Solving a Hamiltonian Path Problem with a bacterial computer
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
Shakeri, Nadim; Jalili, Saeed; Ahmadi, Vahid; Rasoulzadeh Zali, Aref; Goliaei, Sama
2015-01-01
The problem of finding the Hamiltonian path in a graph, or deciding whether a graph has a Hamiltonian path or not, is an NP-complete problem. No exact solution has been found yet, to solve this problem using polynomial amount of time and space. In this paper, we propose a two dimensional (2-D) optical architecture based on optical electronic devices such as micro ring resonators, optical circulators and MEMS based mirror (MEMS-M) to solve the Hamiltonian Path Problem, for undirected graphs in linear time. It uses a heuristic algorithm and employs n+1 different wavelengths of a light ray, to check whether a Hamiltonian path exists or not on a graph with n vertices. Then if a Hamiltonian path exists, it reports the path. The device complexity of the proposed architecture is O(n2).
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.
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.
Chromatic roots and hamiltonian paths
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...
On the Reaction Path Hamiltonian
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.
Hamiltonian formalism and path entropy maximization
Davis, Sergio; González, Diego
2015-10-01
Maximization of the path information entropy is a clear prescription for constructing models in non-equilibrium statistical mechanics. Here it is shown that, following this prescription under the assumption of arbitrary instantaneous constraints on position and velocity, a Lagrangian emerges which determines the most probable trajectory. Deviations from the probability maximum can be consistently described as slices in time by a Hamiltonian, according to a nonlinear Langevin equation and its associated Fokker-Planck equation. The connections unveiled between the maximization of path entropy and the Langevin/Fokker-Planck equations imply that missing information about the phase space coordinate never decreases in time, a purely information-theoretical version of the second law of thermodynamics. All of these results are independent of any physical assumptions, and thus valid for any generalized coordinate as a function of time, or any other parameter. This reinforces the view that the second law is a fundamental property of plausible inference.
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.
Baras, John
2010-01-01
The algebraic path problem is a generalization of the shortest path problem in graphs. Various instances of this abstract problem have appeared in the literature, and similar solutions have been independently discovered and rediscovered. The repeated appearance of a problem is evidence of its relevance. This book aims to help current and future researchers add this powerful tool to their arsenal, so that they can easily identify and use it in their own work. Path problems in networks can be conceptually divided into two parts: A distillation of the extensive theory behind the algebraic path pr
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.
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} \
Barth, A. M.; Vagov, A.; Axt, V. M.
2016-09-01
We present a numerical path-integral iteration scheme for the low-dimensional reduced density matrix of a time-dependent quantum dissipative system. Our approach simultaneously accounts for the combined action of a microscopically modeled pure-dephasing-type coupling to a continuum of harmonic oscillators representing, e.g., phonons, and further environmental interactions inducing non-Hamiltonian dynamics in the inner system represented, e.g., by Lindblad-type dissipation or relaxation. Our formulation of the path-integral method allows for a numerically exact treatment of the coupling to the oscillator modes and moreover is general enough to provide a natural way to include Markovian processes that are sufficiently described by rate equations. We apply this new formalism to a model of a single semiconductor quantum dot which includes the coupling to longitudinal acoustic phonons for two cases: (a) external laser excitation taking into account a phenomenological radiative decay of the excited dot state and (b) a coupling of the quantum dot to a single mode of an optical cavity taking into account cavity photon losses.
Covariant Hamiltonian for the electromagnetic two-body problem
De Luca, Jayme
2005-09-01
We give a Hamiltonian formalism for the delay equations of motion of the electromagnetic two-body problem with arbitrary masses and with either repulsive or attractive interaction. This dynamical system based on action-at-a-distance electrodynamics appeared 100 years ago and it was popularized in the 1940s by the Wheeler and Feynman program to quantize it as a means to overcome the divergencies of perturbative QED. Our finite-dimensional implicit Hamiltonian is closed and involves no series expansions. As an application, the Hamiltonian formalism is used to construct a semiclassical canonical quantization based on the numerical trajectories of the attractive problem.
Formal language constrained path problems
Barrett, C.; Jacob, R.; Marathe, M.
1997-07-08
In many path finding problems arising in practice, certain patterns of edge/vertex labels in the labeled graph being traversed are allowed/preferred, while others are disallowed. Motivated by such applications as intermodal transportation planning, the authors investigate the complexity of finding feasible paths in a labeled network, where the mode choice for each traveler is specified by a formal language. The main contributions of this paper include the following: (1) the authors show that the problem of finding a shortest path between a source and destination for a traveler whose mode choice is specified as a context free language is solvable efficiently in polynomial time, when the mode choice is specified as a regular language they provide algorithms with improved space and time bounds; (2) in contrast, they show that the problem of finding simple paths between a source and a given destination is NP-hard, even when restricted to very simple regular expressions and/or very simple graphs; (3) for the class of treewidth bounded graphs, they show that (i) the problem of finding a regular language constrained simple path between source and a destination is solvable in polynomial time and (ii) the extension to finding context free language constrained simple paths is NP-complete. Several extensions of these results are presented in the context of finding shortest paths with additional constraints. These results significantly extend the results in [MW95]. As a corollary of the results, they obtain a polynomial time algorithm for the BEST k-SIMILAR PATH problem studied in [SJB97]. The previous best algorithm was given by [SJB97] and takes exponential time in the worst case.
2016-07-22
techniques and the use of sphere packing results in analyzing the performance of the two approximation algorithms may also find other applications in...problem in 2-D networks. We then develop two polynomial-time approximation algorithms that offer and approximation ratios for general directed hypergraphs...eavesdropperswitharbitraryunknownloca- tions (the so-called1.5-Dnetworks).Weproposea linear-complexity algorithm based on nested backward induction that obtains the op- timal solution
黄海燕; 姚秀美; 朱海燕; 陈亚江
2016-01-01
Based on the Hamilton principle,a numerical algorithm associated with Lagrange multiplier method for the classical motion path problem is proposed. Different from traditional variational method,the present algorithm transforms the classical motion path problem into the conditional extremum problem with respect to the motion equation. By utilizing this algorithm,numerical solutions to motion path problems in one-dimensional gravitation potential and one-dimensional elastic potential are obtained and compared with the corresponding analytical results,respectively. Such two examples can be used as practical and interesting teaching cases for the relevant curriculums,e.g. Mechanics in college physics,Hamilton principle in theoretical mechanics and numerical calculation in computational mathematics. These examples are helpful for students to understand the Hamilton principle more deeply,and improve the ability of applying the knowledge in the fields of physics,mathematics, and computer science.%基于哈密顿原理，提出经典运动路径问题的拉格朗日乘数数值算法。与传统的变分方法不同，该算法将经典运动路径问题改写为关于路径方程的条件极值问题。利用该算法得到了一维重力势中的运动路径和一维弹性势中的运动路径的数值解，并与各自的解析解作了比较分析。这2个例子可以作为大学物理力学、理论力学哈密顿原理以及计算数学数值计算等相关课程内容实用教学案例，其有助于学生更深刻地理解哈密顿原理，提高综合应用物理、数学、计算机科学等知识的能力。
Kepler Problem in Hamiltonian Formulation Discussed from Topological Viewpoint
XU Gong-Ou; XU Ming-Jie; YANG Ya-Tian
2005-01-01
@@ The Kepler problem in Hamiltonian formulation is discussed from a topological viewpoint. Topological properties for a set of cases designated with conserved quantities l, e and E(l, e) (0 ≤ e ＜ 1) are expressed with actionangle variables. The involved canonical transformations are all carried out with classical Poisson brackets. Thus it is possible to extend such a formulation to corresponding quantum-mechanical study under quasi-classical conditions.
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.
A weak Hamiltonian finite element method for optimal control problems
Hodges, Dewey H.; Bless, Robert R.
1990-01-01
A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.
Weak Hamiltonian finite element method for optimal control problems
Hodges, Dewey H.; Bless, Robert R.
1991-01-01
A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.
LP-Based Approximation Algorithms for Traveling Salesman Path Problems
An, Hyung-Chan
2011-01-01
We present a (5/3 - epsilon)-approximation algorithm for some constant epsilon>0 for the traveling salesman path problem under the unit-weight graphical metric, and prove an upper bound on the integrality gap of the path-variant Held-Karp relaxation both under this metric and the general metric. Given a complete graph with the metric cost and two designated endpoints in the graph, the traveling salesman path problem is to find a minimum Hamiltonian path between these two endpoints. The best previously known performance guarantee for this problem was 5/3 and was due to Hoogeveen. We give the first constant upper bound on the integrality gap of the path-variant Held-Karp relaxation, showing it to be at most 5/3 by providing a new analysis of Hoogeveen's algorithm. This analysis exhibits a well-characterized critical case, and we show that the recent result of Oveis Gharan, Saberi and Singh on the traveling salesman circuit problem under the unit-weight graphical metric can be modified for the path case to compl...
A phenomenological Hamiltonian for the Lotka-Volterra problem
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.
THE HAMILTONIAN EQUATIONS IN SOME MATHEMATICS AND PHYSICS PROBLEMS
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.
