matrix intertwining operator are introduced. Criterion of strong minimizability of a matrix intertwining operator is revealed. Criterion and sufficient condition of existence of a constant symmetry matrix for a matrix Hamiltonian are presented. A method of constructing of a matrix Hamiltonian with a given constant symmetry matrix in terms of a set of arbitrary scalar functions and eigen- and associated vectors of this matrix is offered. Examples of constructing of 2×2 matrix Hamiltonians with given symmetry matrices for the cases of different structure of Jordan form of these matrices are elucidated. - Highlights: • Weak and strong minimization of a matrix intertwining operator. • Criterion of strong minimizability from the right of a matrix intertwining operator. • Conditions of existence of a constant symmetry matrix for a matrix Hamiltonian. • Method of constructing of a matrix Hamiltonian with a given constant symmetry matrix. • Examples of constructing of 2×2 matrix Hamiltonians with a given symmetry matrix.
Input-output decoupling of Hamiltonian systems : The linear case
Nijmeijer, H.; Schaft, A.J. van der
1985-01-01
In this note we give necessary and sufficient conditions for a linear Hamiltonian system to be input-output decouplable by Hamiltonian feedback, i.e. feedback that preserves the Hamiltonian structure. In a second paper we treat the same problem for nonlinear Hamiltonian systems.
Input-output decoupling of Hamiltonian systems: The linear case
Nijmeijer, H.
1985-01-01
In this note we give necessary and sufficient conditions for a linear Hamiltonian system to be input-output decouplable by Hamiltonian feedback, i.e. feedback that preserves the Hamiltonian structure. In a second paper we treat the same problem for nonlinear Hamiltonian systems.
Hamiltonian Dynamics at Spatial Infinity.
Alexander, Matthew
We employ a projective construction of spatial infinity in four-dimensional spacetimes which are asymptotically flat. In this construction, points of the spatial boundary of the spacetime manifold are identified with congruences of asymptotically parallel spacelike curves that are asymptotically geodesic. It is shown that for this type of construction spatial infinity is represented by a three-dimensional timelike hyperboloid, and that this follows as a consequence of the vacuum Einstein equations. We then construct tensor fields which are defined at spatial infinity, and which embody the information carried by the gravitational field regarding the total mass, linear, and angular momentum of the spacetime. It is shown that these tensor fields must satisfy a set of second order partial differential field equations at spatial infinity. The asymptotic symmetry group implied by the projective construction is examined, and is identified with the Spi group. The field equations satisfied by the tensor fields at spatial infinity can be derived from an action principle, however this action does not appear to be related in any obvious way to the Hilbert-Einstein action of general relativity. Under mappings generated by the Spi group our Lagrangian is left form -invariant, and the corresponding Noether-conserved quantities are examined. It is found that for spacetimes which are stationary or axisymmetric, these conserved quantities are not the limits of the conserved quantities associated with the infinitesimal four-dimensional coordinate transformations. It is shown that using the tensor fields at spatial infinity one can define a set of canonical variables. Further, we show that the "time" derivatives of the configuration variables can be expressed in terms of some of the momentum densities; the remaining momentum densities are constrained. Finally, we construct the Hamiltonian, and examine the transformations generated by it.
Mode signature and stability for a Hamiltonian model of electron temperature gradient turbulence
Tassi, Emanuele
2010-01-01
Stability properties and mode signature for equilibria of a model of electron temperature gradient (ETG) driven turbulence are investigated by Hamiltonian techniques. After deriving the infinite families of Casimir invariants, associated with the noncanonical Poisson bracket of the model, a sufficient condition for stability is obtained by means of the Energy-Casimir method. Mode signature is then investigated for linear motions about homogeneous equilibria. Depending on the sign of the equilibrium "translated" pressure gradient, stable equilibria can either be energy stable, i.e.\\ possess definite linearized perturbation energy (Hamiltonian), or spectrally stable with the existence of negative energy modes (NEMs). The ETG instability is then shown to arise through a Kre\\u{\\i}n-type bifurcation, due to the merging of a positive and a negative energy mode, corresponding to two modified drift waves admitted by the system. The Hamiltonian of the linearized system is then explicitly transformed into normal form, ...
Symmetry of Hamiltonian and conserved quantity for a system of generalized classical mechanics
Institute of Scientific and Technical Information of China (English)
Zhang Yi
2011-01-01
This paper focuses on a new symmetry of Hamiltonian and its conserved quantity for a system of generalized classical mechanics. The differential equations of motion of the system are established. The definition and the criterion of the symmetry of Hamiltonian of the system are given. A conserved quantity directly derived from the symmetry of Hamiltonian of the generalized classical mechanical system is given. Since a Hamilton system is a special case of the generalized classical mechanics, the results above are equally applicable to the Hamilton system. The results of the paper are the generalization of a theorem known for the existing nonsingular equivalent Lagrangian. Finally, two examples are given to illustrate the application of the results.
Quadratically constrained quadratic programs on acyclic graphs with application to power flow
Bose, Subhonmesh; Low, Steven H; Chandy, K Mani
2012-01-01
This paper proves that non-convex quadratically constrained quadratic programs have an exact semidefinite relaxation when their underlying graph is acyclic, provided the constraint set satisfies a certain technical condition. When the condition is not satisfied, we propose a heuristic to obtain a feasible point starting from a solution of the relaxed problem. These methods are then demonstrated to provide exact solutions to a richer class of optimal power flow problems than previously solved.
Lie symmetries and conserved quantities of discrete nonholonomic Hamiltonian systems
Institute of Scientific and Technical Information of China (English)
Wang Xing-Zhong; Fu Hao; Fu Jing-Li
2012-01-01
This paper focuses on studying Lie symmetries and conserved quantities of discrete nonholonomic Hamiltonian systems.Firstly,the discrete generalized Hamiltonian canonical equations and discrete energy equation of nonholonomic Hamiltonian systems are derived from discrete Hamiltonian action.Secondly,the determining equations and structure equation of Lie symmetry of the system are obtained.Thirdly,the Lie theorems and the conservation quantities are given for the discrete nonholonomic Hamiltonian systems.Finally,an example is discussed to illustrate the application of the results.
Incorporation of New Information in an Approximate Hamiltonian
Viazminsky, C. P.; Baza, S
2002-01-01
Additional information about the eigenvalues and eigenvectors of a physical system demands extension of the effective Hamiltonian in use. In this work we extend the effective Hamiltonian that describes partially a physical system so that the new Hamiltonian comprises, in addition to the information in the old Hamiltonian, new information, available by means of experiment or theory. A simple expression of the enlarged Hamiltonian, which does not involve matrix inversion, is obtained. It is als...
Geometric Approaches to Quadratic Equations from Other Times and Places.
Allaire, Patricia R.; Bradley, Robert E.
2001-01-01
Focuses on geometric solutions of quadratic problems. Presents a collection of geometric techniques from ancient Babylonia, classical Greece, medieval Arabia, and early modern Europe to enhance the quadratic equation portion of an algebra course. (KHR)
Ying, Zu-guang; Luo, Yin-miao; Zhu, Wei-qiu; Ni, Yi-qing; Ko, Jan-ming
2012-04-01
A semi-analytical direct optimal control solution for strongly excited and dissipative Hamiltonian systems is proposed based on the extended Hamiltonian principle, the Hamilton-Jacobi-Bellman (HJB) equation and its variational integral equation, and the finite time element approximation. The differential extended Hamiltonian equations for structural vibration systems are replaced by the variational integral equation, which can preserve intrinsic system structure. The optimal control law dependent on the value function is determined by the HJB equation so as to satisfy the overall optimality principle. The partial differential equation for the value function is converted into the integral equation with variational weighting. Then the successive solution of optimal control with system state is designed. The two variational integral equations are applied to sequential time elements and transformed into the algebraic equations by using the finite time element approximation. The direct optimal control on each time element is obtained respectively by solving the algebraic equations, which is unconstrained by the system state observed. The proposed control algorithm is applicable to linear and nonlinear systems with the quadratic performance index, and takes into account the effects of external excitations measured on control. Numerical examples are given to illustrate the optimal control effectiveness.
On quadratic residue codes and hyperelliptic curves
Directory of Open Access Journals (Sweden)
David Joyner
2008-01-01
Full Text Available For an odd prime p and each non-empty subset S⊂GF(p, consider the hyperelliptic curve X S defined by y 2 =f S (x, where f S (x = ∏ a∈S (x-a. Using a connection between binary quadratic residue codes and hyperelliptic curves over GF(p, this paper investigates how coding theory bounds give rise to bounds such as the following example: for all sufficiently large primes p there exists a subset S⊂GF(p for which the bound |X S (GF(p| > 1.39p holds. We also use the quasi-quadratic residue codes defined below to construct an example of a formally self-dual optimal code whose zeta function does not satisfy the ``Riemann hypothesis.''
Higgsed Stueckelberg vector and Higgs quadratic divergence
Directory of Open Access Journals (Sweden)
Durmuş Ali Demir
2015-01-01
Full Text Available Here we show that, a hidden vector field whose gauge invariance is ensured by a Stueckelberg scalar and whose mass is spontaneously generated by the Standard Model Higgs field contributes to quadratic divergences in the Higgs boson mass squared, and even leads to its cancellation at one-loop when Higgs coupling to gauge field is fine-tuned. In contrast to mechanisms based on hidden scalars where a complete cancellation cannot be achieved, stabilization here is complete in that the hidden vector and the accompanying Stueckelberg scalar are both free from quadratic divergences at one-loop. This stability, deriving from hidden exact gauge invariance, can have important implications for modeling dark phenomena like dark matter, dark energy, dark photon and neutrino masses. The hidden fields can be produced at the LHC.
Linear quadratic output tracking and disturbance rejection
Karimi-Ghartemani, Masoud; Khajehoddin, S. Ali; Jain, Praveen; Bakhshai, Alireza
2011-08-01
This article introduces the problem of linear quadratic tracking (LQT) where the objective is to design a closed-loop control scheme such that the output signal of the system optimally tracks a given reference signal and rejects a given disturbance. Different performance indices that have been used to address the tracking problem are discussed and an appropriate new form is introduced. It is shown that a solution to the proposed optimality index exists under very mild conditions of stabilisability and detectability of the plant state-space equations. The solution is formulated based on converting the LQT problem to a standard linear quadratic regulation problem. The method is applied to two examples, a first-order plant and a third-order plant, and their simulation results are presented and discussed.
Estimating quadratic variation using realized variance
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole Eiler; Shephard, N.
2002-01-01
This paper looks at some recent work on estimating quadratic variation using realized variance (RV) - that is, sums of M squared returns. This econometrics has been motivated by the advent of the common availability of high-frequency financial return data. When the underlying process is a semimar......This paper looks at some recent work on estimating quadratic variation using realized variance (RV) - that is, sums of M squared returns. This econometrics has been motivated by the advent of the common availability of high-frequency financial return data. When the underlying process...... have to impose some weak regularity assumptions. We illustrate the use of the limit theory on some exchange rate data and some stock data. We show that even with large values of M the RV is sometimes a quite noisy estimator of integrated variance. Copyright © 2002 John Wiley & Sons, Ltd....
Lambda-Lifting in Quadratic Time
DEFF Research Database (Denmark)
Danvy, Olivier; Schultz, Ulrik Pagh
2002-01-01
Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....
Lambda-Lifting in Quadratic Time
DEFF Research Database (Denmark)
Danvy, Olivier; Schultz, Ulrik Pagh
2004-01-01
Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....
Lambda-Lifting in Quadratic Time
DEFF Research Database (Denmark)
Danvy, Olivier; Schultz, Ulrik Pagh
2003-01-01
Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....
Lambda-lifting in Quadratic Time
DEFF Research Database (Denmark)
Danvy, O.; Schultz, U.P.
2004-01-01
Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....
Quaternion orders, quadratic forms, and Shimura curves
Alsina, Montserrat
2004-01-01
Shimura curves are a far-reaching generalization of the classical modular curves. They lie at the crossroads of many areas, including complex analysis, hyperbolic geometry, algebraic geometry, algebra, and arithmetic. The text provides an introduction to the subject from a theoretic and algorithmic perspective. The main topics covered in it are Shimura curves defined over the rational number field, the construction of their fundamental domains, and the determination of their complex multiplication points. The study of complex multiplication points in Shimura curves leads to the study of families of binary quadratic forms with algebraic coefficients and to their classification by arithmetic Fuchsian groups. In this regard, the authors develop a theory full of new possibilities which parallels Gauss' theory on the classification of binary quadratic forms with integral coefficients by the action of the modular group. Each topic covered in the book begins with a theoretical discussion followed by carefully worked...
A Finite Continuation Algorithm for Bound Constrained Quadratic Programming
DEFF Research Database (Denmark)
Madsen, Kaj; Nielsen, Hans Bruun; Pinar, Mustafa C.
1999-01-01
The dual of the strictly convex quadratic programming problem with unit bounds is posed as a linear $\\ell_1$ minimization problem with quadratic terms. A smooth approximation to the linear $\\ell_1$ function is used to obtain a parametric family of piecewise-quadratic approximation problems...
Elementary Components of the Quadratic Assignment Problem
Chicano, Francisco; Alba, Enrique
2011-01-01
The Quadratic Assignment Problem (QAP) is a well-known NP-hard combinatorial optimization problem that is at the core of many real-world optimization problems. We prove that QAP can be written as the sum of three elementary landscapes when the swap neighborhood is used. We present a closed formula for each of the three elementary components and we compute bounds for the autocorrelation coefficient.
Cubic Lienard Equations with Quadratic Damping (Ⅱ)
Institute of Scientific and Technical Information of China (English)
Yu-quan Wang; Zhu-jun Jing
2002-01-01
Applying Hopf bifurcation theory and qualitative theory, we show that the general cubic Lienard equations with quadratic damping have at most three limit cycles. This implies that the guess in which the system has at most two limit cycles is false. We give the sufficient conditions for the system has at most three limit cycles or two limit cycles. We present two examples with three limit cycles or two limit cycles by using numerical simulation.
Characterization of a Quadratic Function in Rn
Xu, Conway
2010-01-01
It is proved that a scalar-valued function "f"(x) defined in "n"-dimensional space must be quadratic, if the intersection of tangent planes at x[subscript 1] and x[subscript 2] always contains the midpoint of the line joining x[subscript 1] and x[subscript 2]. This is the converse of a result of Stenlund proved in this JOURNAL in 2001.
An intuitive Hamiltonian for quantum search
Fenner, S A
2000-01-01
We present new intuition behind Grover's quantum search algorithm by means of a Hamiltonian. Given a black-box Boolean function f mapping strings of length n into {0,1} such that f(w) = 1 for exactly one string w, L. K. Grover describes a quantum algorithm that finds w in O(2^{n/2}) time. Farhi & Gutmann show that w can also be found in the same amount time by letting the quantum system evolve according to a simple Hamiltonian depending only on f. Their system evolves along a path far from that taken by Grover's original algorithm, however. The current paper presents an equally simple Hamiltonian matching Grover's algorithm step for step. The new Hamiltonian is similar in appearance from that of Farhi & Gutmann, but has some important differences, and provides new intuition for Grover's algorithm itself. This intuition both contrasts with and supplements other explanations of Grover's algorithm as a rotation in two dimensions, and suggests that the Hamiltonian-based approach to quantum algorithms can ...
A phenomenological Hamiltonian for the Lotka-Volterra problem
Energy Technology Data Exchange (ETDEWEB)
Georgian, T. [Corps of Engineers, Omaha, NE (United States); Findley, G.L. [Northeast Louisiana Univ., Monroe, LA (United States)
1996-12-31
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{sub 1},x{sub 2}) for the Lotka-Volterra problem, which leads to the rate equations x{sub 1}=ax{sub 1}-bx{sub 1}x{sub 2}, x{sub 2}=-cx{sub 2}+bx{sub 1}x{sub 2}, with a,b and c being real constants. We thereafter present a Hamiltonian function H(x,y)[y{sub 1} = x{sub 1} and y{sub 2} = x{sub 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.
Optimal Approximation of Quadratic Interval Functions
Koshelev, Misha; Taillibert, Patrick
1997-01-01
Measurements are never absolutely accurate, as a result, after each measurement, we do not get the exact value of the measured quantity; at best, we get an interval of its possible values, For dynamically changing quantities x, the additional problem is that we cannot measure them continuously; we can only measure them at certain discrete moments of time t(sub 1), t(sub 2), ... If we know that the value x(t(sub j)) at a moment t(sub j) of the last measurement was in the interval [x-(t(sub j)), x + (t(sub j))], and if we know the upper bound D on the rate with which x changes, then, for any given moment of time t, we can conclude that x(t) belongs to the interval [x-(t(sub j)) - D (t - t(sub j)), x + (t(sub j)) + D (t - t(sub j))]. This interval changes linearly with time, an is, therefore, called a linear interval function. When we process these intervals, we get an expression that is quadratic and higher order w.r.t. time t, Such "quadratic" intervals are difficult to process and therefore, it is necessary to approximate them by linear ones. In this paper, we describe an algorithm that gives the optimal approximation of quadratic interval functions by linear ones.
Equivalent Hamiltonians with additional discrete states
Energy Technology Data Exchange (ETDEWEB)
Chinn, C.R. (Physics Department, Lawrence Livermore National Laboratory, Livermore, CA (USA)); Thaler, R.M. (Los Alamos National Laboratory, Los Alamos, NM (USA) Department of Physics, Case Western Reserve University, Cleveland, OH (USA))
1991-01-01
Given a particular Hamiltonian {ital H}, we present a method to generate a new Hamiltonian {ital {tilde H}}, which has the same discrete energy eigenvalues and the same continuum phase shifts as {ital H}, but which also has additional given discrete eigenstates. This method is used to generate a Hamiltonian {ital h}{sub 1}, which gives rise to a complete orthonormal set of basis states, which contain a given set of biorthonormal discrete states, the continuum states of which are asymptotic to plane waves (have zero phase shifts). Such a set of states may be helpful in representing the medium modification of the Green's function due to the Pauli principle, as well as including Pauli exclusion effects into scattering calculations.
Equivalent Hamiltonians with additional discrete states
Chinn, C. R.; Thaler, R. M.
1991-01-01
Given a particular Hamiltonian H, we present a method to generate a new Hamiltonian H~, which has the same discrete energy eigenvalues and the same continuum phase shifts as H, but which also has additional given discrete eigenstates. This method is used to generate a Hamiltonian h1, which gives rise to a complete orthonormal set of basis states, which contain a given set of biorthonormal discrete states, the continuum states of which are asymptotic to plane waves (have zero phase shifts). Such a set of states may be helpful in representing the medium modification of the Green's function due to the Pauli principle, as well as including Pauli exclusion effects into scattering calculations.
Hamiltonian Dynamics of Cosmological Quintessence Models
Ivanov, Rossen I
2016-01-01
The time-evolution dynamics of two nonlinear cosmological real gas models has been reexamined in detail with methods from the theory of Hamiltonian dynamical systems. These examples are FRWL cosmologies, one based on a gas, satisfying the van der Waals equation and another one based on the virial expansion gas equation. The cosmological variables used are the expansion rate, given by the Hubble parameter, and the energy density. The analysis is aided by the existence of global first integral as well as several special (second) integrals in each case. In addition, the global first integral can serve as a Hamiltonian for a canonical Hamiltonian formulation of the evolution equations. The conserved quantities lead to the existence of stable periodic solutions (closed orbits) which are models of a cyclic Universe. The second integrals allow for explicit solutions as functions of time on some special trajectories and thus for a deeper understanding of the underlying physics. In particular, it is shown that any pos...
Gravitational surface Hamiltonian and entropy quantization
Directory of Open Access Journals (Sweden)
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.
Gravitational surface Hamiltonian and entropy quantization
Bakshi, Ashish; Majhi, Bibhas Ranjan; Samanta, Saurav
2017-02-01
The surface Hamiltonian corresponding to the surface part of a gravitational action has xp structure where p is conjugate momentum of x. Moreover, it leads to TS on the horizon of a black hole. Here T and S are temperature and entropy of the horizon. Imposing the hermiticity condition we quantize this Hamiltonian. This leads to an equidistant spectrum of its eigenvalues. Using this we show that the entropy of the horizon is quantized. This analysis holds for any order of Lanczos-Lovelock gravity. For general relativity, the area spectrum is consistent with Bekenstein's observation. This provides a more robust confirmation of this earlier result as the calculation is based on the direct quantization of the Hamiltonian in the sense of usual quantum mechanics.
Manifest Covariant Hamiltonian Theory of General Relativity
Cremaschini, Claudio
2016-01-01
The problem of formulating a manifest covariant Hamiltonian theory of General Relativity in the presence of source fields is addressed, by extending the so-called "DeDonder-Weyl" formalism to the treatment of classical fields in curved space-time. The theory is based on a synchronous variational principle for the Einstein equation, formulated in terms of superabundant variables. The technique permits one to determine the continuum covariant Hamiltonian structure associated with the Einstein equation. The corresponding continuum Poisson bracket representation is also determined. The theory relies on first-principles, in the sense that the conclusions are reached in the framework of a non-perturbative covariant approach, which allows one to preserve both the 4-scalar nature of Lagrangian and Hamiltonian densities as well as the gauge invariance property of the theory.
Entanglement in a model for Hawking radiation: An Application of Quadratic Algebras
Bambah, Bindu A; Shreecharan, T; Prasad, K Siva
2012-01-01
Quadratic polynomially deformed $su(1,1)$ and $su(2)$ algebras are utilised in model Hamiltonians to show how the gravitational system consisting of a black hole, infalling radiation and outgoing (Hawking) radiation can be solved exactly. The models allow us to study the long-time behaviour of the black hole and its outgoing modes. In particular, we calculate the bipartite entanglement entropies of subsystems consisting of a) infalling plus outgoing modes and b) black hole modes plus the infalling modes,using the Janus-faced nature of the model.The long-time behaviour also gives us glimpses of modifications in the character of Hawking radiation. Lastly, we study the phenomenon of superradiance in our model in analogy with atomic Dicke superradiance.
The canonical form of the Rabi hamiltonian
Szopa, M; Ceulemans, A; Szopa, Marek; Mys, Geert; Ceulemans, Arnout
1996-01-01
The Rabi Hamiltonian, describing the coupling of a two-level system to a single quantized boson mode, is studied in the Bargmann-Fock representation. The corresponding system of differential equations is transformed into a canonical form in which all regular singularities between zero and infinity have been removed. The canonical or Birkhoff-transformed equations give rise to a two-dimensional eigenvalue problem, involving the energy and a transformational parameter which affects the coupling strength. The known isolated exact solutions of the Rabi Hamiltonian are found to correspond to the uncoupled form of the canonical system.
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.......Our Hamiltonians are compared to an equivalent one for graphene. For silicene, the expressionfor band warping is obtained analytically and found to be of different order than for graphene. Weprove that a uniaxial strain does not open a gap, resolving contradictory numerical results in the literature...
Hamiltonian Dynamics of Protein Filament Formation.
Michaels, Thomas C T; Cohen, Samuel I A; Vendruscolo, Michele; Dobson, Christopher M; Knowles, Tuomas P J
2016-01-22
We establish the Hamiltonian structure of the rate equations describing the formation of protein filaments. We then show that this formalism provides a unified view of the behavior of a range of biological self-assembling systems as diverse as actin, prions, and amyloidogenic polypeptides. We further demonstrate that the time-translation symmetry of the resulting Hamiltonian leads to previously unsuggested conservation laws that connect the number and mass concentrations of fibrils and allow linear growth phenomena to be equated with autocatalytic growth processes. We finally show how these results reveal simple rate laws that provide the basis for interpreting experimental data in terms of specific mechanisms controlling the proliferation of fibrils.
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.
Hamiltonian adaptive resolution simulation for molecular liquids.
Potestio, Raffaello; Fritsch, Sebastian; Español, Pep; Delgado-Buscalioni, Rafael; Kremer, Kurt; Everaers, Ralf; Donadio, Davide
2013-03-08
Adaptive resolution schemes allow the simulation of a molecular fluid treating simultaneously different subregions of the system at different levels of resolution. In this work we present a new scheme formulated in terms of a global Hamiltonian. Within this approach equilibrium states corresponding to well-defined statistical ensembles can be generated making use of all standard molecular dynamics or Monte Carlo methods. Models at different resolutions can thus be coupled, and thermodynamic equilibrium can be modulated keeping each region at desired pressure or density without disrupting the Hamiltonian framework.
Stability of Frustration-Free Hamiltonians
Michalakis, Spyridon
2011-01-01
We prove stability of the spectral gap for gapped, frustration-free Hamiltonians under general, quasi-local perturbations. We present a necessary and sufficient condition for stability, which we call "Local Topological Quantum Order" and show that this condition implies an area law for the entanglement entropy of the groundstate subspace. This result extends previous work by Bravyi et al., on the stability of topological quantum order for Hamiltonians composed of commuting projections with a common zero-energy subspace. We conclude with a list of open problems relevant to spectral gaps and topological quantum order.
Hamiltonian theory of guiding-center motion
Energy Technology Data Exchange (ETDEWEB)
Cary, John R.; Brizard, Alain J. [Center for Integrated Plasma Studies and Department of Physics, University of Colorado, Boulder, Colorado 80309-0390 (United States) and Tech-X Corporation, Boulder, Colorado 80303 (United States); Department of Chemistry and Physics, Saint Michael' s College, Colchester, Vermont 05439 (United States)
2009-04-15
Guiding-center theory provides the reduced dynamical equations for the motion of charged particles in slowly varying electromagnetic fields, when the fields have weak variations over a gyration radius (or gyroradius) in space and a gyration period (or gyroperiod) in time. Canonical and noncanonical Hamiltonian formulations of guiding-center motion offer improvements over non-Hamiltonian formulations: Hamiltonian formulations possess Noether's theorem (hence invariants follow from symmetries), and they preserve the Poincare invariants (so that spurious attractors are prevented from appearing in simulations of guiding-center dynamics). Hamiltonian guiding-center theory is guaranteed to have an energy conservation law for time-independent fields--something that is not true of non-Hamiltonian guiding-center theories. The use of the phase-space Lagrangian approach facilitates this development, as there is no need to transform a priori to canonical coordinates, such as flux coordinates, which have less physical meaning. The theory of Hamiltonian dynamics is reviewed, and is used to derive the noncanonical Hamiltonian theory of guiding-center motion. This theory is further explored within the context of magnetic flux coordinates, including the generic form along with those applicable to systems in which the magnetic fields lie on nested tori. It is shown how to return to canonical coordinates to arbitrary accuracy by the Hazeltine-Meiss method and by a perturbation theory applied to the phase-space Lagrangian. This noncanonical Hamiltonian theory is used to derive the higher-order corrections to the magnetic moment adiabatic invariant and to compute the longitudinal adiabatic invariant. Noncanonical guiding-center theory is also developed for relativistic dynamics, where covariant and noncovariant results are presented. The latter is important for computations in which it is convenient to use the ordinary time as the independent variable rather than the proper time
Hamiltonian dynamics of the parametrized electromagnetic field
G., J Fernando Barbero; Villaseñor, Eduardo J S
2015-01-01
We study the Hamiltonian formulation for a parametrized electromagnetic field with the purpose of clarifying the interplay between parametrization and gauge symmetries. We use a geometric approach which is tailor-made for theories where embeddings are part of the dynamical variables. Our point of view is global and coordinate free. The most important result of the paper is the identification of sectors in the primary constraint submanifold in the phase space of the model where the number of independent components of the Hamiltonian vector fields that define the dynamics changes. This explains the non-trivial behavior of the system and some of its pathologies.
Hamiltonian dynamics of the parametrized electromagnetic field
Barbero G, J. Fernando; Margalef-Bentabol, Juan; Villaseñor, Eduardo J. S.
2016-06-01
We study the Hamiltonian formulation for a parametrized electromagnetic field with the purpose of clarifying the interplay between parametrization and gauge symmetries. We use a geometric approach which is tailor-made for theories where embeddings are part of the dynamical variables. Our point of view is global and coordinate free. The most important result of the paper is the identification of sectors in the primary constraint submanifold in the phase space of the model where the number of independent components of the Hamiltonian vector fields that define the dynamics changes. This explains the non-trivial behavior of the system and some of its pathologies.
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.
Incorporation of New Information in an Approximate Hamiltonian
Viazminsky, C P
2002-01-01
Additional information about the eigenvalues and eigenvectors of a physical system demands extension of the effective Hamiltonian in use. In this work we extend the effective Hamiltonian that describes partially a physical system so that the new Hamiltonian comprises, in addition to the information in the old Hamiltonian, new information, available by means of experiment or theory. A simple expression of the enlarged Hamiltonian, which does not involve matrix inversion, is obtained. It is also shown that the Lee-Suzuki transformation effectively put the initial Hamiltonian in a diagonal block form.
Variational viewpoint of the quadratic Markov measure field models: theory and algorithms.
Rivera, Mariano; Dalmau, Oscar
2012-03-01
We present a framework for image segmentation based on quadratic programming, i.e., by minimization of a quadratic regularized energy linearly constrained. In particular, we present a new variational derivation of the quadratic Markov measure field (QMMF) models, which can be understood as a procedure for regularizing model preferences (memberships or likelihoods). We also present efficient optimization algorithms. In the QMMFs, the uncertainty in the computed regularized probability measure field is controlled by penalizing Gini's coefficient, and hence, it affects the convexity of the quadratic programming problem. The convex case is reduced to the solution of a positive definite linear system, and for that case, an efficient Gauss-Seidel (GS) scheme is presented. On the other hand, we present an efficient projected GS with subspace minimization for optimizing the nonconvex case. We demonstrate the proposal capabilities by experiments and numerical comparisons with interactive two-class segmentation, as well as the simultaneous estimation of segmentation and (parametric and nonparametric) generative models. We present extensions to the original formulation for including color and texture clues, as well as imprecise user scribbles in an interactive framework.
Lorenzen, Konstantin; Mathias, Gerald; Tavan, Paul
2015-11-14
Hamiltonian Dielectric Solvent (HADES) is a recent method [S. Bauer et al., J. Chem. Phys. 140, 104103 (2014)] which enables atomistic Hamiltonian molecular dynamics (MD) simulations of peptides and proteins in dielectric solvent continua. Such simulations become rapidly impractical for large proteins, because the computational effort of HADES scales quadratically with the number N of atoms. If one tries to achieve linear scaling by applying a fast multipole method (FMM) to the computation of the HADES electrostatics, the Hamiltonian character (conservation of total energy, linear, and angular momenta) may get lost. Here, we show that the Hamiltonian character of HADES can be almost completely preserved, if the structure-adapted fast multipole method (SAMM) as recently redesigned by Lorenzen et al. [J. Chem. Theory Comput. 10, 3244-3259 (2014)] is suitably extended and is chosen as the FMM module. By this extension, the HADES/SAMM forces become exact gradients of the HADES/SAMM energy. Their translational and rotational invariance then guarantees (within the limits of numerical accuracy) the exact conservation of the linear and angular momenta. Also, the total energy is essentially conserved-up to residual algorithmic noise, which is caused by the periodically repeated SAMM interaction list updates. These updates entail very small temporal discontinuities of the force description, because the employed SAMM approximations represent deliberately balanced compromises between accuracy and efficiency. The energy-gradient corrected version of SAMM can also be applied, of course, to MD simulations of all-atom solvent-solute systems enclosed by periodic boundary conditions. However, as we demonstrate in passing, this choice does not offer any serious advantages.
Energy Technology Data Exchange (ETDEWEB)
Lorenzen, Konstantin; Mathias, Gerald; Tavan, Paul, E-mail: tavan@physik.uni-muenchen.de [Lehrstuhl für BioMolekulare Optik, Ludig–Maximilians Universität München, Oettingenstr. 67, 80538 München (Germany)
2015-11-14
Hamiltonian Dielectric Solvent (HADES) is a recent method [S. Bauer et al., J. Chem. Phys. 140, 104103 (2014)] which enables atomistic Hamiltonian molecular dynamics (MD) simulations of peptides and proteins in dielectric solvent continua. Such simulations become rapidly impractical for large proteins, because the computational effort of HADES scales quadratically with the number N of atoms. If one tries to achieve linear scaling by applying a fast multipole method (FMM) to the computation of the HADES electrostatics, the Hamiltonian character (conservation of total energy, linear, and angular momenta) may get lost. Here, we show that the Hamiltonian character of HADES can be almost completely preserved, if the structure-adapted fast multipole method (SAMM) as recently redesigned by Lorenzen et al. [J. Chem. Theory Comput. 10, 3244-3259 (2014)] is suitably extended and is chosen as the FMM module. By this extension, the HADES/SAMM forces become exact gradients of the HADES/SAMM energy. Their translational and rotational invariance then guarantees (within the limits of numerical accuracy) the exact conservation of the linear and angular momenta. Also, the total energy is essentially conserved—up to residual algorithmic noise, which is caused by the periodically repeated SAMM interaction list updates. These updates entail very small temporal discontinuities of the force description, because the employed SAMM approximations represent deliberately balanced compromises between accuracy and efficiency. The energy-gradient corrected version of SAMM can also be applied, of course, to MD simulations of all-atom solvent-solute systems enclosed by periodic boundary conditions. However, as we demonstrate in passing, this choice does not offer any serious advantages.