Rudowicz Czesław
2015-07-01
Full Text Available The interface between optical spectroscopy, electron magnetic resonance (EMR, and magnetism of transition ions forms the intricate web of interrelated notions. Major notions are the physical Hamiltonians, which include the crystal field (CF (or equivalently ligand field (LF Hamiltonians, and the effective spin Hamiltonians (SH, which include the zero-field splitting (ZFS Hamiltonians as well as to a certain extent also the notion of magnetic anisotropy (MA. Survey of recent literature has revealed that this interface, denoted CF (LF ↔ SH (ZFS, has become dangerously entangled over the years. The same notion is referred to by three names that are not synonymous: CF (LF, SH (ZFS, and MA. In view of the strong need for systematization of nomenclature aimed at bringing order to the multitude of different Hamiltonians and the associated quantities, we have embarked on this systematization. In this article, we do an overview of our efforts aimed at providing a deeper understanding of the major intricacies occurring at the CF (LF ↔ SH (ZFS interface with the focus on the EMR-related problems for transition ions.
A Simple Polynomial Algorithm for the Longest Path Problem on Cocomparability Graphs
Mertzios, George B
2010-01-01
Given a graph $G$, the longest path problem asks to compute a simple path of $G$ with the largest number of vertices. This problem is the most natural optimization version of the well known and well studied Hamiltonian path problem, and thus it is NP-hard on general graphs. However, in contrast to the Hamiltonian path problem, there are only few restricted graph families such as trees and some small graph classes where polynomial algorithms for the longest path problem have been found. Recently it has been shown that this problem can be solved in polynomial time on interval graphs by applying dynamic programming to a characterizing ordering of the vertices of the given graph \\cite{longest-int-algo}, thus answering an open question. In the present paper, we provide the first polynomial algorithm for the longest path problem on a much greater class, namely on cocomparability graphs. Our algorithm uses a similar - but essentially simpler - dynamic programming approach, which is applied to a Lexicographic Depth F...
Ramezanpour, A.
2016-06-01
We study the inverse problem of constructing an appropriate Hamiltonian from a physically reasonable set of orthogonal wave functions for a quantum spin system. Usually, we are given a local Hamiltonian and our goal is to characterize the relevant wave functions and energies (the spectrum) of the system. Here, we take the opposite approach; starting from a reasonable collection of orthogonal wave functions, we try to characterize the associated parent Hamiltonians, to see how the wave functions and the energy values affect the structure of the parent Hamiltonian. Specifically, we obtain (quasi) local Hamiltonians by a complete set of (multilayer) product states and a local mapping of the energy values to the wave functions. On the other hand, a complete set of tree wave functions (having a tree structure) results to nonlocal Hamiltonians and operators which flip simultaneously all the spins in a single branch of the tree graph. We observe that even for a given set of basis states, the energy spectrum can significantly change the nature of interactions in the Hamiltonian. These effects can be exploited in a quantum engineering problem optimizing an objective functional of the Hamiltonian.
Topological methods in the instability problem of Hamiltonian systems
Gidea, M
2005-01-01
We use topological methods to investigate some recently proposed mechanisms of instability (Arnol'd diffusion) in Hamiltonian systems. In these mechanisms, chains of heteroclinic connections between whiskered tori are constructed, based on the existence of a normally hyperbolic manifold $\\Lambda$, so that: (a) the manifold $\\Lambda$ is covered rather densely by transitive tori (possibly of different topology), (b) the manifolds $W^\\st_\\Lambda$, $W^\\un_\\Lambda$ intersect transversally, (c) the systems satisfies some explicit non-degeneracy assumptions, which hold generically. In this paper we use the method of correctly aligned windows to show that, under the assumptions (a), (b) (c), there are orbits that move a significant amount. As a matter of fact, the method presented here does not require that the tori are exactly invariant, only that they are approximately invariant. Hence, compared with the previous papers, we do not need to use KAM theory. This lowers the assumptions on differentiability. Also, the m...
吴颖; 罗亚军; 杨晓雪
2003-01-01
We present a novel formalism for energy eigenvalue problems when the corresponding Hamiltonians can be expressed as a function of an angular momentum. The problems are turned into finding operator polynomials by solving a c-number differential equation. Simple and efficient computer-aided analytical and numerical methods may be developed based on the formalism.
High-order Path Integral Monte Carlo methods for solving quantum dot problems
Chin, Siu A
2014-01-01
The conventional second-order Path Integral Monte Carlo method is plagued with the sign problem in solving many-fermion systems. This is due to the large number of anti-symmetric free fermion propagators that are needed to extract the ground state wave function at large imaginary time. In this work, we show that optimized fourth-order Path Integral Monte Carlo methods, which use no more than 5 free-fermion propagators, can yield accurate quantum dot energies for up to 20 polarized electrons with the use of the Hamiltonian energy estimator.
Hamiltonian Systems and Darboux Transformation Associated with a 3 × 3 Matrix Spectral Problem
无
2007-01-01
Starting from a 3 × 3 matrix spectral problem, we derive a hierarchy of nonlinear equations. It is shown that the hierarchy possesses bi-Hamiltonian structure. Under the symmetry constraints between the potentials and the eigenfunctions, Lax pair and adjoint Lax pairs including partial part and temporal part are nonlinearied into two finitedimensional Hamiltonian systems (FDHS) in Liouville sense. Moreover, an explicit N-fold Darboux transformation for CDNS equation is constructed with the help of a gauge transformation of the spectral problem.
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.
冯奇; 周雪忠; 黄厚宽; 张小平
2011-01-01
Trial-based value iteration is a class of efficient algorithms to solve partially observable Markov decision process (POMDP), among which FSVI is one of the fastest algorithms. But the overhead of computing MDP value function by FSVI is not negligible for large-scale POMDP problems. In this paper, we propose a new value iteration method based on the shortest Hamiltonian path (shortest Hamiltonian path-based value iteration, SHP-VI). This method explores an optimal belief trajectory using the shortest Hamiltonian path resulting from ant colony optimization, and updates value function over the encountered belief states in reversed order. Compared with FSVI, the experimental results show that SHP-VI accelerates the computation of belief trajectory greatly in trial-based algorithms.%基于试探(trial-based)的值迭代算法是求解部分可观察Markov决策过程(partially observable Markov decision process,POMDP)模型的一类有效算法,其中FSVI算法是目前最快的算法之一.然而对于较大规模的POMDP问题,FSVI计算MDP值函数的时间是不容忽视的.提出一种基于最短哈密顿通路(shortest Hamiltonian path)的值迭代算法(shortest Hamiltonian path-based value iteration,SHP-VI).该方法用求解最短哈密顿通路问题的蚁群算法计算一条最优信念状态轨迹,然后在这些信念状态上反向更新值函数.通过与FSVI算法的实验比较,结果表明SHP-VI算法很大程度地提高了基于试探的算法计算信念状态轨迹的效率.
The Cauchy Problem for Schrödinger Equations with Time-Dependent Hamiltonian
Massimo Cicognani
2014-12-01
Full Text Available We consider the Cauchy problem for a Schrödinger equation with an Hamiltonian depending also on the time variable and that may vanish at t = 0. We find optimal Levi conditions for well-posedness in Sobolev and Gevrey spaces.
New Hamiltonian expansions adapted to the Trojan problem
Paez, Rocio Isabel; Efthymiopoulos, Christos
2016-01-01
A number of studies, referring to the observed Trojan asteroids of various planets in our Solar System, or to hypothetical Trojan bodies in extrasolar planetary systems, have emphasized the importance of so-called secondary resonances in the problem of the long term stability of Trojan motions. Such resonances describe commensurabilities between the fast, synodic, and secular frequency of the Trojan body, and, possibly, additional slow frequencies produced by more than one perturbing bodies. The presence of secondary resonances sculpts the dynamical structure of the phase space. Hence, identifying their location is a relevant task for theoretical studies. In the present paper we combine the methods introduced in two recent papers (Paez & Efthymiopoulos, 2015, Paez & Locatelli, 2015) in order to analytically predict the location of secondary resonances in the Trojan problem (SEE FILE FOR COMPLETE ABSTRACT)
Introduction to Hamiltonian dynamical systems and the N-body problem
Meyer, Kenneth R
2017-01-01
This third edition text provides expanded material on the restricted three body problem and celestial mechanics. With each chapter containing new content, readers are provided with new material on reduction, orbifolds, and the regularization of the Kepler problem, all of which are provided with applications. The previous editions grew out of graduate level courses in mathematics, engineering, and physics given at several different universities. The courses took students who had some background in differential equations and lead them through a systematic grounding in the theory of Hamiltonian mechanics from a dynamical systems point of view. This text provides a mathematical structure of celestial mechanics ideal for beginners, and will be useful to graduate students and researchers alike. Reviews of the second edition: "The primary subject here is the basic theory of Hamiltonian differential equations studied from the perspective of differential dynamical systems. The N-body problem is used as the primary exa...
Ant colony optimization techniques for the hamiltonian p-median problem
M. Zohrehbandian
2010-12-01
Full Text Available Location-Routing problems involve locating a number of facilitiesamong candidate sites and establishing delivery routes to a set of users in such a way that the total system cost is minimized. A special case of these problems is Hamiltonian p-Median problem (HpMP. This research applies the metaheuristic method of ant colony optimization (ACO to solve the HpMP. Modifications are made to the ACO algorithm used to solve the traditional vehicle routing problem (VRP in order to allow the search of the optimal solution of the HpMP. Regarding this metaheuristic algorithm a computational experiment is reported as well.
ZHANG Zhong-zhi; HAN Xu-li
2005-01-01
By using the characteristic properties of the anti-Hermitian generalized anti-Hamiltonian matrices, we prove some necessary and sufficient conditions of the solvability for algebra inverse eigenvalue problem of anti-Hermitian generalized anti-Hamiltonian matrices, and obtain a general expression of the solution to this problem. By using the properties of the orthogonal projection matrix, we also obtain the expression of the solution to optimal approximate problem of an n× n complex matrix under spectral restriction.