Szalay, Viktor
2015-05-07
A new ro-vibrational Hamiltonian operator, named gateway Hamiltonian operator, with exact kinetic energy term, Tˆ, is presented. It is in the Eckart frame and it is of the same form as Watson's normal coordinate Hamiltonian. However, the vibrational coordinates employed are not normal coordinates. The new Hamiltonian is shown to provide easy access to Eckart frame ro-vibrational Hamiltonians with exact Tˆ given in terms of any desired set of vibrational coordinates. A general expression of the Eckart frame ro-vibrational Hamiltonian operator is given and some of its properties are discussed.
The Extremism of Two Variable Function Based on the Positive Definite Property
Institute of Scientific and Technical Information of China (English)
Lü Bao-xian; LI Xiu-li
2004-01-01
In this paper we give out a sufficientand solution of quadratic function's maximum with theory of quadratic form and give out the definition of the positivedefinite property of the following homogeneous polynomials of degree 2n two variables function, based on the definite of localmaximum of two variables function.
Implicit Hamiltonian formulation of bond graphs
Golo, G.; Schaft, A.J. van der; Breedveld, P.C.; Maschke, B.M.
2003-01-01
This paper deals with mathematical formulation of bond graphs. It is proven that the power continuous part of bond graphs, the junction structure, can be associated with a Dirac structure and that equations describing a bond graph model correspond to an implicit port-controlled Hamiltonian system wi
Hamiltonian Approach to the Gribov Problem
Heinzl, T
1996-01-01
We study the Gribov problem within a Hamiltonian formulation of pure Yang-Mills theory. For a particular gauge fixing, a finite volume modification of the axial gauge, we find an exact characterization of the space of gauge-inequivalent gauge configurations.
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...
Lagrangian tetragons and instabilities in Hamiltonian dynamics
Entov, Michael; Polterovich, Leonid
2017-01-01
We present a new existence mechanism, based on symplectic topology, for orbits of Hamiltonian flows connecting a pair of disjoint subsets in the phase space. The method involves function theory on symplectic manifolds combined with rigidity of Lagrangian submanifolds. Applications include superconductivity channels in nearly integrable systems and dynamics near a perturbed unstable equilibrium.
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...
An underlying geometrical manifold for Hamiltonian mechanics
Horwitz, L. P.; Yahalom, A.; Levitan, J.; Lewkowicz, M.
2017-02-01
We show that there exists an underlying manifold with a conformal metric and compatible connection form, and a metric type Hamiltonian (which we call the geometrical picture), that can be put into correspondence with the usual Hamilton-Lagrange mechanics. The requirement of dynamical equivalence of the two types of Hamiltonians, that the momenta generated by the two pictures be equal for all times, is sufficient to determine an expansion of the conformal factor, defined on the geometrical coordinate representation, in its domain of analyticity with coefficients to all orders determined by functions of the potential of the Hamiltonian-Lagrange picture, defined on the Hamilton-Lagrange coordinate representation, and its derivatives. Conversely, if the conformal function is known, the potential of a Hamilton-Lagrange picture can be determined in a similar way. We show that arbitrary local variations of the orbits in the Hamilton-Lagrange picture can be generated by variations along geodesics in the geometrical picture and establish a correspondence which provides a basis for understanding how the instability in the geometrical picture is manifested in the instability of the the original Hamiltonian motion.
Bifurcations and safe regions in open Hamiltonians
Energy Technology Data Exchange (ETDEWEB)
Barrio, R; Serrano, S [GME, Dpto Matematica Aplicada and IUMA, Universidad de Zaragoza, E-50009 Zaragoza (Spain); Blesa, F [GME, Dpto Fisica Aplicada, Universidad de Zaragoza, E-50009 Zaragoza (Spain)], E-mail: rbarrio@unizar.es, E-mail: fblesa@unizar.es, E-mail: sserrano@unizar.es
2009-05-15
By using different recent state-of-the-art numerical techniques, such as the OFLI2 chaos indicator and a systematic search of symmetric periodic orbits, we get an insight into the dynamics of open Hamiltonians. We have found that this kind of system has safe bounded regular regions inside the escape region that have significant size and that can be located with precision. Therefore, it is possible to find regions of nonzero measure with stable periodic or quasi-periodic orbits far from the last KAM tori and far from the escape energy. This finding has been possible after a careful combination of a precise 'skeleton' of periodic orbits and a 2D plate of the OFLI2 chaos indicator to locate saddle-node bifurcations and the regular regions near them. Besides, these two techniques permit one to classify the different kinds of orbits that appear in Hamiltonian systems with escapes and provide information about the bifurcations of the families of periodic orbits, obtaining special cases of bifurcations for the different symmetries of the systems. Moreover, the skeleton of periodic orbits also gives the organizing set of the escape basin's geometry. As a paradigmatic example, we study in detail the Henon-Heiles Hamiltonian, and more briefly the Barbanis potential and a galactic Hamiltonian.
Bifurcations and safe regions in open Hamiltonians
Barrio, R.; Blesa, F.; Serrano, S.
2009-05-01
By using different recent state-of-the-art numerical techniques, such as the OFLI2 chaos indicator and a systematic search of symmetric periodic orbits, we get an insight into the dynamics of open Hamiltonians. We have found that this kind of system has safe bounded regular regions inside the escape region that have significant size and that can be located with precision. Therefore, it is possible to find regions of nonzero measure with stable periodic or quasi-periodic orbits far from the last KAM tori and far from the escape energy. This finding has been possible after a careful combination of a precise 'skeleton' of periodic orbits and a 2D plate of the OFLI2 chaos indicator to locate saddle-node bifurcations and the regular regions near them. Besides, these two techniques permit one to classify the different kinds of orbits that appear in Hamiltonian systems with escapes and provide information about the bifurcations of the families of periodic orbits, obtaining special cases of bifurcations for the different symmetries of the systems. Moreover, the skeleton of periodic orbits also gives the organizing set of the escape basin's geometry. As a paradigmatic example, we study in detail the Hénon-Heiles Hamiltonian, and more briefly the Barbanis potential and a galactic Hamiltonian.
Basis Optimization Renormalization Group for Quantum Hamiltonian
Sugihara, Takanori
2001-01-01
We find an algorithm of numerical renormalization group for spin chain models. The essence of this algorithm is orthogonal transformation of basis states, which is useful for reducing the number of relevant basis states to create effective Hamiltonian. We define two types of rotations and combine them to create appropriate orthogonal transformation.
Hamiltonian analysis of BHT massive gravity
Blagojević, M
2010-01-01
We study the Hamiltonian structure of the Bergshoeff-Hohm-Townsend (BHT) massive gravity with a cosmological constant. In the space of coupling constants $(\\Lambda_0,m^2)$, our canonical analysis reveals the special role of the condition $\\Lambda_0/m^2\
Hamiltonian and self-adjoint control systems
Schaft, A. van der; Crouch, P.E.
1987-01-01
This paper outlines results recently obtained in the problem of determining when an input-output map has a Hamiltonian realization. The results are obtained in terms of variations of the system trajectories, as in the solution of the Inverse Problem in Classical Mechanics. The variational and adjoin
Hamiltonian constants for several new entire solutions
Institute of Scientific and Technical Information of China (English)
2008-01-01
Using the Hamiltonian identities and the corresponding Hamilto- nian constants for entire solutions of elliptic partial differential equations, we investigate several new entire solutions whose existence were shown recently, and show interesting properties of the solutions such as formulas for contact angles at infinity of concentration curves.
Transparency in Port-Hamiltonian-Based Telemanipulation
Secchi, Cristian; Stramigioli, Stefano; Fantuzzi, Cesare
2008-01-01
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 p
Relativistic Stern-Gerlach Deflection: Hamiltonian Formulation
Mane, S R
2016-01-01
A Hamiltonian formalism is employed to elucidate the effects of the Stern-Gerlach force on beams of relativistic spin-polarized particles, for passage through a localized region with a static magnetic or electric field gradient. The problem of the spin-orbit coupling for nonrelativistic bounded motion in a central potential (hydrogen-like atoms, in particular) is also briefly studied.
Momentum and Hamiltonian in Complex Action Theory
Nagao, Keiichi
2011-01-01
In the complex action theory (CAT) we explicitly examine how the momentum and Hamiltonian are defined from the Feynman path integral (FPI) point of view. In arXiv:1104.3381[quant-ph], introducing a philosophy to keep the analyticity in parameter variables of FPI and defining a modified set of complex conjugate, hermitian conjugates and bras, we have extended $| q >$ and $| p >$ to complex $q$ and $p$ so that we can deal with a complex coordinate $q$ and a complex momentum $p$. After reviewing them briefly, we describe in terms of the newly introduced devices the time development of a $\\xi$-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 to the momentum again via the saddle point for $p$. This study confirms that the momentum and Hamiltonian in the CAT have t...
Notch filters for port-Hamiltonian systems
Dirksz, Daniel; Scherpen, Jacquelien M.A.; van der Schaft, Abraham; Steinbuch, M.
2012-01-01
Network modeling of lumped-parameter physical systems naturally leads to a geometrically defined class of systems, i.e., port-Hamiltonian (PH) systems [4, 6]. The PH modeling framework describes a large class of (nonlinear) systems including passive mechanical systems, electrical systems, electromec
The Maslov indices of Hamiltonian periodic orbits
Energy Technology Data Exchange (ETDEWEB)
Gosson, Maurice de [Blekinge Institute of Technology, SE 371 79 Karlskrona (Sweden); Gosson, Serge de [Vaexjoe University (MSI), SE 351 95 Vaexjoe (Sweden)
2003-12-05
We use the properties of the Leray index to give precise formulae in arbitrary dimensions for the Maslov index of the monodromy matrix arising in periodic Hamiltonian systems. We compare our index with other indices appearing in the literature. (letter to the editor)
Global Properties of Integrable Hamiltonian Systems
Lukina, O.V.; Takens, F.; Broer, H.W.
2008-01-01
This paper deals with Lagrangian bundles which are symplectic torus bundles that occur in integrable Hamiltonian systems. We review the theory of obstructions to triviality, in particular monodromy, as well as the ensuing classification problems which involve the Chern and Lagrange class. Our
Global Properties of Integrable Hamiltonian Systems
Lukina, O.V.; Takens, F.; Broer, H.W.
2008-01-01
This paper deals with Lagrangian bundles which are symplectic torus bundles that occur in integrable Hamiltonian systems. We review the theory of obstructions to triviality, in particular monodromy, as well as the ensuing classification problems which involve the Chern and Lagrange class. Our approa
Scattering for Infinite Dimensional Port Hamiltonian Systems
Macchelli, Alessandro; Stramigioli, Stefano; Schaft, Arjan van der; Melchiorri, Claudio
2002-01-01
In this paper, an introduction to scattering for infinite dimensional systems within the framework of port Hamiltonian system is presented. The classical results on wave propagation can be extended to generic power propagation phenomena, for example to fluid dynamics or flexible structures. The key-
Constrained neural approaches to quadratic assignment problems.
Ishii, S; Sato, M
1998-08-01
In this paper, we discuss analog neural approaches to the quadratic assignment problem (QAP). These approaches employ a hard constraints scheme to restrict the domain space, and are able to obtain much improved solutions over conventional neural approaches. Since only a few strong heuristics for QAP have been known to date, our approaches are good alternatives, capable of obtaining fairly good solutions in a short period of time. Some of them can also be applied to large-scale problems, say of size N>/=300.
Automatic differentiation for reduced sequential quadratic programming
Institute of Scientific and Technical Information of China (English)
Liao Liangcai; Li Jin; Tan Yuejin
2007-01-01
In order to slove the large-scale nonlinear programming (NLP) problems efficiently, an efficient optimization algorithm based on reduced sequential quadratic programming (rSQP) and automatic differentiation (AD) is presented in this paper. With the characteristics of sparseness, relatively low degrees of freedom and equality constraints utilized, the nonlinear programming problem is solved by improved rSQP solver. In the solving process, AD technology is used to obtain accurate gradient information. The numerical results show that the combined algorithm, which is suitable for large-scale process optimization problems, can calculate more efficiently than rSQP itself.
Bianchi I solutions of effective quadratic gravity
Müller, Daniel
2012-01-01
It is believed that soon after the Planck time, Einstein's general relativity theory should be corrected to an effective quadratic theory. Numerical solutions for the anisotropic generalization of the Friedmann "flat" model $E^3$ for this effective gravity are given. It must be emphasized that although numeric, these solutions are exact in the sense that they depend only on the precision of the machine. The solutions are identified asymptotically in a certain sense. It is found solutions which asymptote de Sitter space, Minkowski space and a singularity. This work is a generalization for non diagonal spatial metrics of a previous result obtained by one of us and a collaborator for Bianchi $I$ spaces.
Linear Stability Analysis of Dynamical Quadratic Gravity
Ayzenberg, Dimitry; Yunes, Nicolas
2013-01-01
We perform a linear stability analysis of dynamical, quadratic gravity in the high-frequency, geometric optics approximation. This analysis is based on a study of gravitational and scalar modes propagating on spherically-symmetric and axially-symmetric, vacuum solutions of the theory. We find dispersion relations that do no lead to exponential growth of the propagating modes, suggesting the theory is linearly stable on these backgrounds. The modes are found to propagate at subluminal and superluminal speeds, depending on the propagating modes' direction relative to the background geometry, just as in dynamical Chern-Simons gravity.
Range-based estimation of quadratic variation
DEFF Research Database (Denmark)
Christensen, Kim; Podolskij, Mark
In this paper, we propose using realized range-based estimation to draw inference about the quadratic variation of jump-diffusion processes. We also construct a new test of the hypothesis that an asset price has a continuous sample path. Simulated data shows that our approach is efficient, the te...... is well-sized and more powerful than a return-based t-statistic for sampling frequencies normally used in empirical work. Applied to equity data, we find that the intensity of the jump process is not as high as previously reported....
Range-based estimation of quadratic variation
DEFF Research Database (Denmark)
Christensen, Kim; Podolskij, Mark
This paper proposes using realized range-based estimators to draw inference about the quadratic variation of jump-diffusion processes. We also construct a range-based test of the hypothesis that an asset price has a continuous sample path. Simulated data shows that our approach is efficient, the ......, the test is well-sized and more powerful than a return-based t-statistic for sampling frequencies normally used in empirical work. Applied to equity data, we show that the intensity of the jump process is not as high as previously reported....
Effective Hamiltonian approach to periodically perturbed quantum optical systems
Energy Technology Data Exchange (ETDEWEB)
Sainz, I. [Centro Universitario de los Lagos, Universidad de Guadalajara, Enrique Diaz de Leon, 47460 Lagos de Moreno, Jal. (Mexico)]. E-mail: isa@culagos.udg.mx; Klimov, A.B. [Departamento de Fisica, Universidad de Guadalajara, Revolucion 1500, 44410 Guadalajara, Jal. (Mexico)]. E-mail: klimov@cencar.udg.mx; Saavedra, C. [Center for Quantum Optics and Quantum Information, Departamento de Fisica, Universidad de Concepcion, Casilla 160-C, Concepcion (Chile)]. E-mail: csaaved@udec.cl
2006-02-20
We apply the method of Lie-type transformations to Floquet Hamiltonians for periodically perturbed quantum systems. Some typical examples of driven quantum systems are considered in the framework of this approach and corresponding effective time dependent Hamiltonians are found.
Hamiltonian Structures for the Generalized Dispersionless KdV Hierarchy
Brunelli, J. C.
1996-01-01
We study from a Hamiltonian point of view the generalized dispersionless KdV hierarchy of equations. From the so called dispersionless Lax representation of these equations we obtain three compatible Hamiltonian structures. The second and third Hamiltonian structures are calculated directly from the r-matrix approach. Since the third structure is not related recursively with the first two ones the generalized dispersionless KdV hierarchy can be characterized as a truly tri-Hamiltonian system.
The role of the Hamiltonian in the interpretation of quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Castagnino, M [CONICET-Institutos de Fisica de Rosario y de Astronomia y Fisica del Espacio. Casilla de Correos 67, Sucursal 28, 1428, Buenos Aires (Argentina); Lombardi, O [CONICET-Unversidad de Buenos Aires. Crisologo Larralde 3440, 1430, Buenos Aires (Argentina)], E-mail: mariocastagnino@citynet.net.ar, E-mail: olimpiafilo@arnet.com.ar
2008-08-15
In this paper we propose a new realist, non-collapse interpretation of quantum mechanics, which moves away from the prevailing trend in the subject by paying special attention to the physical relevance of the interpretation. In particular, our proposal endows the Hamiltonian of the system, systematically ignored in the traditional interpretations, with a central role: it distinguishes between systems and subsystems and is the main ingredient in the selection of the definite-valued observables. We show how this interpretation solves the measurement problem, both in the ideal and in the non-ideal version, and we argue for the physical relevance of the new definite-value assignment.
Quadratic forms for Feynman-Kac semigroups
Energy Technology Data Exchange (ETDEWEB)
Hibey, Joseph L. [Department of Electrical Engineering, University of Colorado at Denver, Campus Box 110, Denver, CO 80217 (United States)]. E-mail: joseph.hibey@cudenver.edu; Charalambous, Charalambos D. [Electrical and Computer Engineering Department, University of Cyprus, 75 Kallipoleos Avenue, Nicosia (Cyprus)]. E-mail: chadcha@ucy.ac.cy
2006-05-15
Some problems in a stochastic setting often involve the need to evaluate the Feynman-Kac formula that follows from models described in terms of stochastic differential equations. Equivalent representations in terms of partial differential equations are also of interest, and these establish the well-known connection between probabilistic and deterministic formulations of these problems. In this Letter, this connection is studied in terms of the quadratic form associated with the Feynman-Kac semigroup. The probability measures that naturally arise in this approach, and thus define how Brownian motion is killed at a specified rate while exiting a set, are interpreted as a random time change of the original stochastic differential equation. Furthermore, since random time changes alter the diffusion coefficients in stochastic differential equations while Girsanov-type measure transformations alter their drift coefficients, their simultaneous use should lead to more tractable solutions for some classes of problems. For example, the minimization of some quadratic forms leads to solutions that satisfy certain partial differential equations and, therefore, the techniques discussed provide a variational approach for finding these solutions.
DEFF Research Database (Denmark)
Mak, Vicky; Thomadsen, Tommy
2004-01-01
A well-known extension of the Travelling Salesman Problem (TSP) is the Selective (or Prize-collecting) TSP: In addition to the edge-costs, each node has an associated reward (denoted the node-reward) and instead of visiting all nodes, only profitable nodes are visited. The Quadratic Selective TSP...
Topological Hamiltonian as an exact tool for topological invariants.
Wang, Zhong; Yan, Binghai
2013-04-17
We propose the concept of 'topological Hamiltonian' for topological insulators and superconductors in interacting systems. The eigenvalues of the topological Hamiltonian are significantly different from the physical energy spectra, but we show that the topological Hamiltonian contains the information of gapless surface states, therefore it is an exact tool for topological invariants.
THE HAMILTONIAN EQUATIONS IN SOME MATHEMATICS AND PHYSICS PROBLEMS
Institute of Scientific and Technical Information of China (English)
陈勇; 郑宇; 张鸿庆
2003-01-01
Some new Hamiltonian canonical system are discussed for a series of partialdifferential equations in Mathematics and Physics. It includes the Hamiltonian formalism forthe symmetry second-order equation with the variable coefficients, the new nonhomogeneousHamiltonian representation for fourth-order symmetry equation with constant coefficients,the one of MKdV equation and KP equation.
HAMILTONIAN MECHANICS ON K(A)HLER MANIFOLDS
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Using the mechanical principle, the theory of modern geometry and advanced calculus, Hamiltonian mechanics was generalized to Kahler manifolds, and the Hamiltonian mechanics on Kahler manifolds was established. Then the complex mathematical aspect of Hamiltonian vector field and Hamilton's equations was obtained, and so on.
Introduction to thermodynamics of spin models in the Hamiltonian limit
Berche, B; Berche, Bertrand; Lopez, Alexander
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.
A linear quadratic regulator approach to the stabilization of uncertain linear systems
Shieh, L. S.; Sunkel, J. W.; Wang, Y. J.
1990-01-01
This paper presents a linear quadratic regulator approach to the stabilization of uncertain linear systems. The uncertain systems under consideration are described by state equations with the presence of time-varying unknown-but-bounded uncertainty matrices. The method is based on linear quadratic regulator (LQR) theory and Liapunov stability theory. The robust stabilizing control law for a given uncertain system can be easily constructed from the symmetric positive-definite solution of the associated augmented Riccati equation. The proposed approach can be applied to matched and/or mismatched systems with uncertainty matrices in which only their matrix norms are bounded by some prescribed values and/or their entries are bounded by some prescribed constraint sets. Several numerical examples are presented to illustrate the results.
On a general class of quadratic hopping sequences
Institute of Scientific and Technical Information of China (English)
JIA HuaDing; YUAN Ding; PENG DaiYuan; GUO Ling
2008-01-01
Based upon quadratic polynomials over the finite field, a new class of frequency hopping sequences with large family size suitable for applications in time/frequency hopping CDMA systems, multi-user radar and sonar systems is proposed and investigated. It is shown that the new time/frequency hopping sequences have at most one hit in their autocorrelation functions and at most two hits in their crosscorrelation functions except for a special case, and their family size is much larger than the conventional quadratic hopping sequences. The percentage of full collisions for the new quadratic hopping sequences is discussed. In addition, the average number of hits for the new quadratic hopping sequences, quadratic congruence sequences, extended quadratic congruence sequences and the general linear hopping sequences are also derived.
Quadratic residues and non-residues selected topics
Wright, Steve
2016-01-01
This book offers an account of the classical theory of quadratic residues and non-residues with the goal of using that theory as a lens through which to view the development of some of the fundamental methods employed in modern elementary, algebraic, and analytic number theory. The first three chapters present some basic facts and the history of quadratic residues and non-residues and discuss various proofs of the Law of Quadratic Reciprosity in depth, with an emphasis on the six proofs that Gauss published. The remaining seven chapters explore some interesting applications of the Law of Quadratic Reciprocity, prove some results concerning the distribution and arithmetic structure of quadratic residues and non-residues, provide a detailed proof of Dirichlet’s Class-Number Formula, and discuss the question of whether quadratic residues are randomly distributed. The text is a valuable resource for graduate and advanced undergraduate students as well as for mathematicians interested in number theory.
On Quadratic BSDEs with Final Condition in L2
Yang, Hanlin
2015-01-01
This thesis consists of three parts. In the first part, we study $\\mathbb{L}^p$ solutions of a large class of BSDEs. Existence, comparison theorem, uniqueness and a stability result are proved. In the second part, we establish the solvability of quadratic semimartingale BSDEs. In contrast to current literature, we use Lipschitz-quadratic regularization and obtain the existence and uniqueness results with minimal assumptions. The third part is a brief summary of quadratic semimartingales and t...
Quadratic forms and Clifford algebras on derived stacks
Vezzosi, Gabriele
2013-01-01
In this paper we present an approach to quadratic structures in derived algebraic geometry. We define derived n-shifted quadratic complexes, over derived affine stacks and over general derived stacks, and give several examples of those. We define the associated notion of derived Clifford algebra, in all these contexts, and compare it with its classical version, when they both apply. Finally, we prove three main existence results for derived shifted quadratic forms over derived stacks, define ...
Robust Solutions of Uncertain Complex-valued Quadratically Constrained Programs
Institute of Scientific and Technical Information of China (English)
Da Chuan XU; Zheng Hai HUANG
2008-01-01
In this paper,we discuss complex convex quadratically constrained optimization with uncertain data.Using S-Lemma,we show that the robust counterpart of complex convex quadratically constrained optimization with ellipsoidal or intersection-of-two-ellipsoids uncertainty set leads to a complex semidefinite program.By exploring the approximate S-Lemma,we give a complex semidefinite program which approximates the NP-hard robust counterpart of complex convex quadratic optimization with intersection-of-ellipsoids uncertainty set.
Some Aspects of Quadratic Generalized White Noise Functionals
Si, Si; Hida, Takeyuki
2009-02-01
We shall discuss some particular roles of quadratic generalized white noise functionals. First observation is made from the viewpoint of the so-called "la passage du fini à l'infini". We then come to a dual pairing of spaces formed by quadratic generalized white noise functionals. In this line, we can further discuss quadratic forms of differential operators acting on the space of white noise functionals.
Hamiltonian[k,k+1]-因子%Hamiltonian [k, k + 1]-Factor
Institute of Scientific and Technical Information of China (English)
蔡茂诚; 方奇志; 李延军
2003-01-01
A Hamiltonian [k, k + 1]-factor is a [k, k + 1]-factor containing a Hamiltonian cycle. A simple graph G of order n is n/2-critical if δ(G) ≥ n/2 but δ(G - e) ＜ n/2 for any edge e ∈ E(G). Let k ≥ 2 be an integer and G be an n/2-critical graph with n ≥ 4k - 6 and n ≥ 7. In this paper it is proved that for any given Hamiltonian cycle C of G, G has a [k, k + 1]-factor containing C. This result is an improvement on some recent results about the existence of Hamiltonian [k, k + 1]-factor.%本文考虑n/2-临界图中Hamiltonian[k,k+1]-因子的存在性.Hamiltonian[k,k+1]-因子是指包含Hamiltonian圈的[k,k+1]-因子;给定阶数为n的简单图G,若δ(G)≥n/2而δ(G\\e)＜n/2(对任意的e∈E(G)),则称G为n/2-临界图.设k为大于等于2的整数,G为n/2-临界图(其中n≥4k-6且n≥7),我们证明了对于G的任何Hamiltonian圈C,G中必存在包含C的[k,k+1]-因子.该结果改进了现有的一些有关Hamiltonian[k,k+1]-因子存在性的结果.
Lax operator algebras and Hamiltonian integrable hierarchies
Sheinman, Oleg K
2009-01-01
We consider the theory of Lax equations in complex simple and reductive classical Lie algebras with the spectral parameter on a Riemann surface of finite genus. Our approach is based on the new objects -- the Lax operator algebras, and develops the approach of I.Krichever treating the $\\gl(n)$ case. For every Lax operator considered as the mapping sending a point of the cotangent bundle on the space of extended Tyrin data to an element of the corresponding Lax operator algebra we construct the hierarchy of mutually commuting flows given by Lax equations and prove that those are Hamiltonian with respect to the Krichever-Phong symplectic structure. The corresponding Hamiltonians give integrable finite-dimensional Hitchin-type systems. For example we derive elliptic $A_n$, $C_n$, $D_n$ Calogero-Moser systems in frame of our approach.
Lax operator algebras and Hamiltonian integrable hierarchies
Energy Technology Data Exchange (ETDEWEB)
Sheinman, Oleg K [Steklov Mathematical Institute, Russian Academy of Sciences, Moscow (Russian Federation)
2011-02-28
This paper considers the theory of Lax equations with a spectral parameter on a Riemann surface, proposed by Krichever in 2001. The approach here is based on new objects, the Lax operator algebras, taking into consideration an arbitrary complex simple or reductive classical Lie algebra. For every Lax operator, regarded as a map sending a point of the cotangent bundle on the space of extended Tyurin data to an element of the corresponding Lax operator algebra, a hierarchy of mutually commuting flows given by the Lax equations is constructed, and it is proved that they are Hamiltonian with respect to the Krichever-Phong symplectic structure. The corresponding Hamiltonians give integrable finite-dimensional Hitchin-type systems. For example, elliptic A{sub n}, C{sub n}, and D{sub n} Calogero-Moser systems are derived in the framework of our approach. Bibliography: 13 titles.
An Underlying Geometrical Manifold for Hamiltonian Mechanics
Horwitz, L P; Levitan, J; Lewkowicz, M
2015-01-01
We show that there exists an underlying manifold with a conformal metric and compatible connection form, and a metric type Hamiltonian (which we call the geometrical picture) that can be put into correspondence with the usual Hamilton-Lagrange mechanics. The requirement of dynamical equivalence of the two types of Hamiltonians, that the momenta generated by the two pictures be equal for all times, is sufficient to determine an expansion of the conformal factor, defined on the geometrical coordinate representation, in its domain of analyticity with coefficients to all orders determined by functions of the potential of the Hamilton-Lagrange picture, defined on the Hamilton-Lagrange coordinate representation, and its derivatives. Conversely, if the conformal function is known, the potential of a Hamilton-Lagrange picture can be determined in a similar way. We show that arbitrary local variations of the orbits in the Hamilton-Lagrange picture can be generated by variations along geodesics in the geometrical pictu...
Hamiltonian Approach To Dp-Brane Noncommutativity
Nikolic, B.; Sazdovic, B.
2010-07-01
In this article we investigate Dp-brane noncommutativity using Hamiltonian approach. We consider separately open bosonic string and type IIB superstring which endpoints are attached to the Dp-brane. From requirement that Hamiltonian, as the time translation generator, has well defined derivatives in the coordinates and momenta, we obtain boundary conditions directly in the canonical form. Boundary conditions are treated as canonical constraints. Solving them we obtain initial coordinates in terms of the effective ones as well as effective momenta. Presence of momenta implies noncommutativity of the initial coordinates. Effective theory, defined as initial one on the solution of boundary conditions, is its Ω even projection, where Ω is world-sheet parity transformation Ω:σ→-σ. The effective background fields are expressed in terms of Ω even and squares of the Ω odd initial background fields.
Hamiltonian approach to hybrid plasma models
Tronci, Cesare
2010-01-01
The Hamiltonian structures of several hybrid kinetic-fluid models are identified explicitly, upon considering collisionless Vlasov dynamics for the hot particles interacting with a bulk fluid. After presenting different pressure-coupling schemes for an ordinary fluid interacting with a hot gas, the paper extends the treatment to account for a fluid plasma interacting with an energetic ion species. Both current-coupling and pressure-coupling MHD schemes are treated extensively. In particular, pressure-coupling schemes are shown to require a transport-like term in the Vlasov kinetic equation, in order for the Hamiltonian structure to be preserved. The last part of the paper is devoted to studying the more general case of an energetic ion species interacting with a neutralizing electron background (hybrid Hall-MHD). Circulation laws and Casimir functionals are presented explicitly in each case.
ON THE ELUSIVENESS OF HAMILTONIAN PROPERTY
Institute of Scientific and Technical Information of China (English)
高随祥
2001-01-01
Decision tree complexity is an important measure of computational complexity. A graph property is a set of graphs such that if some graph G is in the set then each isomorphic graph to G is also in the set. Let P be a graph property on n vertices, if every decision tree algorithm recognizing P must examine at least k pairs of vertices in the worst case, then it is said that the decision tree complexity of P is k. If every decision tree algorithm recognizing P must examine all n(n-1)/2 pairs of vertices in the worst case, then P is said to be elusive. Karp conjectured that every nontrivial monotone graph property is elusive. This paper concerns the elusiveness of Hamiltonian property. It is proved that if n=p+1, pq or pq+1, (where p,q are distinct primes),then Hamiltonian property on n vertices is elusive.
A Hamiltonian Formulation of Topological Gravity
Waelbroeck, Henri
2009-01-01
Topological gravity is the reduction of Einstein's theory to spacetimes with vanishing curvature, but with global degrees of freedom related to the topology of the universe. We present an exact Hamiltonian lattice theory for topological gravity, which admits translations of the lattice sites as a gauge symmetry. There are additional symmetries, not present in Einstein's theory, which kill the local degrees of freedom. We show that these symmetries can be fixed by choosing a gauge where the torsion is equal to zero. In this gauge, the theory describes flat space-times. We propose two methods to advance towards the holy grail of lattice gravity: A Hamiltonian lattice theory for curved space-times, with first-class translation constraints.