A Primal-dual Neural Network for Shortest Path Problem
无
2002-01-01
The shortest path (SP) problem is a classical combinatorial optimization problem which plays an important role in a packet-switched computer and communication network. A new primal-dual neural network to solve the shortest path problem (PDSPN) is presented in this paper. The proposed neural network combines many features such as no network coefficients set,easy implementation in a VLSI circuit, and is proved to be completely stable to the exact solutions. The simulation example shows its efficiency in finding the "optimum" path(s) for data transmission in computer and communication network.
Quantum Adiabatic Evolution Algorithms with Different Paths
Farhi, E; Gutmann, S; Farhi, Edward; Goldstone, Jeffrey; Gutmann, Sam
2002-01-01
In quantum adiabatic evolution algorithms, the quantum computer follows the ground state of a slowly varying Hamiltonian. The ground state of the initial Hamiltonian is easy to construct; the ground state of the final Hamiltonian encodes the solution of the computational problem. These algorithms have generally been studied in the case where the "straight line" path from initial to final Hamiltonian is taken. But there is no reason not to try paths involving terms that are not linear combinations of the initial and final Hamiltonians. We give several proposals for randomly generating new paths. Using one of these proposals, we convert an algorithmic failure into a success.
AN INVERSE MAXIMUM CAPACITY PATH PROBLEM WITH LOWER BOUND CONSTRAINTS
杨超; 陈学旗
2002-01-01
The computational complexity of inverse mimimum capacity path problem with lower bound on capacity of maximum capacity path is examined, and it is proved that solution of this problem is NP-complete. A strong polynomial algorithm for a local optimal solution is provided.
INVERSE EIGENVALUE PROBLEM OF HERMITIAN GENERALIZED ANTI-HAMILTONIAN MATRICES%HGAH矩阵的逆特征值问题
张忠志; Liu Changrong
2004-01-01
In this paper, the inverse eigenvalue problem of Hermitian generalized anti-Hamiltonian matrices and relevant optimal approximate problem are considered. The necessary and sufficient conditions of the solvability for inverse eigenvalue problem and an expression of the general solution of the problem are derived. The solution of the relevant optimal approximate problem is given.
The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo
Hoffman, Matthew D
2011-01-01
Hamiltonian Monte Carlo (HMC) is a Markov chain Monte Carlo (MCMC) algorithm that avoids the random walk behavior and sensitivity to correlated parameters that plague many MCMC methods by taking a series of steps informed by first-order gradient information. These features allow it to converge to high-dimensional target distributions much more quickly than simpler methods such as random walk Metropolis or Gibbs sampling. However, HMC's performance is highly sensitive to two user-specified parameters: a step size {\\epsilon} and a desired number of steps L. In particular, if L is too small then the algorithm exhibits undesirable random walk behavior, while if L is too large the algorithm wastes computation. We introduce the No-U-Turn Sampler (NUTS), an extension to HMC that eliminates the need to set a number of steps L. NUTS uses a recursive algorithm to build a set of likely candidate points that spans a wide swath of the target distribution, stopping automatically when it starts to double back and retrace it...
Splitting K-symplectic methods for non-canonical separable Hamiltonian problems
Zhu, Beibei; Zhang, Ruili; Tang, Yifa; Tu, Xiongbiao; Zhao, Yue
2016-10-01
Non-canonical Hamiltonian systems have K-symplectic structures which are preserved by K-symplectic numerical integrators. There is no universal method to construct K-symplectic integrators for arbitrary non-canonical Hamiltonian systems. However, in many cases of interest, by using splitting, we can construct explicit K-symplectic methods for separable non-canonical systems. In this paper, we identify situations where splitting K-symplectic methods can be constructed. Comparative numerical experiments in three non-canonical Hamiltonian problems show that symmetric/non-symmetric splitting K-symplectic methods applied to the non-canonical systems are more efficient than the same-order Gauss' methods/non-symmetric symplectic methods applied to the corresponding canonicalized systems; for the non-canonical Lotka-Volterra model, the splitting algorithms behave better in efficiency and energy conservation than the K-symplectic method we construct via generating function technique. In our numerical experiments, the favorable energy conservation property of the splitting K-symplectic methods is apparent.
Hamiltonian formulations of Yang-Mills quantum theory and the Gribov problem
Heinzl, T
1996-01-01
We review the status of quantising (non-abelian) gauge theories using different versions of a Hamiltonian formulation corresponding to Dirac's instant and front form of dynamics, respectively. In order to control infrared divergences we work in a finite spatial volume, chosing a torus geometry for convenience. We focus on the determination of the physical configuration space of gauge invariant variables via gauge fixing. This naturally leads us to the issue of the Gribov problem. We discuss it for different gauge choices, in particular finite volume modifications of the axial gauge. Conventional and light-front quantisation are compared and the differences pointed out.
Mielke, Alexander
1991-01-01
The theory of center manifold reduction is studied in this monograph in the context of (infinite-dimensional) Hamil- tonian and Lagrangian systems. The aim is to establish a "natural reduction method" for Lagrangian systems to their center manifolds. Nonautonomous problems are considered as well assystems invariant under the action of a Lie group ( including the case of relative equilibria). The theory is applied to elliptic variational problemson cylindrical domains. As a result, all bounded solutions bifurcating from a trivial state can be described by a reduced finite-dimensional variational problem of Lagrangian type. This provides a rigorous justification of rod theory from fully nonlinear three-dimensional elasticity. The book will be of interest to researchers working in classical mechanics, dynamical systems, elliptic variational problems, and continuum mechanics. It begins with the elements of Hamiltonian theory and center manifold reduction in order to make the methods accessible to non-specialists,...
Finster, Felix
2015-01-01
We consider a boundary value problem for the Dirac equation in a four-dimensional, smooth, asymptotically flat Lorentzian manifold admitting a Killing field which is timelike near and tangential to the boundary. A self-adjoint extension of the Dirac Hamiltonian is constructed. Our results also apply to the situation that the space-time includes horizons, where the Hamiltonian fails to be elliptic.
Memristor-based memory: The sneak paths problem and solutions
Zidan, Mohammed A.
2012-10-29
In this paper, we investigate the read operation of memristor-based memories. We analyze the sneak paths problem and provide a noise margin metric to compare the various solutions proposed in the literature. We also analyze the power consumption associated with these solutions. Moreover, we study the effect of the aspect ratio of the memory array on the sneak paths. Finally, we introduce a new technique for solving the sneak paths problem by gating the memory cell using a three-terminal memistor device.
Partial Path Column Generation for the Vehicle Routing Problem
Jepsen, Mads Kehlet; Petersen, Bjørn
This paper presents a column generation algorithm for the Capacitated Vehicle Routing Problem (CVRP) and the Vehicle Routing Problem with Time Windows (VRPTW). Traditionally, column generation models of the CVRP and VRPTW have consisted of a Set Partitioning master problem with each column repres...... of the giant tour’; a so-called partial path, i.e., not necessarily starting and ending in the depot. This way, the length of the partial path can be bounded and a better control of the size of the solution space for the pricing problem can be obtained....
The traffic equilibrium problem with nonadditive path costs
Gabriel, S.A. [Argonne National Lab., IL (United States). Mathematics and Computer Science Div.; Bernstein, D. [Princeton Univ., NJ (United States). Dept. of Civil Engineering and Operations Research
1995-08-21
In this paper the authors present a version of the (static) traffic equilibrium problem in which the cost incurred on a path is not simply the sum of the costs on the arcs that constitute that path. The authors motivate this nonadditive version of the problem by describing several situations in which the classical additivity assumption fails. They also present an algorithm for solving nonadditive problems that is based on the recent NE/SQP algorithm, a fast and robust method for the nonlinear complementarity problem. Finally, they present a small example that illustrates both the importance of using nonadditive costs and the effectiveness of the NE/SQP method.
Solving the constrained shortest path problem using random search strategy
无
2010-01-01
In this paper, we propose an improved walk search strategy to solve the constrained shortest path problem. The proposed search strategy is a local search algorithm which explores a network by walker navigating through the network. In order to analyze and evaluate the proposed search strategy, we present the results of three computational studies in which the proposed search algorithm is tested. Moreover, we compare the proposed algorithm with the ant colony algorithm and k shortest paths algorithm. The analysis and comparison results demonstrate that the proposed algorithm is an effective tool for solving the constrained shortest path problem. It can not only be used to solve the optimization problem on a larger network, but also is superior to the ant colony algorithm in terms of the solution time and optimal paths.
Path integrals for awkward actions
Amdahl, David
2016-01-01
Time derivatives of scalar fields occur quadratically in textbook actions. A simple Legendre transformation turns the lagrangian into a hamiltonian that is quadratic in the momenta. The path integral over the momenta is gaussian. Mean values of operators are euclidian path integrals of their classical counterparts with positive weight functions. Monte Carlo simulations can estimate such mean values. This familiar framework falls apart when the time derivatives do not occur quadratically. The Legendre transformation becomes difficult or so intractable that one can't find the hamiltonian. Even if one finds the hamiltonian, it usually is so complicated that one can't path-integrate over the momenta and get a euclidian path integral with a positive weight function. Monte Carlo simulations don't work when the weight function assumes negative or complex values. This paper solves both problems. It shows how to make path integrals without knowing the hamiltonian. It also shows how to estimate complex path integrals b...