Quantum Hamiltonian complexity and the detectability lemma
Aharonov, Dorit; Landau, Zeph; Vazirani, Umesh
2010-01-01
Quantum Hamiltonian complexity studies computational complexity aspects of local Hamiltonians and ground states; these questions can be viewed as generalizations of classical computational complexity problems related to local constraint satisfaction (such as SAT), with the additional ingredient of multi-particle entanglement. This additional ingredient of course makes generalizations of celebrated theorems such as the PCP theorem from classical to the quantum domain highly non-trivial; it also raises entirely new questions such as bounds on entanglement and correlations in ground states, and in particular area laws. We propose a simple combinatorial tool that helps to handle such questions: it is a simplified, yet more general version of the detectability lemma introduced by us in the more restricted context on quantum gap amplification a year ago. Here, we argue that this lemma is applicable in much more general contexts. We use it to provide a simplified and more combinatorial proof of Hastings' 1D area law...
General formalism for singly thermostated Hamiltonian dynamics.
Ramshaw, John D
2015-11-01
A general formalism is developed for constructing modified Hamiltonian dynamical systems which preserve a canonical equilibrium distribution by adding a time evolution equation for a single additional thermostat variable. When such systems are ergodic, canonical ensemble averages can be computed as dynamical time averages over a single trajectory. Systems of this type were unknown until their recent discovery by Hoover and colleagues. The present formalism should facilitate the discovery, construction, and classification of other such systems by encompassing a wide class of them within a single unified framework. This formalism includes both canonical and generalized Hamiltonian systems in a state space of arbitrary dimensionality (either even or odd) and therefore encompasses both few- and many-particle systems. Particular attention is devoted to the physical motivation and interpretation of the formalism, which largely determine its structure. An analogy to stochastic thermostats and fluctuation-dissipation theorems is briefly 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.
The Quadratic Selective Travelling Salesman Problem
DEFF Research Database (Denmark)
Thomadsen, Tommy; Stidsen, Thomas K.
2003-01-01
complication that each pair of nodes have an associated profit which can be gained only if both nodes are visited. The QSTSP is a subproblem when constructing hierarchical ring networks. We describe an integer linear programming model for the QSTSP. The QSTSP is solved by two construction heuristics...... solutions at a cost of much higher running time. All problems with up to 50 nodes are solved within one hour.......A well-known extension of the Travelling Salesman Problem (TSP) is the Selective TSP (STSP): Each node has an associated profit and instead of visiting all nodes, the most profitable set of nodes, taking into account the tour cost, is visited. The Quadratic STSP (QSTSP) adds the additional...
Compact stars with quadratic equation of state
Ngubelanga, Sifiso A; Ray, Subharthi
2015-01-01
We provide new exact solutions to the Einstein-Maxwell system of equations for matter configurations with anisotropy and charge. The spacetime is static and spherically symmetric. A quadratic equation of state is utilised for the matter distribution. By specifying a particular form for one of the gravitational potentials and the electric field intensity we obtain new exact solutions in isotropic coordinates. In our general class of models, an earlier model with a linear equation of state is regained. For particular choices of parameters we regain the masses of the stars PSR J1614-2230, 4U 1608-52, PSR J1903+0327, EXO 1745-248 and SAX J1808.4-3658. A comprehensive physical analysis for the star PSR J1903+0327 reveals that our model is reasonable.
Low-rank quadratic semidefinite programming
Yuan, Ganzhao
2013-04-01
Low rank matrix approximation is an attractive model in large scale machine learning problems, because it can not only reduce the memory and runtime complexity, but also provide a natural way to regularize parameters while preserving learning accuracy. In this paper, we address a special class of nonconvex quadratic matrix optimization problems, which require a low rank positive semidefinite solution. Despite their non-convexity, we exploit the structure of these problems to derive an efficient solver that converges to their local optima. Furthermore, we show that the proposed solution is capable of dramatically enhancing the efficiency and scalability of a variety of concrete problems, which are of significant interest to the machine learning community. These problems include the Top-k Eigenvalue problem, Distance learning and Kernel learning. Extensive experiments on UCI benchmarks have shown the effectiveness and efficiency of our proposed method. © 2012.
Directed animals, quadratic and rewriting systems
Marckert, Jean-François
2011-01-01
A directed animal is a percolation cluster in the directed site percolation model. The aim of this paper is to exhibit a strong relation between in one hand, the problem of computing the generating function $\\G$ of directed animals on the square lattice, counted according to the area and the perimeter, and on the other hand, the problem to find a solution to a system of quadratic equations involving unknown matrices. The matrices solution of this problem can be finite or infinite. We were unable to find finite solutions. We present some solid clues that some infinite explicit matrices, fix points of a rewriting like system are the natural solutions of this system of equations: some strong evidences are given that the problem of finding $\\G$ reduces then to the problem of finding an eigenvector to an explicit infinite matrix. Similar properties are shown for other combinatorial questions concerning directed animals, and for different lattices.
Lambda-Lifting in Quadratic Time
DEFF Research Database (Denmark)
Danvy, Olivier; Schultz, Ulrik Pagh
2002-01-01
Lambda-lifting is a program transformation used in compilers and in partial evaluators and that operates in cubic time. In this article, we show how to reduce this complexity to quadratic time. Lambda-lifting transforms a block-structured program into a set of recursive equations, one for each...... local function in the source program. Each equation carries extra parameters to account for the free variables of the corresponding local function and of all its callees. It is the search for these extra parameters that yields the cubic factor in the traditional formulation of lambda-lifting, which...... is not needed. We therefore simplify the search for extra parameters by treating each strongly connected component instead of each function as a unit, thereby reducing the time complexity of lambda-lifting from O(n 3 log n)toO(n2 log n), where n is the size of the program. Since a lambda-lifter can output...
A SPLITTING METHOD FOR QUADRATIC PROGRAMMING PROBLEM
Institute of Scientific and Technical Information of China (English)
魏紫銮
2001-01-01
A matrix splitting method is presented for minimizing a quadratic programming (QP)problem, and a general algorithm is designed to solve the QP problem and generates a sequence of iterative points. We prove that the sequence generated by the algorithm converges to the optimal solution and has an R-linear rate of convergence if the QP problem is strictly convex and nondegenerate, and that every accumulation point of the sequence generated by the general algorithm is a KKT point of the original problem under the hypothesis that the value of the objective function is bounded below on the constrained region, and that the sequence converges to a KKT point if the problem is nondegenerate and the constrained region is bounded.
Linear ultrasonic motor using quadrate plate transducer
Institute of Scientific and Technical Information of China (English)
Jiamei JIN; Chunsheng ZHAO
2009-01-01
A linear ultrasonic motor using a quadrate plate transducer was developed for precision positioning. This motor consists of two pairs of Pb(Zr, Ti)O3 piezo-electric ceramic elements, which are piezoelectrically excited into the second-bending mode of the motor stator's neutral surface in two orthogonal directions, on which the tops of four projections move along an elliptical trajectory, which in turn drives a contacted slider into linear motion via frictional forces. The coincident frequency of the stator is easily obtained for its coincident characteristic dimen-sion in two orthogonal directions. The performance characteristics achieved by the motor are: 1) a maximum linear speed of more than 60 mm/s; 2) a stroke of more than 150 mm; 3) a driving force of more than 5.0 N; and 4) a response time of about 2 ms.
Hamiltonian hierarchy and the Hulthen potential
Gönül, B
2000-01-01
We deal with the Hamiltonian hierarchy problem of the Hulth\\'{e}n potential within the frame of the supersymmetric quantum mechanics and find that the associated superymmetric partner potentials simulate the effect of the centrifugal barrier. Incorporating the supersymmetric solutions and using the first-order perturbation theory we obtain an expression for the energy levels of theHulth\\'{e}n potential which gives satisfactory values for the non-zero angular momentum states.
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.
Analytical Special Solutions of the Bohr Hamiltonian
Bonatsos, D; Petrellis, D; Terziev, P A; Yigitoglu, I
2005-01-01
The following special solutions of the Bohr Hamiltonian are briefly described: 1) Z(5) (approximately separable solution in five dimensions with gamma close to 30 degrees), 2) Z(4) (exactly separable gamma-rigid solution in four dimensions with gamma = 30 degrees), 3) X(3) (exactly separable gamma-rigid solution in three dimensions with gamma =0). The analytical solutions obtained using Davidson potentials in the E(5), X(5), Z(5), and Z(4) frameworks are also mentioned.
Information, disturbance and Hamiltonian quantum feedback control
Doherty, A C; Jungman, G; Doherty, Andrew C.; Jacobs, Kurt; Jungman, Gerard
2001-01-01
We consider separating the problem of designing Hamiltonian quantum feedback control algorithms into a measurement (estimation) strategy and a feedback (control) strategy, and consider optimizing desirable properties of each under the minimal constraint that the available strength of both is limited. This motivates concepts of information extraction and disturbance which are distinct from those usually considered in quantum information theory. Using these concepts we identify an information trade-off in quantum feedback control.
Some Oscillation Results for Linear Hamiltonian Systems
Nan Wang; Fanwei Meng
2012-01-01
The purpose of this paper is to develop a generalized matrix Riccati technique for the selfadjoint matrix Hamiltonian system ${U}^{\\prime }=A(t)U+B(t)V$ , ${V}^{\\prime }=C(t)U-{A}^{\\ast }(t)V$ . By using the standard integral averaging technique and positive functionals, new oscillation and interval oscillation criteria are established for the system. These criteria extend and improve some results that have been required before. An interesting example is included to illustrate the...
Obtaining breathers in nonlinear Hamiltonian lattices
Flach, S
1995-01-01
Abstract We present a numerical method for obtaining high-accuracy numerical solutions of spatially localized time-periodic excitations on a nonlinear Hamiltonian lattice. We compare these results with analytical considerations of the spatial decay. We show that nonlinear contributions have to be considered, and obtain very good agreement between the latter and the numerical results. We discuss further applications of the method and results.
Monte Carlo Hamiltonian:Inverse Potential
Institute of Scientific and Technical Information of China (English)
LUO Xiang-Qian; CHENG Xiao-Ni; Helmut KR(O)GER
2004-01-01
The Monte Carlo Hamiltonian method developed recently allows to investigate the ground state and low-lying excited states of a quantum system,using Monte Carlo(MC)algorithm with importance sampling.However,conventional MC algorithm has some difficulties when applied to inverse potentials.We propose to use effective potential and extrapolation method to solve the problem.We present examples from the hydrogen system.
Spectral analysis of tridiagonal Fibonacci Hamiltonians
Yessen, William
2011-01-01
We consider a family of discrete Jacobi operators on the one-dimensional integer lattice, with the diagonal and the off-diagonal entries given by two sequences generated by the Fibonacci substitution on two letters. We show that the spectrum is a Cantor set of zero Lebesgue measure, and discuss its fractal structure and Hausdorff dimension. We also extend some known results on the diagonal and the off-diagonal Fibonacci Hamiltonians.
Gauge symmetry enhancement in Hamiltonian formalism
Hong, S T; Lee, T H; Oh, P; Oh, Phillial
2003-01-01
We study the Hamiltonian structure of the gauge symmetry enhancement in the enlarged CP(N) model coupled with U(2) chern-Simons term, which contains a free parameter governing explicit symmetry breaking and symmetry enhancement. After giving a general discussion of the geometry of constrained phase space suitable for the symmetry enhancement, we explicitly perform the Dirac analysis of out model and compute the Dirac brackets for the symmetry enhanced and broken cases. We also discuss some related issues.
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.
Hamiltonian methods in the theory of solitons
Fadeev, Ludwig
1987-01-01
The main characteristic of this classic exposition of the inverse scattering method and its applications to soliton theory is its consistent Hamiltonian approach to the theory. The nonlinear Schrodinger equation is considered as a main example, forming the first part of the book. The second part examines such fundamental models as the sine-Gordon equation and the Heisenberg equation, the classification of integrable models and methods for constructing their solutions.
Large-scale sequential quadratic programming algorithms
Energy Technology Data Exchange (ETDEWEB)
Eldersveld, S.K.
1992-09-01
The problem addressed is the general nonlinear programming problem: finding a local minimizer for a nonlinear function subject to a mixture of nonlinear equality and inequality constraints. The methods studied are in the class of sequential quadratic programming (SQP) algorithms, which have previously proved successful for problems of moderate size. Our goal is to devise an SQP algorithm that is applicable to large-scale optimization problems, using sparse data structures and storing less curvature information but maintaining the property of superlinear convergence. The main features are: 1. The use of a quasi-Newton approximation to the reduced Hessian of the Lagrangian function. Only an estimate of the reduced Hessian matrix is required by our algorithm. The impact of not having available the full Hessian approximation is studied and alternative estimates are constructed. 2. The use of a transformation matrix Q. This allows the QP gradient to be computed easily when only the reduced Hessian approximation is maintained. 3. The use of a reduced-gradient form of the basis for the null space of the working set. This choice of basis is more practical than an orthogonal null-space basis for large-scale problems. The continuity condition for this choice is proven. 4. The use of incomplete solutions of quadratic programming subproblems. Certain iterates generated by an active-set method for the QP subproblem are used in place of the QP minimizer to define the search direction for the nonlinear problem. An implementation of the new algorithm has been obtained by modifying the code MINOS. Results and comparisons with MINOS and NPSOL are given for the new algorithm on a set of 92 test problems.
Optimal Hamiltonian Simulation by Quantum Signal Processing
Low, Guang Hao; Chuang, Isaac L.
2017-01-01
The physics of quantum mechanics is the inspiration for, and underlies, quantum computation. As such, one expects physical intuition to be highly influential in the understanding and design of many quantum algorithms, particularly simulation of physical systems. Surprisingly, this has been challenging, with current Hamiltonian simulation algorithms remaining abstract and often the result of sophisticated but unintuitive constructions. We contend that physical intuition can lead to optimal simulation methods by showing that a focus on simple single-qubit rotations elegantly furnishes an optimal algorithm for Hamiltonian simulation, a universal problem that encapsulates all the power of quantum computation. Specifically, we show that the query complexity of implementing time evolution by a d -sparse Hamiltonian H ^ for time-interval t with error ɛ is O [t d ∥H ^ ∥max+log (1 /ɛ ) /log log (1 /ɛ ) ] , which matches lower bounds in all parameters. This connection is made through general three-step "quantum signal processing" methodology, comprised of (i) transducing eigenvalues of H ^ into a single ancilla qubit, (ii) transforming these eigenvalues through an optimal-length sequence of single-qubit rotations, and (iii) projecting this ancilla with near unity success probability.
Redesign of the DFT/MRCI Hamiltonian.
Lyskov, Igor; Kleinschmidt, Martin; Marian, Christel M
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.
Reinforcement learning for port-hamiltonian systems.
Sprangers, Olivier; Babuška, Robert; Nageshrao, Subramanya P; Lopes, Gabriel A D
2015-05-01
Passivity-based control (PBC) for port-Hamiltonian systems provides an intuitive way of achieving stabilization by rendering a system passive with respect to a desired storage function. However, in most instances the control law is obtained without any performance considerations and it has to be calculated by solving a complex partial differential equation (PDE). In order to address these issues we introduce a reinforcement learning (RL) approach into the energy-balancing passivity-based control (EB-PBC) method, which is a form of PBC in which the closed-loop energy is equal to the difference between the stored and supplied energies. We propose a technique to parameterize EB-PBC that preserves the systems's PDE matching conditions, does not require the specification of a global desired Hamiltonian, includes performance criteria, and is robust. The parameters of the control law are found by using actor-critic (AC) RL, enabling the search for near-optimal control policies satisfying a desired closed-loop energy landscape. The advantage is that the solutions learned can be interpreted in terms of energy shaping and damping injection, which makes it possible to numerically assess stability using passivity theory. From the RL perspective, our proposal allows for the class of port-Hamiltonian systems to be incorporated in the AC framework, speeding up the learning thanks to the resulting parameterization of the policy. The method has been successfully applied to the pendulum swing-up problem in simulations and real-life experiments.