GRASP with Path Relinking for the SumCut Problem
Jesús Sánchez-Oro
2012-01-01
Full Text Available This paper proposes a GRASP algorithm combined with Path Relinking to solve the SumCut minimization problem. In the SumCut problem one is given a graph with n nodes and must label the nodes in a way that each node receives a unique label from the set{1,2,…,n}, in order to minimize the sum cut of the generated solution. The SumCut problem is really important in archeology (in seriation tasks and in genetics, helping in the Human Genome Project. This problem is equivalent to the Profile problem, because a solution for SumCut is reversal solution for Profile problem. Experimental results show that the GRASP and Path Relinking methods presented outperform in terms of average percentage deviation the results from the State of the Art using shorter CPU time.
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.
Path following algorithm for the graph matching problem
Zaslavskiy, Mikhail; Vert, Jean-Philippe
2008-01-01
We propose a convex-concave programming approach for the labeled weighted graph matching problem. The convex-concave programming formulation is obtained by rewriting the graph matching problem as a least-square problem on the set of permutation matrices and relaxing it to two different optimization problems: a quadratic convex and a quadratic concave optimization problem on the set of doubly stochastic matrices. The concave relaxation has the same global minimum as the initial graph matching problem, but the search for its global minimum is also a hard combinatorial problem. We therefore construct an approximation of the concave problem solution by following a solution path of a convex-concave problem obtained by linear interpolation of the convex and concave formulations, starting from the convex relaxation. This method allows to easily integrate the information on graph label similarities into the optimization problem, and therefore to perform labeled graph matching. The algorithm is compared with some of t...
The shortest path problem ninth DIMACS implementation challenge
Demetrescu, Camil; Johnson, David S
2009-01-01
Shortest path problems are among the most fundamental combinatorial optimization problems with many applications, both direct and as subroutines. They arise naturally in a remarkable number of real-world settings. A limited list includes transportation planning, network optimization, packet routing, image segmentation, speech recognition, document formatting, robotics, compilers, traffic information systems, and dataflow analysis. Shortest path algorithms have been studied since the 1950's and still remain an active area of research. This volume reports on the research carried out by participants during the Ninth DIMACS Implementation Challenge, which led to several improvements of the state of the art in shortest path algorithms. The infrastructure developed during the Challenge facilitated further research in the area, leading to substantial follow-up work as well as to better and more uniform experimental standards. The results of the Challenge included new cutting-edge techniques for emerging applications...
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
Experiments with the auction algorithm for the shortest path problem
Larsen, Jesper; Pedersen, Ib
1999-01-01
The auction approach for the shortest path problem (SPP) as introduced by Bertsekas is tested experimentally. Parallel algorithms using the auction approach are developed and tested. Both the sequential and parallel auction algorithms perform significantly worse than a state-of-the-art Dijkstra......-like reference algorithm. Experiments are run on a distributed-memory MIMD class Meiko parallel computer....
An Application of Calculus: Optimum Parabolic Path Problem
Atasever, Merve; Pakdemirli, Mehmet; Yurtsever, Hasan Ali
2009-01-01
A practical and technological application of calculus problem is posed to motivate freshman students or junior high school students. A variable coefficient of friction is used in modelling air friction. The case in which the coefficient of friction is a decreasing function of altitude is considered. The optimum parabolic path for a flying object…
An Application of Calculus: Optimum Parabolic Path Problem
Atasever, Merve; Pakdemirli, Mehmet; Yurtsever, Hasan Ali
2009-01-01
A practical and technological application of calculus problem is posed to motivate freshman students or junior high school students. A variable coefficient of friction is used in modelling air friction. The case in which the coefficient of friction is a decreasing function of altitude is considered. The optimum parabolic path for a flying object…
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
Mikryukov, D. V.
2016-08-01
An expansion of the Hamiltonian for the N-planet problem into a Poisson series using a system of modified (complex) Poincaré canonical elements in the heliocentric coordinate system is constructed. The Lagrangian and Hamiltonian formalisms are used. The first terms in the expansions of the principal and complementary parts of the disturbing function are presented. Estimates of the number of terms in the presented expansions have been obtained through numerical experiments. A comparison with the results of other authors is made.
Metaheuristic ILS with path relinking for the number partitioning problem
Cesar Augusto Souza de Oliveira
2017-07-01
Full Text Available This study brings an implementation of a metaheuristic procedure to solve the Number Partitioning Problem (NPP, which is a classic NP-hard combinatorial optimization problem. The presented problem has applications in different areas, such as: logistics, production and operations management, besides important relationships with other combinatorial problems. This paper aims to perform a comparative analysis between the proposed algorithm with others metaheuristics using a group of instances available on the literature. Implementations of constructive heuristics, local search and metaheuristics ILS with path relinking as mechanism of intensification and diversification were made in order to improve solutions, surpassing the others algorithms.
The shortest-path problem analysis and comparison of methods
Ortega-Arranz, Hector; Gonzalez-Escribano, Arturo
2014-01-01
Many applications in different domains need to calculate the shortest-path between two points in a graph. In this paper we describe this shortest path problem in detail, starting with the classic Dijkstra's algorithm and moving to more advanced solutions that are currently applied to road network routing, including the use of heuristics and precomputation techniques. Since several of these improvements involve subtle changes to the search space, it may be difficult to appreciate their benefits in terms of time or space requirements. To make methods more comprehensive and to facilitate their co
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.
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.
Qiuping A. Wang
2014-02-01
Full Text Available A numerical experiment of ideal stochastic motion of a particle subject to conservative forces and Gaussian noise reveals that the path probability depends exponentially on action. This distribution implies a fundamental principle generalizing the least action principle of the Hamiltonian/Lagrangian mechanics and yields an extended formalism of mechanics for random dynamics. Within this theory, Liouville’s theorem of conservation of phase density distribution must be modified to allow time evolution of phase density and consequently the Boltzmann H theorem. We argue that the gap between the regular Newtonian dynamics and the random dynamics was not considered in the criticisms of the H theorem.
An Improved Physarum polycephalum Algorithm for the Shortest Path Problem
Xiaoge Zhang
2014-01-01
Full Text Available Shortest path is among classical problems of computer science. The problems are solved by hundreds of algorithms, silicon computing architectures and novel substrate, unconventional, computing devices. Acellular slime mould P. polycephalum is originally famous as a computing biological substrate due to its alleged ability to approximate shortest path from its inoculation site to a source of nutrients. Several algorithms were designed based on properties of the slime mould. Many of the Physarum-inspired algorithms suffer from a low converge speed. To accelerate the search of a solution and reduce a number of iterations we combined an original model of Physarum-inspired path solver with a new a parameter, called energy. We undertook a series of computational experiments on approximating shortest paths in networks with different topologies, and number of nodes varying from 15 to 2000. We found that the improved Physarum algorithm matches well with existing Physarum-inspired approaches yet outperforms them in number of iterations executed and a total running time. We also compare our algorithm with other existing algorithms, including the ant colony optimization algorithm and Dijkstra algorithm.
An improved Physarum polycephalum algorithm for the shortest path problem.
Zhang, Xiaoge; Wang, Qing; Adamatzky, Andrew; Chan, Felix T S; Mahadevan, Sankaran; Deng, Yong
2014-01-01
Shortest path is among classical problems of computer science. The problems are solved by hundreds of algorithms, silicon computing architectures and novel substrate, unconventional, computing devices. Acellular slime mould P. polycephalum is originally famous as a computing biological substrate due to its alleged ability to approximate shortest path from its inoculation site to a source of nutrients. Several algorithms were designed based on properties of the slime mould. Many of the Physarum-inspired algorithms suffer from a low converge speed. To accelerate the search of a solution and reduce a number of iterations we combined an original model of Physarum-inspired path solver with a new a parameter, called energy. We undertook a series of computational experiments on approximating shortest paths in networks with different topologies, and number of nodes varying from 15 to 2000. We found that the improved Physarum algorithm matches well with existing Physarum-inspired approaches yet outperforms them in number of iterations executed and a total running time. We also compare our algorithm with other existing algorithms, including the ant colony optimization algorithm and Dijkstra algorithm.
Inverse minimum spanning tree problem and reverse shortest-path problem with discrete values
LIU Longcheng; HE Yong
2006-01-01
In this paper, we consider two network improvement problems with given discrete values: the inverse minimum spanning tree problem and the reverse shortest-path problem, where the decrements of the weight of the edges are given discrete values. First,for the three models of the inverse minimum spanning tree problem (the sum-type, the bottleneck-type and the constrained bottlenecktype), we present their respective strongly polynomial algorithms. Then, we show that the reverse shortest-path problem is strongly NP-complete.
Bui-Thanh, T.; Girolami, M.