Dynamics of Hamiltonian Systems and Memristor Circuits
Itoh, Makoto; Chua, Leon
In this paper, we show that any n-dimensional autonomous systems can be regarded as subsystems of 2n-dimensional Hamiltonian systems. One of the two subsystems is identical to the n-dimensional autonomous system, which is called the driving system. Another subsystem, called the response system, can exhibit interesting behaviors in the neighborhood of infinity. That is, the trajectories approach infinity with complicated nonperiodic (chaotic-like) behaviors, or periodic-like behavior. In order to show the above results, we project the trajectories of the Hamiltonian systems onto n-dimensional spheres, or n-dimensional balls by using the well-known central projection transformation. Another interesting behavior is that the transient regime of the subsystems can exhibit Chua corsage knots. We next show that generic memristors can be used to realize the above Hamiltonian systems. Finally, we show that the internal state of two-element memristor circuits can have the same dynamics as n-dimensional autonomous systems.
Energy Technology Data Exchange (ETDEWEB)
Margetan, F.J.
1979-01-01
A closed expression is presented for intrinsic-coordinate (..beta.., ..gamma.., theta/sub i/) eigenfunctions of the hydrodynamic, quadrupole-vibration Hamiltonian of A. Bohr. These functions are used as an expansion basis for the treatment of more general collective Hamiltonians. Two classes of such Hamiltonians are considered. In each the potential energy term of the Bohr Hamiltonian, 1/2 C..beta../sup 2/, was replaced with a more general function of the shape coordinates, V(..beta.., ..gamma..). The potential of Gneuss and Greiner (1) is used to demonstrate the soundness of the calculational techniques, and to illustrate convergence properties of calculated energies. Potentials possessing a single minimum on 0 less than or equal to ..gamma.. less than or equal to 60/sup 0/ are considered through the study of a quadratic-potential (QP) Hamiltonian. The smooth development from spherical to asymmetrically deformed nuclear shapes is investigated by systematically varying the parameters ..beta../sub 0/ and C/sub ..gamma../. Model energies and E2 transition rates are traced during this process. The QP model is then applied to /sup 106/Pd, /sup 166/Er, /sup 182/W, /sup 122/Te, and /sup 186/ /sup 188/ /sup 190/ /sup 192/Os. Low-energy ..gamma.. vibrations appear to play a prominent role in the latter five nuclei, and the QP model offers a better accounting of experimental spectra than does the model of Davydov and Chaban (2). 74 references.
Hamiltonian formulation and exact solutions of the Bianchi type I space-time in conformal gravity
Demaret, J; Scheen, C
1999-01-01
We develop a Hamiltonian formulation of the Bianchi type I space-time in conformal gravity, i.e. the theory described by a Lagrangian that is defined by the contracted quadratic product of the Weyl tensor, in a four-dimensional space-time. We derive the explicit forms of the super-Hamiltonian and of the constraint expressing the conformal invariance of the theory and we write down the system of canonical equations. To seek out exact solutions of this system we add extra constraints on the canonical variables and we go through a global involution algorithm which eventually leads to the closure of the constraint algebra. The Painleve approach provides us with a proof of non-integrability, as a consequence of the presence of movable logarithms in the general solution of the problem. We extract all possible particular solutions that may be written in closed analytical form. This enables us to demonstrate that the global involution algorithm has brought forth the complete list of exact solutions that may be writte...
New Heuristic Rounding Approaches to the Quadratic Assignment Problem
Gharibi, Wajeb
2011-01-01
Quadratic assignment problem is one of the great challenges in combinatorial optimization. It has many applications in Operations research and Computer Science. In this paper, the author extends the most-used rounding approach to a one-parametric optimization model for the quadratic assignment problems. A near-optimum parameter is also predestinated. The numerical experiments confirm the efficiency.
Quadratic elongation: A quantitative measure of distortion in coordination polyhedra
Robinson, Kelly F.; Gibbs, G.V.; Ribbe, P.H.
1971-01-01
Quadratic elongation and the variance of bond angles are linearly correlated for distorted octahedral and tetrahedral coordination complexes, both of which show variations in bond length and bond angle. The quadratic elonga tion is dimensionless, giving a quantitative measure of polyhedral distortion which is independent of the effective size of the polyhedron.
Binary GCD like Algorithms for Some Complex Quadratic Rings
DEFF Research Database (Denmark)
Agarwal, Saurabh; Frandsen, Gudmund Skovbjerg
2004-01-01
binary gcd like algorithms for the ring of integers in and , one now has binary gcd like algorithms for all complex quadratic Euclidean domains. The running time of our algorithms is O(n 2) in each ring. While there exists an O(n 2) algorithm for computing the gcd in quadratic number rings by Erich...
Geometric quadratic stochastic operator on countable infinite set
Energy Technology Data Exchange (ETDEWEB)
Ganikhodjaev, Nasir; Hamzah, Nur Zatul Akmar [Department of Computational and Theoretical Sciences, Kulliyyah of Science, International Islamic University, Jalan Sultan Ahmad Shah, Bandar InderaMahkota, 25200 Kuantan, Pahang (Malaysia)
2015-02-03
In this paper we construct the family of Geometric quadratic stochastic operators defined on the countable sample space of nonnegative integers and investigate their trajectory behavior. Such operators can be reinterpreted in terms of of evolutionary operator of free population. We show that Geometric quadratic stochastic operators are regular transformations.
Immunizing Conic Quadratic Optimization Problems Against Implementation Errors
Ben-Tal, A.; den Hertog, D.
2011-01-01
We show that the robust counterpart of a convex quadratic constraint with ellipsoidal implementation error is equivalent to a system of conic quadratic constraints. To prove this result we first derive a sharper result for the S-lemma in case the two matrices involved can be simultaneously diagonali
A Constructive Transition from Linear to Quadratic Functions.
Movshovitz-Hadar, Nitsa
1993-01-01
Presents an approach to quadratic functions that draws upon knowledge of linear functions by looking at the product of two linear functions. Then considers the quadratic function as the sum of three monomials. Potential advantages of each approach are discussed. (Contains 17 references.) (MDH)
Approximate *-derivations and approximate quadratic *-derivations on C*-algebras
Directory of Open Access Journals (Sweden)
Park Choonkil
2011-01-01
Full Text Available Abstract In this paper, we prove the stability of *-derivations and of quadratic *-derivations on Banach *-algebras. We moreover prove the superstability of *-derivations and of quadratic *-derivations on C*-algebras. 2000 Mathematics Subject Classification: 39B52; 47B47; 46L05; 39B72.
AdS Waves as Exact Solutions to Quadratic Gravity
Gullu, Ibrahim; Sisman, Tahsin Cagri; Tekin, Bayram
2011-01-01
We give an exact solution of the quadratic gravity in D dimensions. The solution is a plane fronted wave metric with a cosmological constant. This metric solves not only the full quadratic gravity field equations but also the linearized ones which include the linearized equations of the recently found critical gravity.
Quantum theory of atoms in molecules: results for the SR-ZORA Hamiltonian.
Anderson, James S M; Ayers, Paul W
2011-11-17
The quantum theory of atoms in molecules (QTAIM) is generalized to include relativistic effects using the popular scalar-relativistic zeroth-order regular approximation (SR-ZORA). It is usually assumed that the definition of the atom as a volume bounded by a zero-flux surface of the electron density is closely linked to the form of the kinetic energy, so it is somewhat surprising that the atoms corresponding to the relativistic kinetic-energy operator in the SR-ZORA Hamiltonian are also bounded by zero-flux surfaces. The SR-ZORA Hamiltonian should be sufficient for qualitative descriptions of molecular electronic structure across the periodic table, which suggests that QTAIM-based analysis can be useful for molecules and solids containing heavy atoms.
Directory of Open Access Journals (Sweden)
Gilles Regniers
2009-11-01
Full Text Available In a system of coupled harmonic oscillators, the interaction can be represented by a real, symmetric and positive definite interaction matrix. The quantization of a Hamiltonian describing such a system has been done in the canonical case. In this paper, we take a more general approach and look at the system as a Wigner quantum system. Hereby, one does not assume the canonical commutation relations, but instead one just requires the compatibility between the Hamilton and Heisenberg equations. Solutions of this problem are related to the Lie superalgebras gl(1|n and osp(1|2n. We determine the spectrum of the considered Hamiltonian in specific representations of these Lie superalgebras and discuss the results in detail. We also make the connection with the well-known canonical case.
Visualizing the zero order basis of the spectroscopic Hamiltonian.
Barnes, George L; Kellman, Michael E
2012-01-14
Recent works have shown that a generalization of the spectroscopic effective Hamiltonian can describe spectra in surprising regions, such as isomerization barriers. In this work, we seek to explain why the effective Hamiltonian is successful where there was reason to doubt that it would work at all. All spectroscopic Hamiltonians have an underlying abstract zero-order basis (ZOB) which is the "ideal" basis for a given form and parameterization of the Hamiltonian. Without a physical model there is no way to transform this abstract basis into a coordinate representation. To this end, we present a method of obtaining the coordinate space representation of the abstract ZOB of a spectroscopic effective Hamiltonian. This method works equally well for generalized effective Hamiltonians that encompass above-barrier multiwell behavior, and standard effective Hamiltonians for the vicinity of a single potential minimum. Our approach relies on a set of converged eigenfunctions obtained from a variational calculation on a potential surface. By making a one-to-one correspondence between the energy eigenstates of the effective Hamiltonian and those of the coordinate space Hamiltonian, a physical representation of the abstract ZOB is calculated. We find that the ZOB basis naturally adjusts its complexity depending on the underlying nature of phase space, which allows spectroscopic Hamiltonians to succeed for systems sampling multiple stationary points.
Hamiltonian realization of power system dynamic models and its applications
Institute of Scientific and Technical Information of China (English)
2008-01-01
Power system is a typical energy system. Because Hamiltonian approaches are closely related to the energy of the physical system, they have been widely re-searched in recent years. The realization of the Hamiltonian structure of the nonlinear dynamic system is the basis for the application of the Hamiltonian methods. However, there have been no systematically investigations on the Ham-iltonian realization for different power system dynamic models so far. This paper researches the Hamiltonian realization in power systems dynamics. Starting from the widely used power system dynamic models, the paper reveals the intrinsic Hamiltonian structure of the nonlinear power system dynamics and also proposes approaches to formulate the power system Hamiltonian structure. Furthermore, this paper shows the application of the Hamiltonian structure of the power system dynamics to design non-smooth controller considering the nonlinear ceiling effects from the real physical limits. The general procedure to design controllers via the Hamiltonian structure is also summarized in the paper. The controller design based on the Hamiltonian structure is a completely nonlinear method and there is no lin-earization during the controller design process. Thus, the nonlinear characteristics of the dynamic system are completely kept and fully utilized.
A Sequential Quadratic Programming Algorithm Using An Incomplete Solution of the Subproblem
1993-05-01
Research Stanford University tDept. de Estadistica y Econometria Universidad Carlos III de Madrid Abstract We analyze sequential quadratic programming...xEK- NP s.t. c(x) > 0, where F : R " --+ R and c : R1 --+ Rm. Since we shall not assume second derivatives are known, computing x*, a point satisfying...algorithm We first present an outline of the algorithm. Given Ho positive definite, z0 and A0, select P-1 0 O, 0 < a < r 1,/7 < > jc-(xo)lo,, _ Ž IIAoll
A sequential quadratic programming algorithm using an incomplete solution of the subproblem
Energy Technology Data Exchange (ETDEWEB)
Murray, W. [Stanford Univ., CA (United States). Systems Optimization Lab.; Prieto, F.J. [Universidad `Carlos III` de Madrid (Spain). Dept. de Estadistica y Econometria
1993-05-01
We analyze sequential quadratic programming (SQP) methods to solve nonlinear constrained optimization problems that are more flexible in their definition than standard SQP methods. The type of flexibility introduced is motivated by the necessity to deviate from the standard approach when solving large problems. Specifically we no longer require a minimizer of the QP subproblem to be determined or particular Lagrange multiplier estimates to be used. Our main focus is on an SQP algorithm that uses a particular augmented Lagrangian merit function. New results are derived for this algorithm under weaker conditions than previously assumed; in particular, it is not assumed that the iterates lie on a compact set.
QUADRATIC ADMISSIBLE ESTIMATE OF COVARIANCE IN PSEUDO-ELLIPTICAL CONTOURED DISTRIBUTION
Institute of Scientific and Technical Information of China (English)
Hengjian CUI; Xiuhong GAO
2006-01-01
This article mainly discusses the admissibility of quadratic estimate of covariance in pseudoelliptical distribution. Under the quadratic loss function, the necessary and sufficient conditions that a quadratic estimator is an admissible estimator of covariance in the class of quadratic estimators are obtained. A complete class of the quadratic estimator class is also given.
Directory of Open Access Journals (Sweden)
Rocío Meza-Moreno
2015-01-01
Full Text Available Let p=4k+1 be a prime number and Fp the finite field with p elements. For x∈1,n, Nx will denote the set of quadratic nonresidues less than or equal to x. In this work we calculate the number of quadratic nonresidues in the shifted set N(p-1/2+a.
Bound constrained quadratic programming via piecewise
DEFF Research Database (Denmark)
Madsen, Kaj; Nielsen, Hans Bruun; Pinar, M. C.
1999-01-01
of a symmetric, positive definite matrix, and is solved by Newton iteration with line search. The paper describes the algorithm and its implementation including estimation of lambda/sub 1/ , how to get a good starting point for the iteration, and up- and downdating of Cholesky factorization. Results of extensive...... testing and comparison with other methods for constrained QP are given....
Approximate Graph Edit Distance in Quadratic Time.
Riesen, Kaspar; Ferrer, Miquel; Bunke, Horst
2015-09-14
Graph edit distance is one of the most flexible and general graph matching models available. The major drawback of graph edit distance, however, is its computational complexity that restricts its applicability to graphs of rather small size. Recently the authors of the present paper introduced a general approximation framework for the graph edit distance problem. The basic idea of this specific algorithm is to first compute an optimal assignment of independent local graph structures (including substitutions, deletions, and insertions of nodes and edges). This optimal assignment is complete and consistent with respect to the involved nodes of both graphs and can thus be used to instantly derive an admissible (yet suboptimal) solution for the original graph edit distance problem in O(n3) time. For large scale graphs or graph sets, however, the cubic time complexity may still be too high. Therefore, we propose to use suboptimal algorithms with quadratic rather than cubic time for solving the basic assignment problem. In particular, the present paper introduces five different greedy assignment algorithms in the context of graph edit distance approximation. In an experimental evaluation we show that these methods have great potential for further speeding up the computation of graph edit distance while the approximated distances remain sufficiently accurate for graph based pattern classification.
A Quadratic Closure for Compressible Turbulence
Energy Technology Data Exchange (ETDEWEB)
Futterman, J A
2008-09-16
We have investigated a one-point closure model for compressible turbulence based on third- and higher order cumulant discard for systems undergoing rapid deformation, such as might occur downstream of a shock or other discontinuity. In so doing, we find the lowest order contributions of turbulence to the mean flow, which lead to criteria for Adaptive Mesh Refinement. Rapid distortion theory (RDT) as originally applied by Herring closes the turbulence hierarchy of moment equations by discarding third order and higher cumulants. This is similar to the fourth-order cumulant discard hypothesis of Millionshchikov, except that the Millionshchikov hypothesis was taken to apply to incompressible homogeneous isotropic turbulence generally, whereas RDT is applied only to fluids undergoing a distortion that is 'rapid' in the sense that the interaction of the mean flow with the turbulence overwhelms the interaction of the turbulence with itself. It is also similar to Gaussian closure, in which both second and fourth-order cumulants are retained. Motivated by RDT, we develop a quadratic one-point closure for rapidly distorting compressible turbulence, without regard to homogeneity or isotropy, and make contact with two equation turbulence models, especially the K-{var_epsilon} and K-L models, and with linear instability growth. In the end, we arrive at criteria for Adaptive Mesh Refinement in Finite Volume simulations.
Optimal power flow using sequential quadratic programming
Nejdawi, Imad M.
1999-11-01
Optimal power flow (OPF) is an operational as well as a planning tool used by electric utilities to help them operate their network in the most economic and secure mode of operation. Various algorithms to solve the OPF problem evolved over the past three decades; linear programming (LP) techniques were among the major mathematical programming methods utilized. The linear models of the objective function and the linearization of the constraints are the main features of these techniques. The main advantages of the LP approach are simplicity and speed. Nonlinear programming techniques have been applied to OPF solution. The major drawback is the expensive solution of large sparse systems of equations. This research is concerned with the development of a new OPF solution algorithm using sequential quadratic programming (SQP). In this formulation, a small dense system the size of which is equal to the number of control variables is solved in an inner loop. The Jacobian and Hessian terms are calculated in an outer loop. The total number of outer loop iterations is comparable to those in an ordinary load flow in contrast to 20--30 iterations in other nonlinear methods. In addition, the total number of floating point operations is less than that encountered in direct methods by two orders of magnitude. We also model dispatch over a twenty four-hour time horizon in a transmission constrained power network that includes price-responsive loads where large energy customers can operate their loads in time intervals with lowest spot prices.