2014-11-01
We consider the Riemann manifold Hamiltonian Monte Carlo (RMHMC) method for solving statistical inverse problems governed by partial differential equations (PDEs). The Bayesian framework is employed to cast the inverse problem into the task of statistical inference whose solution is the posterior distribution in infinite dimensional parameter space conditional upon observation data and Gaussian prior measure. We discretize both the likelihood and the prior using the H1-conforming finite element method together with a matrix transfer technique. The power of the RMHMC method is that it exploits the geometric structure induced by the PDE constraints of the underlying inverse problem. Consequently, each RMHMC posterior sample is almost uncorrelated/independent from the others providing statistically efficient Markov chain simulation. However this statistical efficiency comes at a computational cost. This motivates us to consider computationally more efficient strategies for RMHMC. At the heart of our construction is the fact that for Gaussian error structures the Fisher information matrix coincides with the Gauss-Newton Hessian. We exploit this fact in considering a computationally simplified RMHMC method combining state-of-the-art adjoint techniques and the superiority of the RMHMC method. Specifically, we first form the Gauss-Newton Hessian at the maximum a posteriori point and then use it as a fixed constant metric tensor throughout RMHMC simulation. This eliminates the need for the computationally costly differential geometric Christoffel symbols, which in turn greatly reduces computational effort at a corresponding loss of sampling efficiency. We further reduce the cost of forming the Fisher information matrix by using a low rank approximation via a randomized singular value decomposition technique. This is efficient since a small number of Hessian-vector products are required. The Hessian-vector product in turn requires only two extra PDE solves using the adjoint
Prizing on Paths: A PTAS for the Highway Problem
Grandoni, Fabrizio
2010-01-01
In the highway problem, we are given an n-edge line graph (the highway), and a set of paths (the drivers), each one with its own budget. For a given assignment of edge weights (the tolls), the highway owner collects from each driver the weight of the associated path, when it does not exceed the budget of the driver, and zero otherwise. The goal is choosing weights so as to maximize the profit. A lot of research has been devoted to this apparently simple problem. The highway problem was shown to be strongly NP-hard only recently [Elbassioni,Raman,Ray-'09]. The best-known approximation is O(\\log n/\\log\\log n) [Gamzu,Segev-'10], which improves on the previous-best O(\\log n) approximation [Balcan,Blum-'06]. In this paper we present a PTAS for the highway problem, hence closing the complexity status of the problem. Our result is based on a novel randomized dissection approach, which has some points in common with Arora's quadtree dissection for Euclidean network design [Arora-'98]. The basic idea is enclosing the ...
Hamiltonian formulation of generalized quantum dynamics——Quantum mechanical problem
吴宁; 阮图南
1997-01-01
The Hamiltonian formulation of the usual complex quantum mechanics in the theory of generalized quantum dynamics is discussed. After the total trace Lagrangian, total trace Hamiltonian and two kinds of Poisson brackets are introduced, both the equations of motion of some total trace functionals which are expressed by total trace Poisson brackets and the equations of motion of some operators which are expressed by the without-total-trace Poisson brackets are obtained. Then a set of basic equations of motion of the usual complex quantum mechanics are obtained, which are also expressed by the Poisson brackets and total trace Hamiltonian in the generalized quantum dynamics. The set of equations of motion are consistent with the corresponding Heisenberg equations.
Shestakova, T P
2009-01-01
About 50 years ago, in 1958, Dirac published his formulation of generalized Hamiltonian dynamics for gravitation. Several years later Arnowitt, Deser and Misner (ADM) proposed their description of the dynamics of General Relativity which became a basis of the Wheeler - DeWitt Quantum Geometrodynamics. There exist also other works where the Hamiltonian formulation of gravitational theory was discussed. In spite of decades passed from the famous papers by Dirac and ADM, there are unsolved problems. Namely, are the Dirac and ADM formulations equivalent to each other? Are these formulations equivalent to the original (Lagrangian) Einstein theory? Is the group of transformation in phase space the same as the group of gauge transformation of the Einstein theory? What are rules according to which a generator of transformations in phase space should be constructed? Let us mention also another approach based on extended phase space where gauge degrees of freedom are treated on the equal ground with physical degrees of...
HOU Guo-Lin; Alatancang
2009-01-01
In the present paper, the spectrums of off-diagonal infinite-dimensional Hamiltonian operators are studied.At first, we prove that the spectrum, the continuous-spectrum, and the union of the point-spectrum and residual-spectrum of the operators are symmetric with respect to real axis and imaginary axis.Then for the purpose of reducing the dimension of the studied problems, the spectrums of the operators are expressed by the spectrums of the product of two self-adjoint operators in state space.At last, the above-mentioned results are applied to plane elasticity problems, which shows the practicability of the results.
A constraint programming solution for the military unit path finding problem
Leenen, L
2012-01-01
Full Text Available In this chapter the authors present an algorithm to solve the Dynamic Military Unit Path Finding Problem (DMUPFP) which is based on Stentz’s well-known D* algorithm to solve dynamic path finding problems. The Military Unit Path Finding Problem...
Randomized shortest-path problems: two related models.
Saerens, Marco; Achbany, Youssef; Fouss, François; Yen, Luh
2009-08-01
This letter addresses the problem of designing the transition probabilities of a finite Markov chain (the policy) in order to minimize the expected cost for reaching a destination node from a source node while maintaining a fixed level of entropy spread throughout the network (the exploration). It is motivated by the following scenario. Suppose you have to route agents through a network in some optimal way, for instance, by minimizing the total travel cost-nothing particular up to now-you could use a standard shortest-path algorithm. Suppose, however, that you want to avoid pure deterministic routing policies in order, for instance, to allow some continual exploration of the network, avoid congestion, or avoid complete predictability of your routing strategy. In other words, you want to introduce some randomness or unpredictability in the routing policy (i.e., the routing policy is randomized). This problem, which will be called the randomized shortest-path problem (RSP), is investigated in this work. The global level of randomness of the routing policy is quantified by the expected Shannon entropy spread throughout the network and is provided a priori by the designer. Then, necessary conditions to compute the optimal randomized policy-minimizing the expected routing cost-are derived. Iterating these necessary conditions, reminiscent of Bellman's value iteration equations, allows computing an optimal policy, that is, a set of transition probabilities in each node. Interestingly and surprisingly enough, this first model, while formulated in a totally different framework, is equivalent to Akamatsu's model ( 1996 ), appearing in transportation science, for a special choice of the entropy constraint. We therefore revisit Akamatsu's model by recasting it into a sum-over-paths statistical physics formalism allowing easy derivation of all the quantities of interest in an elegant, unified way. For instance, it is shown that the unique optimal policy can be obtained by
Fully dynamic output bounded single source shortest path problem
Frigioni, D. [Universita di L`Aquila, Coppito (Italy); Marchetti-Spaccamela, A.; Nanni, U. [Universita di Roma (Italy)
1996-12-31
We consider the problem of maintaining the distances and the shortest paths from a single source in either a directed or an undirected graph with positive real edge weights, handling insertions, deletions and cost updates of edges. We propose fully dynamic algorithms with optimal space requirements and query time. The cost of update operations depends on the class of the considered graph and on the number of vertices that, due to an edge modification, either change their distance from the source or change their parent in the shortest path tree. In the case of graphs with bounded genus (including planar graphs), bounded degree graphs, bounded treewidth graphs and O-near-planar graphs with bounded {beta}, the update procedures require O(log n) amortized time per vertex update, while for general graphs with n vertices and m edges they require O({radical}m log n) amortized time per vertex update. The solution is based on a dynamization of Dijkstra`s algorithm and requires simple data structures that are suitable for a practical and straightforward implementation.
Self-organization and solution of shortest-path optimization problems with memristive networks
Pershin, Yuriy V.; Di Ventra, Massimiliano
2013-07-01
We show that memristive networks, namely networks of resistors with memory, can efficiently solve shortest-path optimization problems. Indeed, the presence of memory (time nonlocality) promotes self organization of the network into the shortest possible path(s). We introduce a network entropy function to characterize the self-organized evolution, show the solution of the shortest-path problem and demonstrate the healing property of the solution path. Finally, we provide an algorithm to solve the traveling salesman problem. Similar considerations apply to networks of memcapacitors and meminductors, and networks with memory in various dimensions.
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.
The Tower of Hanoi problem on Path_h graphs
Berend, Daniel; Solomon, Shay
2011-01-01
The generalized Tower of Hanoi problem with h \\ge 4 pegs is known to require a sub-exponentially fast growing number of moves in order to transfer a pile of n disks from one peg to another. In this paper we study the Path_h variant, where the pegs are placed along a line, and disks can be moved from a peg to its nearest neighbor(s) only. Whereas in the simple variant there are h(h-1)/2 possible bi-directional interconnections among pegs, here there are only h-1 of them. Despite the significant reduction in the number of interconnections, the number of moves needed to transfer a pile of n disks between any two pegs also grows sub-exponentially as a function of n. We study these graphs, identify sets of mutually recursive tasks, and obtain a relatively tight upper bound for the number of moves, depending on h, n and the source and destination pegs.
Optimal parallel algorithm for shortest-paths problem on interval graphs
MISHRA P.K.
2004-01-01
This paper presents an efficient parallel algorithm for the shortest-path problem in interval graph for computing shortest-paths in a weighted interval graph that runs in O(n) time with n intervals in a graph. A linear processor CRCW algorithm for determining the shortest-paths in an interval graphs is given.
Mastromatteo, Michael; Jackson, Bret
2013-11-21
Electronic structure methods based on density functional theory are used to construct a reaction path Hamiltonian for CH4 dissociation on the Ni(100) and Ni(111) surfaces. Both quantum and quasi-classical trajectory approaches are used to compute dissociative sticking probabilities, including all molecular degrees of freedom and the effects of lattice motion. Both approaches show a large enhancement in sticking when the incident molecule is vibrationally excited, and both can reproduce the mode specificity observed in experiments. However, the quasi-classical calculations significantly overestimate the ground state dissociative sticking at all energies, and the magnitude of the enhancement in sticking with vibrational excitation is much smaller than that computed using the quantum approach or observed in the experiments. The origin of this behavior is an unphysical flow of zero point energy from the nine normal vibrational modes into the reaction coordinate, giving large values for reaction at energies below the activation energy. Perturbative assumptions made in the quantum studies are shown to be accurate at all energies studied.
Kulshreshtha, Usha, E-mail: ushakulsh@gmail.com [Department of Physics and Astronomy, Iowa State University, 50011, Ames, IA (United States); Department of Physics, Kirori Mal College, University of Delhi, 110007, Delhi (India); Kulshreshtha, Daya Shankar, E-mail: dskulsh@gmail.com [Department of Physics and Astronomy, Iowa State University, 50011, Ames, IA (United States); Department of Physics and Astrophysics, University of Delhi, 110007, Delhi (India); Vary, James P., E-mail: jvary@iastate.edu [Department of Physics and Astronomy, Iowa State University, 50011, Ames, IA (United States)
2015-04-28
Recently Grinstein, Jora, and Polosa have studied a theory of large-N scalar quantum chromodynamics in one space and one time dimension. This theory admits a Bethe–Salpeter equation describing the discrete spectrum of quark–antiquark bound states. They consider gauge fields in the adjoint representation of SU(N) and scalar fields in the fundamental representation. The theory is asymptotically free and linearly confining. The theory could possibly provide a good field theoretic framework for the description of a large class of diquark–antidiquark (tetra-quark) states. Recently we have studied the light-front quantization of this theory without a Higgs potential. In the present work, we study the light-front Hamiltonian, path integral, and BRST formulations of the theory in the presence of a Higgs potential. The light-front theory is seen to be gauge invariant, possessing a set of first-class constraints. The explicit occurrence of spontaneous symmetry breaking in the theory is shown in unitary gauge as well as in the light-front ’t Hooft gauge.
Kulshreshtha, Usha [Iowa State University, Department of Physics and Astronomy, Ames, IA (United States); University of Delhi, Department of Physics, Kirori Mal College, Delhi (India); Kulshreshtha, Daya Shankar [Iowa State University, Department of Physics and Astronomy, Ames, IA (United States); University of Delhi, Department of Physics and Astrophysics, Delhi (India); Vary, James P. [Iowa State University, Department of Physics and Astronomy, Ames, IA (United States)
2015-04-01
Recently Grinstein, Jora, and Polosa have studied a theory of large- N scalar quantum chromodynamics in one space and one time dimension. This theory admits a Bethe-Salpeter equation describing the discrete spectrum of quark-antiquark bound states. They consider gauge fields in the adjoint representation of SU(N) and scalar fields in the fundamental representation. The theory is asymptotically free and linearly confining. The theory could possibly provide a good field theoretic framework for the description of a large class of diquark-antidiquark (tetra-quark) states. Recently we have studied the light-front quantization of this theory without a Higgs potential. In the present work, we study the light-front Hamiltonian, path integral, and BRST formulations of the theory in the presence of a Higgs potential. The light-front theory is seen to be gauge invariant, possessing a set of first-class constraints. The explicit occurrence of spontaneous symmetry breaking in the theory is shown in unitary gauge as well as in the light-front 't Hooft gauge. (orig.)
Kulshreshtha, Usha; Vary, James P
2015-01-01
Recently Grinstein, Jora, and Polosa have studied a theory of large-$N$ scalar quantum chromodynamics in one-space one-time dimension. This theory admits a Bethe-Salpeter equation describing the discrete spectrum of quark-antiquark bound states. They consider gauge fields in the adjoint representation of $SU(N)$ and scalar fields in the fundamental representation. The theory is asymptotically free and linearly confining. The theory could possibly provide a good field theoretic framework for the description of a large class of diquark-antidiquark (tetra-quark) states. Recently we have studied the light-front quantization of this theory without a Higgs potential. In the present work, we study the light-front Hamiltonian, path integral and BRST formulations of the theory in the presence of a Higgs potential. The light-front theory is seen to be gauge-invariant, possessing a set of first-class constraints. The explicit occurrence of spontaneous symmetry breaking in the theory is shown in unitary gauge as well as ...
Removable partial dentures with rotational paths of insertion: problem analysis.
Firtell, D N; Jacobson, T E
1983-07-01
Removable partial dentures designed to use a rotational path of insertion are technique sensitive. When indicated and when the principles discussed are followed, a denture that uses a rotational path can be highly successful. Tooth coverage can be decreased, which is an advantage in plaque control, caries reduction, and periodontal support. Esthetics can be improved without resorting to intracoronal retainers, and the number of components subject to distortion is reduced. When properly designed and constructed, use of a rotational path of insertion can result in a removable partial denture that is strong, hygienic, and esthetic.
An improved Physarum polycephalum algorithm for the shortest path problem
Zhang, Xiaoge; Wang, Qing; Adamatzky, Andrew; Chan, Felix T S; Mahadevan, Sankaran; Deng, Yong
2014-01-01
.... Acellular slime mould P. polycephalum is originally famous as a computing biological substrate due to its alleged ability to approximate shortest path from its inoculation site to a source of nutrients...
Multi-Objective and Multi-Constrained Non-Additive Shortest Path Problems
Reinhardt, Line Blander; Pisinger, David
of this paper is to give a general framework for dominance tests for problems involving a number of non-additive criteria. These dominance tests can help eliminate paths in a dynamic programming framework when using multiple objectives. Results on real-life multi-objective problems containing non......Shortest path problems appear as subproblems in numerous optimization problems. In most papers concerning multiple objective shortest path problems, additivity of the objective is a de-facto assumption, but in many real-life situations objectives and criteria, can be non-additive. The purpose...
Multi-Objective and Multi-Constrained Non-Additive Shortest Path Problems
Reinhardt, Line Blander; Pisinger, David
2011-01-01
of this paper is to give a general framework for dominance tests for problems involving a number of non-additive criteria. These dominance tests can help to eliminate paths in a dynamic programming framework when using multiple objectives. Results on real-life multi-objective problems containing non......Shortest path problems appear as subproblems in numerous optimization problems. In most papers concerning multiple objective shortest path problems, additivity of the objective is a de-facto assumption, but in many real-life situations objectives and criteria, can be non-additive. The purpose...
Buksman Hollander, Efrain; de Luca, Jayme
2003-02-01
We find a two-degree-of-freedom Hamiltonian for the time-symmetric problem of straight line motion of two electrons in direct relativistic interaction. This time-symmetric dynamical system appeared 100 years ago and it was popularized in the 1940s by the work of Wheeler and Feynman in electrodynamics, which was left incomplete due to the lack of a Hamiltonian description. The form of our Hamiltonian is such that the action of a Lorentz transformation is explicitly described by a canonical transformation (with rescaling of the evolution parameter). The method is closed and defines the Hamitonian in implicit form without power expansions. We outline the method with an emphasis on the physics of this complex conservative dynamical system. The Hamiltonian orbits are calculated numerically at low energies using a self-consistent steepest-descent method (a stable numerical method that chooses only the nonrunaway solution). The two-degree-of-freedom Hamiltonian suggests a simple prescription for the canonical quantization of the relativistic two-body problem.
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
Hamiltonian矩阵特征值问题的Lanczos-型算法%Lanczos Algorithms-Type for Hamiltonian Eigenvalue Problems
郭蔚
2001-01-01
In the paper,we applicate Lanczos algorithms-type to Hamiltonian eigenvalue problems and give an error analysis in iterative procedure.%应用Lanczos-型算法求Hamiltonian矩阵的特征根问题，并且给出了在迭代过程中的误差估计．
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...
Fractal structures for the Jacobi Hamiltonian of restricted three-body problem
Rollin, G; Shepelyansky, D L
2015-01-01
We study the dynamical chaos and integrable motion in the planar circular restricted three-body problem and determine the fractal dimension of the spiral strange repeller set of non-escaping orbits at different values of mass ratio of binary bodies and of Jacobi integral of motion. We find that the spiral fractal structure of the Poincar\\'e section leads to a spiral density distribution of particles remaining in the system. We also show that the initial exponential drop of survival probability with time is followed by the algebraic decay related to the universal algebraic statistics of Poincar\\'e recurrences in generic symplectic maps.
胡云卿; 刘兴高; 薛安克
2014-01-01
This paper considers dealing with path constraints in the framework of the improved control vector it-eration (CVI) approach. Two available ways for enforcing equality path constraints are presented, which can be di-rectly incorporated into the improved CVI approach. Inequality path constraints are much more difficult to deal with, even for small scale problems, because the time intervals where the inequality path constraints are active are unknown in advance. To overcome the challenge, the l1 penalty function and a novel smoothing technique are in-troduced, leading to a new effective approach. Moreover, on the basis of the relevant theorems, a numerical algo-rithm is proposed for nonlinear dynamic optimization problems with inequality path constraints. Results obtained from the classic batch reactor operation problem are in agreement with the literature reports, and the computational efficiency is also high.
Fusion proteins as alternate crystallization paths to difficult structure problems
Carter, Daniel C.; Rueker, Florian; Ho, Joseph X.; Lim, Kap; Keeling, Kim; Gilliland, Gary; Ji, Xinhua
1994-01-01
The three-dimensional structure of a peptide fusion product with glutathione transferase from Schistosoma japonicum (SjGST) has been solved by crystallographic methods to 2.5 A resolution. Peptides or proteins can be fused to SjGST and expressed in a plasmid for rapid synthesis in Escherichia coli. Fusion proteins created by this commercial method can be purified rapidly by chromatography on immobilized glutathione. The potential utility of using SjGST fusion proteins as alternate paths to the crystallization and structure determination of proteins is demonstrated.