Designing Camera Networks by Convex Quadratic Programming
Ghanem, Bernard
2015-05-04
In this paper, we study the problem of automatic camera placement for computer graphics and computer vision applications. We extend the problem formulations of previous work by proposing a novel way to incorporate visibility constraints and camera-to-camera relationships. For example, the placement solution can be encouraged to have cameras that image the same important locations from different viewing directions, which can enable reconstruction and surveillance tasks to perform better. We show that the general camera placement problem can be formulated mathematically as a convex binary quadratic program (BQP) under linear constraints. Moreover, we propose an optimization strategy with a favorable trade-off between speed and solution quality. Our solution is almost as fast as a greedy treatment of the problem, but the quality is significantly higher, so much so that it is comparable to exact solutions that take orders of magnitude more computation time. Because it is computationally attractive, our method also allows users to explore the space of solutions for variations in input parameters. To evaluate its effectiveness, we show a range of 3D results on real-world floorplans (garage, hotel, mall, and airport).
Linear quadratic regulator for laser beam shaping
Escárate, Pedro; Agüero, Juan C.; Zúñiga, Sebastián; Castro, Mario; Garcés, Javier
2017-07-01
The performance of an adaptive optics system depends on multiple factors, including the quality of the laser beam before being projected to the mesosphere. In general, cumbersome procedures are required to optimize the laser beam in terms of amplitude and phase. However, aberrations produced by the optics of the laser beam system are still detected during the operations due to, for example, uncertainty in the utilized models. In this paper we propose the use of feedback to overcome the presence of model uncertainty and disturbances. In particular we use a Linear Quadratic Regulator (LQR) for closed loop laser beam shaping using a setup of two deformable mirrors. The proposed method is studied and simulated to provide an automatic optimization of the Amplitude of the laser beam. The performance of the LQR control algorithm is evaluated via numerical simulations using the root mean square error (RMSE). The results show an effective amplitude correction of the laser system aberrations after 20 iterations of the algorithm, a RMSE less than 0.7 was obtained, with about 140 actuators per mirror and a separation of z=3 [m] among the mirrors.
Proton radius puzzle in Hamiltonian dynamics
Glazek, Stanislaw D
2014-01-01
Relativistic lepton-proton bound-state eigenvalue equations for Hamiltonians derived from quantum field theory using second-order renormalization group procedure for effective particles, are reducible to two-body Schroedinger eigenvalue equations with the effective Coulomb potential that exhibits a tiny sensitivity to the characteristic momentum-scale of the bound system. The scale dependence is shown to be relevant to the theoretical interpretation of precisely measured lepton-proton bound-state energy levels in terms of a 4 percent difference between the proton radii in muon-proton and electron-proton bound states.
Linear representation of energy-dependent Hamiltonians
Znojil, Miloslav
2004-05-01
Quantum mechanics abounds in models with Hamiltonian operators which are energy-dependent. A linearization of the underlying Schrödinger equation with H= H( E) is proposed here via an introduction of a doublet of separate energy-independent representatives K and L of the respective right and left action of H( E). Both these new operators are non-Hermitian so that our formalism admits a natural extension to non-Hermitian initial H( E)s. Its applicability may range from pragmatic phenomenology and variational calculations (where all the subspace-projected effective operators depend on energy by construction) up to perturbation theory and quasi-exact constructions.
Riccati group invariants of linear hamiltonian systems
Garzia, M. R.; Loparo, K. A.; Martin, C. F.
1983-01-01
The action of the Riccati group on the Riccati differential equation is associated with the action of a subgroup of the symplectic group on a set of hamiltonian matrices. Within this framework various sets of canonical forms are developed for the matrix coefficients of the Riccati differential equation. The canonical forms presented are valid for arbitrary Kronecker indices, and it is shown that the Kronecker indices are invariants for this group action. These canonical forms are useful for studying problems arising in the areas of optimal decentralized control and the spectral theory of optimal control problems.
Dyson--Schwinger Approach to Hamiltonian QCD
Campagnari, Davide R; Huber, Markus Q; Vastag, Peter; Ebadati, Ehsan
2016-01-01
Dyson--Schwinger equations are an established, powerful non-perturbative tool for QCD. In the Hamiltonian formulation of a quantum field theory they can be used to perform variational calculations with non-Gaussian wave functionals. By means of the DSEs the various $n$-point functions, needed in expectation values of observables like the Hamilton operator, can be thus expressed in terms of the variational kernels of our trial ansatz. Equations of motion for these variational kernels are derived by minimizing the energy density and solved numerically.
Enumeration of Hamiltonian Cycles in 6-cube
Deza, Michel
2010-01-01
Finding the number 2H6 of directed Hamiltonian cycles in 6-cube is problem 43 in Section 7.2.1.1 of Knuth's ' The Art of Computer Programming'; various proposed estimates are surveyed below. We computed exact value: H6=14,754,666,508,334,433,250,560=6*2^4*217,199*1,085,989*5,429,923. Also the number Aut6 of those cycles up to automorphisms of 6-cube was computed as 147,365,405,634,413,085
Hamiltonian analysis of BHT massive gravity
Blagojević, M.; Cvetković, B.
2011-01-01
We study the Hamiltonian structure of the Bergshoeff-Hohm-Townsend (BHT) massive gravity with a cosmological constant. In the space of coupling constants ( Λ 0, m 2), our canonical analysis reveals the special role of the condition Λ 0/ m 2 ≠ -1. In this sector, the dimension of the physical phase space is found to be N ∗ = 4, which corresponds to two Lagrangian degree of freedom. When applied to the AdS asymptotic region, the canonical approach yields the conserved charges of the BTZ black hole, and central charges of the asymptotic symmetry algebra.
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
Statistical mechanics of Hamiltonian adaptive resolution simulations.
Español, P; Delgado-Buscalioni, R; Everaers, R; Potestio, R; Donadio, D; Kremer, K
2015-02-14
The Adaptive Resolution Scheme (AdResS) is a hybrid scheme that allows to treat a molecular system with different levels of resolution depending on the location of the molecules. The construction of a Hamiltonian based on the this idea (H-AdResS) allows one to formulate the usual tools of ensembles and statistical mechanics. We present a number of exact and approximate results that provide a statistical mechanics foundation for this simulation method. We also present simulation results that illustrate the theory.
The quantization of the Rabi Hamiltonian
Vandaele, Eva R. J.; Arvanitidis, Athanasios; Ceulemans, Arnout
2017-03-01
The Rabi Hamiltonian addresses the proverbial paradigmatic case of a two-level fermionic system coupled to a single bosonic mode. It is expressed by a system of two coupled first-order differential equations in the complex field, which may be rewritten in a canonical form under the Birkhoff transformation. The transformation gives rise to leapfrog recurrence relations, from which the eigenvalues and eigenvectors could be obtained. The interesting feature of this approach is that it generates integer quantum numbers, which rationalize the spectrum by relating the solutions to the Juddian baselines. The relationship with Braak’s integrability claim (Braak 2011 Phys. Rev. Lett. 107 100401) is discussed.
Quantum Hamiltonian Identification from Measurement Time Traces
Zhang, Jun; Sarovar, Mohan
2014-08-01
Precise identification of parameters governing quantum processes is a critical task for quantum information and communication technologies. In this Letter, we consider a setting where system evolution is determined by a parametrized Hamiltonian, and the task is to estimate these parameters from temporal records of a restricted set of system observables (time traces). Based on the notion of system realization from linear systems theory, we develop a constructive algorithm that provides estimates of the unknown parameters directly from these time traces. We illustrate the algorithm and its robustness to measurement noise by applying it to a one-dimensional spin chain model with variable couplings.
Connecting orbits for families of Tonelli Hamiltonians
Mandorino, Vito
2011-01-01
We investigate the existence of Arnold diffusion-type orbits for systems obtained by iterating in any order the time-one maps of a family of Tonelli Hamiltonians. Such systems are known as 'polysystems' or 'iterated function systems'. When specialized to families of twist maps on the cylinder, our results are similar to those obtained by Moeckel [20] and Le Calvez [15]. Our approach is based on weak KAM theory and is close to the one used by Bernard in [3] to study the case of a single Tonell...
Hamiltonian BF theory and projected Borromean Rings
Contreras, Ernesto; Leal, Lorenzo
2011-01-01
It is shown that the canonical formulation of the abelian BF theory in D = 3 allows to obtain topological invariants associated to curves and points in the plane. The method consists on finding the Hamiltonian on-shell of the theory coupled to external sources with support on curves and points in the spatial plane. We explicitly calculate a non-trivial invariant that could be seen as a "projection" of the Milnor's link invariant MU(1; 2; 3), and as such, it measures the entanglement of generalized (or projected) Borromeans Rings in the Euclidean plane.
Geometry and Hamiltonian mechanics on discrete spaces
Talasila, V.; Clemente-Gallardo, J.; van der Schaft, A. J.
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...
Nonabelian N=2 Superstrings: Hamiltonian Structure
Isaev, A P
2009-01-01
We examine the Hamiltonian structure of nonabelian N=2 superstrings 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 choices of the background.
Subsystem's dynamics under random Hamiltonian evolution
Vinayak,
2011-01-01
We study time evolution of a subsystem's density matrix under a unitary evolution, generated by a sufficiently complex, say quantum chaotic, Hamiltonian. We exactly calculate all coherences, purity and fluctuations. The reduced density matrix is described in terms of a noncentral correlated Wishart ensemble. Our description accounts for a transition from an arbitrary initial state towards a random state at large times, enabling us to determine the convergence time after which random states are reached. We identify and describe a number of other interesting features, like a series of collisions between the largest eigenvalue and the bulk, accompanied by a phase transition in its distribution function.
New approaches to generalized Hamiltonian realization of autonomous nonlinear systems
Institute of Scientific and Technical Information of China (English)
王玉振; 李春文; 程代展
2003-01-01
The Hamiltonian function method plays an important role in stability analysis and stabilization. The key point in applying the method is to express the system under consideration as the form of dissipative Hamiltonian systems, which yields the problem of generalized Hamiltonian realization. This paper deals with the generalized Hamiltonian realization of autonomous nonlinear systems. First, this paper investigates the relation between traditional Hamiltonian realizations and first integrals, proposes a new method of generalized Hamiltonian realization called the orthogonal decomposition method, and gives the dissipative realization form of passive systems. This paper has proved that an arbitrary system has an orthogonal decomposition realization and an arbitrary asymptotically stable system has a strict dissipative realization. Then this paper studies the feedback dissipative realization problem and proposes a control-switching method for the realization. Finally,this paper proposes several sufficient conditions for feedback dissipative realization.
Perturbation Theory for Parent Hamiltonians of Matrix Product States
Szehr, Oleg; Wolf, Michael M.
2015-05-01
This article investigates the stability of the ground state subspace of a canonical parent Hamiltonian of a Matrix product state against local perturbations. We prove that the spectral gap of such a Hamiltonian remains stable under weak local perturbations even in the thermodynamic limit, where the entire perturbation might not be bounded. Our discussion is based on preceding work by Yarotsky that develops a perturbation theory for relatively bounded quantum perturbations of classical Hamiltonians. We exploit a renormalization procedure, which on large scale transforms the parent Hamiltonian of a Matrix product state into a classical Hamiltonian plus some perturbation. We can thus extend Yarotsky's results to provide a perturbation theory for parent Hamiltonians of Matrix product states and recover some of the findings of the independent contributions (Cirac et al in Phys Rev B 8(11):115108, 2013) and (Michalakis and Pytel in Comm Math Phys 322(2):277-302, 2013).
On Hamiltonian realization of time-varying nonlinear systems
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
This paper Investigates Hamiltonian realization of time-varying nonlinear (TVN) systems, and proposes a number of new methods for the problem. It is shown that every smooth TVN system can be expressed as a generalized Hamiltonian system if the origin is the equilibrium of the system. If the Jacooian matrix of a TVN system is nonsingu-lar, the system has a generalized Hamiltonian realization whose structural matrix and Hamiltonian function are given explicitly. For the case that the Jacobian matrix is singular, this paper provides a constructive decomposition method, and then proves that a TVN system has a generalized Hamiltonian realization if its Jacobian matrix has a nonsingular main diagonal block. Furthermore, some sufficient (necessary and sufficient) conditions for dissipative Hamiltonian realization of TVN systems are also presented in this paper.
Equivalence of two sets of deformed Calogero-Moser Hamiltonians
Gorbe, T F
2015-01-01
The equivalence of two complete sets of Poisson commuting Hamiltonians of the (super)integrable rational BC(n) Ruijsenaars-Schneider-van Diejen system is established. Specifically, the commuting Hamiltonians constructed by van Diejen are shown to be linear combinations of the Hamiltonians generated by the characteristic polynomial of the Lax matrix obtained recently by Pusztai, and the explicit formula of this invertible linear transformation is found.
Hamiltonian and non-Hamiltonian perturbation theory for nearly periodic motion
Larsson, Jonas
1986-02-01
Kruskal's asymptotic theory of nearly period motion [M. Kruskal, J. Math. Phys. 4, 806 (1962)] (with applications to nonlinear oscillators, guiding center motion, etc.) is generalized and modified. A new more natural recursive formula, with considerable advantages in applications, determining the averaging transformations and the drift equations is derived. Also almost quasiperiodic motion is considered. For a Hamiltonian system, a manifestly Hamiltonian extension of Kruskal's theory is given by means of the phase-space Lagrangian formulation of Hamiltonian mechanics. By performing an averaging transformation on the phase-space Lagrangian for the system (L → L¯) and adding a total derivative dS/dτ, a nonoscillatory Lagrangian Λ=L¯+dS/dτ is obtained. The drift equations and the adiabatic invariant are now obtained from Λ. By truncating Λ to some finite order in the small parameter ɛ, manifestly Hamiltonian approximating systems are obtained. The utility of the method for treating the guiding-center motion is demonstrated in a separate paper.
Hamiltonian Cycles in Regular 2-Connected Claw-Free Graphs
Institute of Scientific and Technical Information of China (English)
李明楚
2003-01-01
A known result by Jackson Bill is that every 2-connected k-regular graph on at most 3k vertices is Hamiltonian. In this paper,it is proved that every 2-connected k-regular claw-free graph on at most 5k(k≥10)vertices is Hamiltonian. Moreover, the bound 5k is best possible. A counterexample of a 2-connected k-regular claw-free non-Hamiltonian graph on 5k+1 vertices is given, and it is conjectured that every 3-connected k-regular claw-free graph on at most 12k-7 vertices is Hamiltonian.
Hamiltonian description of closed configurations of the vacuum magnetic field
Energy Technology Data Exchange (ETDEWEB)
Skovoroda, A. A., E-mail: skovoroda-aa@nrcki.ru [National Research Centre Kurchatov Institute (Russian Federation)
2015-05-15
Methods of obtaining and using the Hamiltonians of closed vacuum magnetic configurations of fusion research systems are reviewed. Various approaches to calculate the flux functions determining the Hamiltonian are discussed. It is shown that the Hamiltonian description allows one not only to reproduce all traditional results, but also to study the behavior of magnetic field lines by using the theory of dynamic systems. The potentialities of the Hamiltonian formalism and its close relation to traditional methods are demonstrated using a large number of classical examples adopted from the fundamental works by A.I. Morozov, L.S. Solov’ev, and V.D. Shafranov.
Covariant hamiltonian spin dynamics in curved space–time
Energy Technology Data Exchange (ETDEWEB)
D' Ambrosi, G., E-mail: gdambros@nikhef.nl [Nikhef, Science Park 105, Amsterdam (Netherlands); Satish Kumar, S., E-mail: satish@lorentz.leidenuniv.nl [Lorentz Institute, Leiden University, Niels Bohrweg 2, Leiden (Netherlands); Holten, J.W. van, E-mail: t32@nikhef.nl [Nikhef, Science Park 105, Amsterdam (Netherlands); Lorentz Institute, Leiden University, Niels Bohrweg 2, Leiden (Netherlands)
2015-04-09
The dynamics of spinning particles in curved space–time is discussed, emphasizing the hamiltonian formulation. Different choices of hamiltonians allow for the description of different gravitating systems. We give full results for the simplest case with minimal hamiltonian, constructing constants of motion including spin. The analysis is illustrated by the example of motion in Schwarzschild space–time. We also discuss a non-minimal extension of the hamiltonian giving rise to a gravitational equivalent of the Stern–Gerlach force. We show that this extension respects a large class of known constants of motion for the minimal case.
Covariant hamiltonian spin dynamics in curved space-time
d'Ambrosi, G; van Holten, J W
2015-01-01
The dynamics of spinning particles in curved space-time is discussed, emphasizing the hamiltonian formulation. Different choices of hamiltonians allow for the description of different gravitating systems. We give full results for the simplest case with minimal hamiltonian, constructing constants of motion including spin. The analysis is illustrated by the example of motion in Schwarzschild space-time. We also discuss a non-minimal extension of the hamiltonian giving rise to a gravitational equivalent of the Stern-Gerlach force. We show that this extension respects a large class of known constants of motion for the minimal case.
How is Lorentz invariance encoded in the Hamiltonian?
Kajuri, Nirmalya
2016-07-01
One of the disadvantages of the Hamiltonian formulation is that Lorentz invariance is not manifest in the former. Given a Hamiltonian, there is no simple way to check whether it is relativistic or not. One would either have to solve for the equations of motion or calculate the Poisson brackets of the Noether charges to perform such a check. In this paper we show that, for a class of Hamiltonians, it is possible to check Lorentz invariance directly from the Hamiltonian. Our work is particularly useful for theories where the other methods may not be readily available.
How is Lorentz Invariance encoded in the Hamiltonian?
Kajuri, Nirmalya
2016-01-01
One of the disadvantages of the Hamiltonian formulation is that Lorentz invariance is not manifest in the former. Given a Hamiltonian, there is no simple way to check whether it is relativistic or not. One would either have to solve for the equations of motion or calculate the Poisson Brackets of the Noether charges to perform such a check. In this paper we show that, for a class of Hamiltonians, it is possible to check Lorentz invariance directly from the Hamiltonian. Our work is particularly useful for theories where the other methods may not be readily available.
A New Scheme of Integrability for (bi)Hamiltonian PDE
De Sole, Alberto; Kac, Victor G.; Valeri, Daniele
2016-10-01
We develop a new method for constructing integrable Hamiltonian hierarchies of Lax type equations, which combines the fractional powers technique of Gelfand and Dickey, and the classical Hamiltonian reduction technique of Drinfeld and Sokolov. The method is based on the notion of an Adler type matrix pseudodifferential operator and the notion of a generalized quasideterminant. We also introduce the notion of a dispersionless Adler type series, which is applied to the study of dispersionless Hamiltonian equations. Non-commutative Hamiltonian equations are discussed in this framework as well.
Position-dependent mass quantum Hamiltonians: general approach and duality
Rego-Monteiro, M. A.; Rodrigues, Ligia M. C. S.; Curado, E. M. F.
2016-03-01
We analyze a general family of position-dependent mass (PDM) quantum Hamiltonians which are not self-adjoint and include, as particular cases, some Hamiltonians obtained in phenomenological approaches to condensed matter physics. We build a general family of self-adjoint Hamiltonians which are quantum mechanically equivalent to the non-self-adjoint proposed ones. Inspired by the probability density of the problem, we construct an ansatz for the solutions of the family of self-adjoint Hamiltonians. We use this ansatz to map the solutions of the time independent Schrödinger equations generated by the non-self-adjoint Hamiltonians into the Hilbert space of the solutions of the respective dual self-adjoint Hamiltonians. This mapping depends on both the PDM and on a function of position satisfying a condition that assures the existence of a consistent continuity equation. We identify the non-self-adjoint Hamiltonians here studied with a very general family of Hamiltonians proposed in a seminal article of Harrison (1961 Phys. Rev. 123 85) to describe varying band structures in different types of metals. Therefore, we have self-adjoint Hamiltonians that correspond to the non-self-adjoint ones found in Harrison’s article.
Hamiltonian realization of power system dynamic models and its applications
Institute of Scientific and Technical Information of China (English)
MA Jin; MEI ShengWei
2008-01-01
Power system is a typical energy system. Because Hamiltonian approaches are closely related to the energy of the physical system, they have been widely re-searched in recent years. The realization of the Hamiltonian structure of the nonlinear dynamic system is the basis for the application of the Hamiltonian methods. However, there have been no systematically investigations on the Ham-iltonian realization for different power system dynamic models so far. This paper researches the Hamiltonian realization in power systems dynamics. Starting from the widely used power system dynamic models, the paper reveals the intrinsic Hamiltonian structure of the nonlinear power system dynamics and also proposes approaches to formulate the power system Hamiltonian structure. Furthermore, this paper shows the application of the Hemiltonian structure of the power system dynamics to design non-smooth controller considering the nonlinear ceiling effects from the real physical limits. The general procedure to design controllers via the Hamiltonian structure is also summarized in the paper. The controller design based on the Hamiltonian structure is a completely nonlinear method and there is no lin-earization during the controller design process. Thus, the nonlinear characteristics of the dynamic system are completely kept and fully utilized.
Hamiltonian theory of nonlinear waves in planetary rings
Stewart, G. R.
1987-01-01
The derivation of a Hamiltonian field theory for nonlinear density waves in Saturn's rings is discussed. Starting with a Hamiltonian for a discrete system of gravitating streamlines, an averaged Hamiltonian is obtained by successive applications of Lie transforms. The transformation may be carried out to any desired order in q, where q is the nonlinearity parameter defined in the work of Shu, et al (1985) and Borderies et al (1985). Subsequent application of the Wentzel-Kramer-Brillouin Method approximation yields an asymptotic field Hamiltonian. Both the nonlinear dispersion relation and the wave action transport equation are easily derived from the corresponding Lagrangian by the standard variational principle.
Non-isospectral Hamiltonians, intertwining operators and hidden hermiticity
Bagarello, Fabio
2011-01-01
We have recently proposed a strategy to produce, starting from a given hamiltonian $h_1$ and a certain operator $x$ for which $[h_1,xx^\\dagger]=0$ and $x^\\dagger x$ is invertible, a second hamiltonian $h_2$ with the same eigenvalues as $h_1$ and whose eigenvectors are related to those of $h_1$ by $x^\\dagger$. Here we extend this procedure to build up a second hamiltonian, whose eigenvalues are different from those of $h_1$, and whose eigenvectors are still related as before. This new procedure is also extended to crypto-hermitian hamiltonians.
The Cyclicity of the Period Annulus Around the Quadratic Isochronous Center
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The number of the limit cycles bifurcating in small quadratic perturbations of quadratic systems with an isochronous center is studied, it turns out that the cyclicity of the period annulus around one kind of quadratic isochronous center is two.
Solutions of the Bohr Hamiltonian, a compendium
Fortunato, L.
2005-10-01
The Bohr Hamiltonian, also called collective Hamiltonian, is one of the cornerstones of nuclear physics and a wealth of solutions (analytic or approximated) of the associated eigenvalue equation have been proposed over more than half a century (confining ourselves to the quadrupole degree of freedom). Each particular solution is associated with a peculiar form for the V(β,γ) potential. The large number and the different details of the mathematical derivation of these solutions, as well as their increased and renewed importance for nuclear structure and spectroscopy, demand a thorough discussion. It is the aim of the present monograph to present in detail all the known solutions in γ-unstable and γ-stable cases, in a taxonomic and didactical way. In pursuing this task we especially stressed the mathematical side leaving the discussion of the physics to already published comprehensive material. The paper contains also a new approximate solution for the linear potential, and a new solution for prolate and oblate soft axial rotors, as well as some new formulae and comments. The quasi-dynamical SO(2) symmetry is proposed in connection with the labeling of bands in triaxial nuclei.
Historical Hamiltonian Dynamics: symplectic and covariant
Lachieze-Rey, M
2016-01-01
This paper presents a "historical" formalism for dynamical systems, in its Hamiltonian version (Lagrangian version was presented in a previous paper). It is universal, in the sense that it applies equally well to time dynamics and to field theories on space-time. It is based on the notion of (Hamiltonian) histories, which are sections of the (extended) phase space bundle. It is developed in the space of sections, in contradistinction with the usual formalism which works in the bundle manifold. In field theories, the formalism remains covariant and does not require a spitting of space-time. It considers space-time exactly in the same manner than time in usual dynamics, both being particular cases of the evolution domain. It applies without modification when the histories (the fields) are forms rather than scalar functions, like in electromagnetism or in tetrad general relativity. We develop a differential calculus in the infinite dimensional space of histories. It admits a (generalized) symplectic form which d...
Dirac Hamiltonian with superstrong Coulomb field
Voronov, B L; Tyutin, I V
2006-01-01
We consider the quantum-mechanical problem of a relativistic Dirac particle moving in the Coulomb field of a point charge $Ze$. In the literature, it is often declared that a quantum-mechanical description of such a system does not exist for charge values exceeding the so-called critical charge with Z=137 based on the fact that the standard expression for energy eigenvalues yields complex values at overcritical charges. We show that from the mathematical standpoint, there is no problem in defining a self-adjoint Hamiltonian for any value of charge. What is more, the transition through the critical charge does not lead to any qualitative changes in the mathematical description of the system. A specific feature of overcritical charges is the nonuniqueness of the self-adjoint Hamiltonian, but this nonuniqueness is also characteristic for charge values less than the critical one (and larger than the subcritical charge with Z=118). We present the spectra and (generalized) eigenfunctions for all self-adjoint Hamilt...
A Hamiltonian Five-Field Gyrofluid Model
Keramidas Charidakos, Ioannis; Waelbroeck, Francois; Morrison, Philip
2015-11-01
Reduced fluid models constitute versatile tools for the study of multi-scale phenomena. Examples include magnetic islands, edge localized modes, resonant magnetic perturbations, and fishbone and Alfven modes. Gyrofluid models improve over Braginskii-type models by accounting for the nonlocal response due to particle orbits. A desirable property for all models is that they not only have a conserved energy, but also that they be Hamiltonian in the ideal limit. Here, 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 electron and ion densities, the parallel component of ion and electron velocities and ion temperature. Quasineutrality and Ampere's law determine respectively the electrostatic potential and magnetic flux. The Casimir invariants are presented, and shown to be associated to 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. This work was funded by U.S. DOE Contract No. DE-FG02-04ER-54742.
Combinatorial quantization of the Hamiltonian Chern-Simons theory, 2
Alekseev, A Yu; Schomerus, V; Grosse, H; Schomerus, V
1994-01-01
This paper further develops the combinatorial approach to quantization of the Hamiltonian Chern Simons theory advertised in \\cite{AGS}. 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 mathe- matically 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 \\omega (``integration''). We prove that this data does not depend on the particular choices which have been made in the construction. Following ideas of Fock and Rosly \\cite{FoRo}, 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 Verl...
A Finite Continuation Algorithm for Bound Constrained Quadratic Programming
DEFF Research Database (Denmark)
Madsen, Kaj; Nielsen, Hans Bruun; Pinar, Mustafa C.
1999-01-01
The dual of the strictly convex quadratic programming problem with unit bounds is posed as a linear $\\ell_1$ minimization problem with quadratic terms. A smooth approximation to the linear $\\ell_1$ function is used to obtain a parametric family of piecewise-quadratic approximation problems. The u....... The unique path generated by the minimizers of these problems yields the solution to the original problem for finite values of the approximation parameter. Thus, a finite continuation algorithm is designed. Results of extensive computational experiments are reported....
Capillary wave Hamiltonian for the Landau-Ginzburg-Wilson density functional.
Chacón, Enrique; Tarazona, Pedro
2016-06-22
We study the link between the density functional (DF) formalism and the capillary wave theory (CWT) for liquid surfaces, focused on the Landau-Ginzburg-Wilson (LGW) model, or square gradient DF expansion, with a symmetric double parabola free energy, which has been extensively used in theoretical studies of this problem. We show the equivalence between the non-local DF results of Parry and coworkers and the direct evaluation of the mean square fluctuations of the intrinsic surface, as is done in the intrinsic sampling method for computer simulations. The definition of effective wave-vector dependent surface tensions is reviewed and we obtain new proposals for the LGW model. The surface weight proposed by Blokhuis and the surface mode analysis proposed by Stecki provide consistent and optimal effective definitions for the extended CWT Hamiltonian associated to the DF model. A non-local, or coarse-grained, definition of the intrinsic surface provides the missing element to get the mesoscopic surface Hamiltonian from the molecular DF description, as had been proposed a long time ago by Dietrich and coworkers.
Computing the real-time Green's Functions of large Hamiltonian matrices
Iitaka, T
1996-01-01
A numerical method is developed for calculating the real time Green's functions of very large sparse Hamiltonian matrices, which exploits the numerical solution of the inhomogeneous time-dependent Schroedinger equation. The method has a clear-cut structure reflecting the most naive definition of the Green's functions, and is very suitable to parallel and vector supercomputers. The effectiveness of the method is illustrated by applying it to simple lattice models. An application of this method to condensed matter physics will be found in H. Tanaka, Phys. PRB 57, 2168 (1998).
Combinatorics on Words in Symbolic Dynamics: The Quadratic Map
Institute of Scientific and Technical Information of China (English)
Wan Ji DAI; Kebo L(U); Jun WANG
2008-01-01
This paper is contributed to the combinatorial properties of the MSS sequences, which are the periodic kneading words of quadratic maps denned on a interval. An explicit expression of adjacency relations on MSS sequences of given lengths is established.
Modulational stability and dark solitons in periodic quadratic nonlinear media
DEFF Research Database (Denmark)
Corney, Joel Frederick; Bang, Ole
2000-01-01
We show that stable dark solitons exist in quadratic nonlinear media with periodic linear and nonlinear susceptibilities. We investigate the modulational stability of plane waves in such systems, a necessary condition for stable dark solitons....
Reconsideration on Homogeneous Quadratic Riemann Boundary Value Problem
Institute of Scientific and Technical Information of China (English)
Lu Jian-ke
2004-01-01
The homogeneous quadratic Riemann boundary value problem (1) with Hǒlder continuous coefficients for the normal case was considered by the author in 1997. But the solutions obtained there are incomplete. Here its general method of solution is obtained.
A Trust-region-based Sequential Quadratic Programming Algorithm
DEFF Research Database (Denmark)
Henriksen, Lars Christian; Poulsen, Niels Kjølstad
This technical note documents the trust-region-based sequential quadratic programming algorithm used in other works by the authors. The algorithm seeks to minimize a convex nonlinear cost function subject to linear inequalty constraints and nonlinear equality constraints....
Geometric structure of pseudo-plane quadratic flows
Sun, Che
2017-03-01
Quadratic flows have the unique property of uniform strain and are commonly used in turbulence modeling and hydrodynamic analysis. While previous applications focused on two-dimensional homogeneous fluid, this study examines the geometric structure of three-dimensional quadratic flows in stratified fluid by solving a steady-state pseudo-plane flow model. The complete set of exact solutions reveals that steady quadratic flows have an invariant conic type in the non-rotating frame and a non-rotatory vertical structure in the rotating frame. Three baroclinic solutions with vertically non-aligned formulation disprove an earlier conjecture. All elliptic and hyperbolic solutions, except for the inertial ones, exhibit vertical concentricity. The rich geometry of quadratic flows stands in contrast to the depleted geometry of high-degree polynomial flows. A paradox in the steady solutions of shallow-water reduced-gravity models is also explained.
Finite dimensional semigroup quadratic algebras with minimal number of relations
Iyudu, Natalia
2011-01-01
A quadratic semigroup algebra is an algebra over a field given by the generators $x_1,...,x_n$ and a finite set of quadratic relations each of which either has the shape $x_jx_k=0$ or the shape $x_jx_k=x_lx_m$. We prove that a quadratic semigroup algebra given by $n$ generators and $d\\leq \\frac{n^2+n}{4}$ relations is always infinite dimensional. This strengthens the Golod--Shafarevich estimate for the above class of algebras. Our main result however is that for every $n$, there is a finite dimensional quadratic semigroup algebra with $n$ generators and $\\delta_n$ generators, where $\\delta_n$ is the first integer greater than $\\frac{n^2+n}{4}$. This shows that the above Golod-Shafarevich type estimate for semigroup algebras is sharp.