Path inequalities for the vehicle routing problem with time windows
Kallehauge, Brian; Boland, Natashia; Madsen, Oli B.G.
2007-01-01
In this paper we introduce a new formulation of the vehicle routing problem with time windows (VRPTW) involving only binary variables. The new formulation is based on the formulation of the asymmetric traveling salesman problem with time windows by Ascheuer et al. (Networks 36 (2000) 69-79) and has...
Computational methods for long mean free path problems
Christlieb, Andrew Jason
This document describes work being done on particle transport in long mean free path environments. Two non statistical computational models are developed based on the method of propagators, which can have significant advantages in accuracy and efficiency over other methods. The first model has been developed primarily for charged particle transport and the second primarily for neutral particle transport. Both models are intended for application to transport in complex geometry using irregular meshes. The transport model for charged particles was inspired by the notion of obtaining a simulation that could handle complex geometry and resolve the bulk and sheath characteristics of a discharge, in a reasonable amount of computation time. The charged particle transport model has been applied in a self- consistent manner to the ion motion in a low density inductively coupled discharge. The electrons were assumed to have a Boltzmann density distribution for the computation of the electric field. This work assumes cylindrical geometry and focuses on charge exchange collisions as the primary ion collisional effect that takes place in the discharge. The results are compared to fluid simulations. The neutral transport model was constructed to solve the steady state Boltzmann equation on 3-D arbitrary irregular meshes. The neutral transport model was developed with the intent of investigating gas glow on the scale of micro-electrical-mechanical systems (MEMS), and is meant for tracking multiple species. The advantage of these methods is that the step size is determined by the mean free path of the particles rather than the mesh employed in the simulation.
Realizable Paths and the NL vs L Problem
Kintali, Shiva
2010-01-01
A celebrated theorem of Savitch states that NSPACE(S) is contained in DSPACE(S^2). In particular, Savitch gave a deterministic algorithm to solve ST-CONNECTIVITY (an NL-complete problem) using O(log^2{n}) space, implying NL is in DSPACE(log^2{n}). While Savitch's theorem itself has not been improved in the last four decades, studying the space complexity of several special cases of ST-CONNECTIVITY has provided new insights into the space-bounded complexity classes. In this paper, we introduce new kind of graph connectivity problems which we call graph realizability problems. All of our graph realizability problems are generalizations of UNDIRECTED ST-CONNECTIVITY. ST-REALIZABILITY, the most general graph realizability problem, is LogCFL-complete. We define the corresponding complexity classes that lie between L and LogCFL and study their relationships. As special cases of our graph realizability problems we define two natural problems, BALANCED ST-CONNECTIVITY and POSITIVE BALANCED ST-CONNECTIVITY, that lie b...
Reta, Daniel; Moreira, Ibério de P R; Illas, Francesc
2016-07-12
In the most general case of three electrons in three symmetry unrelated centers with Ŝ1 = Ŝ2 = Ŝ3 = 1/2 localized magnetic moments, the low energy spectrum consists of one quartet (Q) and two doublet (D1, D2) pure spin states. The energy splitting between these spin states can be described with the well-known Heisenberg-Dirac-Van Vleck (HDVV) model spin Hamiltonian, and their corresponding energy expressions are expressed in terms of the three different two-body magnetic coupling constants J12, J23, and J13. However, the values of all three magnetic coupling constants cannot be extracted using the calculated energy of the three spin-adapted states since only two linearly independent energy differences between pure spin states exist. This problem has been recently investigated by Reta et al. (J. Chem. Theory Comput. 2015, 11, 3650), resulting in an alternative proposal to the original Noodleman's broken symmetry mapping approach. In the present work, this proposal is validated by means of ab initio effective Hamiltonian theory, which allows a direct extraction of all three J values from the one-to-one correspondence between the matrix elements of both effective and HDVV Hamiltonian. The effective Hamiltonian matrix representation has been constructed from configuration interaction wave functions for the three spin states obtained for two model systems showing a different degree of delocalization of the unpaired electrons. These encompass a trinuclear Cu(II) complex and a π-conjugated purely organic triradical.
A survey of the all-pairs shortest paths problem and its variants in graphs
Udaya Kumar Reddy K. R.
2016-06-01
Full Text Available There has been a great deal of interest in the computation of distances and shortest paths problem in graphs which is one of the central, and most studied, problems in (algorithmic graph theory. In this paper, we survey the exact results of the static version of the all-pairs shortest paths problem and its variants namely, the Wiener index, the average distance, and the minimum average distance spanning tree (MAD tree in short in graphs (focusing mainly on algorithmic results for such problems. Along the way we also mention some important open issues and further research directions in these areas.
Regularization Paths for Least Squares Problems with Generalized $\\ell_1$ Penalties
Tibshirani, Ryan J
2010-01-01
We present a path algorithm for least squares problems with generalized $\\ell_1$ penalties. This includes as a special case the lasso and fused lasso problems. The algorithm is based on solving the (equivalent) Lagrange dual problem, an approach which offers both a computational advantage and an interesting geometric interpretation of the solution path. Using insights gathered from the dual formulation, we study degrees of freedom for the generalized problem, and develop an unbiased estimate of the degrees of freedom of the fused lasso fit. Our approach bears similarities to least angle regression (LARS), and a simple modification to our method gives the LARS procedure exactly.
The role of convexity for solving some shortest path problems in plane without triangulation
An, Phan Thanh; Hai, Nguyen Ngoc; Hoai, Tran Van
2013-09-01
Solving shortest path problems inside simple polygons is a very classical problem in motion planning. To date, it has usually relied on triangulation of the polygons. The question: "Can one devise a simple O(n) time algorithm for computing the shortest path between two points in a simple polygon (with n vertices), without resorting to a (complicated) linear-time triangulation algorithm?" raised by J. S. B. Mitchell in Handbook of Computational Geometry (J. Sack and J. Urrutia, eds., Elsevier Science B.V., 2000), is still open. The aim of this paper is to show that convexity contributes to the design of efficient algorithms for solving some versions of shortest path problems (namely, computing the convex hull of a finite set of points and convex rope on rays in 2D, computing approximate shortest path between two points inside a simple polygon) without triangulation on the entire polygons. New algorithms are implemented in C and numerical examples are presented.
Yuqin Yao
2016-01-01
Full Text Available Associated with so~(3,R, a new matrix spectral problem of 2nd degree in a spectral parameter is proposed and its corresponding soliton hierarchy is generated within the zero curvature formulation. Bi-Hamiltonian structures of the presented soliton hierarchy are furnished by using the trace identity, and thus, all presented equations possess infinitely commuting many symmetries and conservation laws, which implies their Liouville integrability.
López, G
2007-01-01
The Lagrangian, the Hamiltonian and the constant of motion of the gravitational attraction of two bodies when one of them has variable mass is considered. This is done by choosing the reference system in one of the bodies which allows to reduce the system of equations to 1-D problem. The trajectories found in the space position-velocity,(x,v), are qualitatively different from those on the space position-momentum,(x,p).
J. R. Cardoso
2007-01-01
Full Text Available The first-order optical nature of an optical system (including an eye is completely characterized by a 55 × matrix called the ray transference. It is known that the image of a ray transference by the matrix logarithm function is an augmented Hamiltonian matrix. It turns out that there are other ways of transforming transferences into augmented Hamiltonian matrices. They include Cayley transforms and modified Cayley transforms. This paper will describe these transforms with a view to finding the most suitable one for quantitative analyses of eyes and other systems in augmented Hamiltonian spaces. In particular we look at the calculation of average systems.
An Evaluation of Potentials of Genetic Algorithm in Shortest Path Problem
Hassany Pazooky, S.; Rahmatollahi Namin, Sh; Soleymani, A.; Samadzadegan, F.
2009-04-01
One of the most typical issues considered in combinatorial systems in transportation networks, is the shortest path problem. In such networks, routing has a significant impact on the network's performance. Due to natural complexity in transportation networks and strong impact of routing in different fields of decision making, such as traffic management and vehicle routing problem (VRP), appropriate solutions to solve this problem are crucial to be determined. During last years, in order to solve the shortest path problem, different solutions are proposed. These techniques are divided into two categories of classic and evolutionary approaches. Two well-known classic algorithms are Dijkstra and A*. Dijkstra is known as a robust, but time consuming algorithm in finding the shortest path problem. A* is also another algorithm very similar to Dijkstra, less robust but with a higher performance. On the other hand, Genetic algorithms are introduced as most applicable evolutionary algorithms. Genetic Algorithm uses a parallel search method in several parts of the domain and is not trapped in local optimums. In this paper, the potentiality of Genetic algorithm for finding the shortest path is evaluated by making a comparison between this algorithm and classic algorithms (Dijkstra and A*). Evaluation of the potential of these techniques on a transportation network in an urban area shows that due to the problem of classic methods in their small search space, GA had a better performance in finding the shortest path.
Cardoso, J. R.
2007-01-01
The first-order optical nature of an optical system (including an eye) is completely characterized by a 55 × matrix called the ray transference. It is known that the image of a ray transference by the matrix logarithm function is an augmented Hamiltonian matrix. It turns out that there are other ways of transforming transferences into augmented Hamiltonian matrices. They include Cayley transforms and modified Cayley transforms. This paper will describe these transforms with a view to fi...
A Local Search Modeling for Constrained Optimum Paths Problems (Extended Abstract
Quang Dung Pham
2009-10-01
Full Text Available Constrained Optimum Path (COP problems appear in many real-life applications, especially on communication networks. Some of these problems have been considered and solved by specific techniques which are usually difficult to extend. In this paper, we introduce a novel local search modeling for solving some COPs by local search. The modeling features the compositionality, modularity, reuse and strengthens the benefits of Constrained-Based Local Search. We also apply the modeling to the edge-disjoint paths problem (EDP. We show that side constraints can easily be added in the model. Computational results show the significance of the approach.
Solving the empty space problem in robot path planning by mathematical morphology
Roerdink, J.B.T.M.
1993-01-01
In this paper we formulate a morphological approach to path planning problems, in particular with respect to the empty-space problem, that is, the question of finding the allowed states for an object, moving in a space with obstacles. Our approach is based upon a recent generalization of mathematic
TRANSPORT CORRIDOR "URAL INDUSTRIAL – URAL POLAR": PROBLEMS, EVOLUTION PATHS
N.V. Tabakov
2007-06-01
Full Text Available The article deals with the theoretic and methodological questions regarding the formation of a transport corridor "Urals industrial – Urals Polar". Analyzed are the main factors that affect the formation of the transport infrastructure. A big effect is centered around the world-view problem, which has to do with the occupation of a human, and the effect of it on nature. Put forth is the possibility to look upon the question of the formation of ma transport corridor "Urals industrial – Urals Polar" in the frame of the forming of the Ural-West-Siberian TPK, taking into account the global transport web.
Imen Châari
2014-07-01
Full Text Available Path planning is a fundamental optimization problem that is crucial for the navigation of a mobile robot. Among the vast array of optimization approaches, we focus in this paper on Ant Colony Optimization (ACO and Genetic Algorithms (GA for solving the global path planning problem in a static environment, considering their effectiveness in solving such a problem. Our objective is to design an efficient hybrid algorithm that takes profit of the advantages of both ACO and GA approaches for the sake of maximizing the chance to find the optimal path even under real-time constraints. In this paper, we present smartPATH, a new hybrid ACO-GA algorithm that relies on the combination of an improved ACO algorithm (IACO for efficient and fast path selection, and a modified crossover operator to reduce the risk of falling into a local minimum. We demonstrate through extensive simulations that smartPATH outperforms classical ACO (CACO, GA algorithms. It also outperforms the Dijkstra exact method in solving the path planning problem for large graph environments. It improves the solution quality up to 57% in comparison with CACO and reduces the execution time up to 83% as compared to Dijkstra for large and dense graphs. In addition, the experimental results on a real robot shows that smartPATH finds the optimal path with a probability up to 80% with a small gap not exceeding 1m in 98%.
Instability Paths in the Kirchhoff-Plateau Problem
Giusteri, Giulio G.; Franceschini, Paolo; Fried, Eliot
2016-08-01
The Kirchhoff-Plateau problem concerns the equilibrium shapes of a system in which a flexible filament in the form of a closed loop is spanned by a soap film, with the filament being modeled as a Kirchhoff rod and the action of the spanning surface being solely due to surface tension. Adopting a variational approach, we define an energy associated with shape deformations of the system and then derive general equilibrium and (linear) stability conditions by considering the first and second variations of the energy functional. We analyze in detail the transition to instability of flat circular configurations, which are ground states for the system in the absence of surface tension, when the latter is progressively increased. Such a theoretical study is particularly useful here, since the many different perturbations that can lead to instability make it challenging to perform an exhaustive experimental investigation. We generalize previous results, since we allow the filament to possess a curved intrinsic shape and also to display anisotropic flexural properties (as happens when the cross section of the filament is noncircular). This is accomplished by using a rod energy which is familiar from the modeling of DNA filaments. We find that the presence of intrinsic curvature is necessary to obtain a first buckling mode which is not purely tangent to the spanning surface. We also elucidate the role of twisting buckling modes, which become relevant in the presence of flexural anisotropy.
Multi-Robot Path-Planning Problem for a Heavy Traffic Control Application: A Survey
Ebtehal Turki Saho Alotaibi
2016-06-01
Full Text Available This survey looked at the methods used to solve multi-autonomous vehicle path-planning for an application of heavy traffic control in cities. Formally, the problem consisted of a graph and a set of robots. Each robot has to reach its destination in the minimum time and number of movements, considering the obstacles and other robots’ paths, hence, the problem is NP-hard. The study found that decoupled centralised approaches are the most relevant approaches for an autonomous vehicle path-planning problem for three reasons: (1 a city is a large environment and coupled centralised approaches scale weakly, (2 the overhead of a coupled decentralised approach to achieve the global optimal will affect the time and memory of the other robots, which is not important in a city configuration and (3 the coupled approaches suppose that the number of robots is defined before they start to find the paths and resolve collisions, while in a city, any car can start at any time and hence, each car should work individually and resolve collisions as they arise. In addition, the study reviewed four decoupled centralised techniques to solve the problem: multi-robot path-planning rapidly exploring random tree (MRRRT, push and swap (PAS, push and rotate (PAR and the Bibox algorithm. The experiments showed that MRRRT is the best for exploring any search space and optimizing the solution. On the other hand, PAS, PAR and Bibox are better in terms of providing a complete solution for the problem and resolving collisions in significantly much less time, the analysis, however, shows that a wider class of solvable instances are excluded from PAS and PAR domain. In addition, Bibox solves a smaller class than the class solved by PAS and PAR in less time, in the worst case, and with a shorter path than PAS and PAR.
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...
Prograph Based Analysis of Single Source Shortest Path Problem with Few Distinct Positive Lengths
B. Bhowmik
2011-08-01
Full Text Available In this paper we propose an experimental study model S3P2 of a fast fully dynamic programming algorithm design technique in finite directed graphs with few distinct nonnegative real edge weights. The Bellman-Ford’s approach for shortest path problems has come out in various implementations. In this paper the approach once again is re-investigated with adjacency matrix selection in associate least running time. The model tests proposed algorithm against arbitrarily but positive valued weighted digraphs introducing notion of Prograph that speeds up finding the shortest path over previous implementations. Our experiments have established abstract results with the intention that the proposed algorithm can consistently dominate other existing algorithms for Single Source Shortest Path Problems. A comparison study is also shown among Dijkstra’s algorithm, Bellman-Ford algorithm, and our algorithm.
An optimal path planning problem for heterogeneous multi-vehicle systems
Klaučo Martin
2016-06-01
Full Text Available A path planning problem for a heterogeneous vehicle is considered. Such a vehicle consists of two parts which have the ability to move individually, but one of them has a shorter range and is therefore required to keep in a close distance to the main vehicle. The objective is to devise an optimal path of minimal length under the condition that at least one part of the heterogeneous system visits all desired waypoints exactly once. Two versions of the problem are considered. One assumes that the order in which the waypoints are visited is known a priori. In such a case we show that the optimal path can be found by solving a mixed-integer second-order cone problem. The second version assumes that the order in which the waypoints are visited is not known a priori, but can be optimized so as to shorten the length of the path. Two approaches to solve this problem are presented and evaluated with respect to computational complexity.
A Branch-and-Cut Algorithm for Elementary Shortest Path Problem with Resource Constraints
Jepsen, Mads Kehlet; Petersen, Bjørn; Spoorendonk, Simon
The elementary shortest path with resource constraints are commonly solved with dynamic programming algorithms. We present a branch-and-cut algorithm for the undirected version. Two types of resources are discussed: A capacity and a fixed charge resource. The former is the subproblem of the capac...... of the capacitated vehicle routing problem and the latter is for the split delivery version....
Runtime analysis of ant colony optimization on dynamic shortest path problems
Lissovoi, Andrei; Witt, Carsten
2013-01-01
A simple ACO algorithm called λ-MMAS for dynamic variants of the single-destination shortest paths problem is studied by rigorous runtime analyses. Building upon previous results for the special case of 1-MMAS, it is studied to what extent an enlarged colony using $\\lambda$ ants per vertex helps...
Analysis of an Automated Vehicle Routing Problem in Logistics considering Path Interruption
Yong Zhang
2017-01-01
Full Text Available The application of automated vehicles in logistics can efficiently reduce the cost of logistics and reduce the potential risks in the last mile. Considering the path restriction in the initial stage of the application of automated vehicles in logistics, the conventional model for a vehicle routing problem (VRP is modified. Thus, the automated vehicle routing problem with time windows (AVRPTW model considering path interruption is established. Additionally, an improved particle swarm optimisation (PSO algorithm is designed to solve this problem. Finally, a case study is undertaken to test the validity of the model and the algorithm. Four automated vehicles are designated to execute all delivery tasks required by 25 stores. Capacities of all of the automated vehicles are almost fully utilised. It is of considerable significance for the promotion of automated vehicles in last-mile situations to develop such research into real problems arising in the initial period.
A branch-and-cut algorithm for the elementary shortest path problem with resource constraints
Jepsen, Mads Kehlet; Petersen, Bjørn; Spoorendonk, Simon
The elementary shortest path with resource constraints have commonly been solved with dynamic programming algorithms. Assuming an undirected graph, we present a compact formulation of this problem and a branch-and-cut algorithm to solve it. Two types of resources are discussed: a capacity...... and a fixed charge resource. The former is the subproblem of the capacitated vehicle routing problem and the latter is from the split delivery version. Computational results are presented and compared to dynamic programming algorithms....
A Path Based Model for a Green Liner Shipping Network Design Problem
Mads K. Jepsen; Berit Lofstedt; Christian E. M. Plum; David Pisinger; Mikkel M. Sigurd
2011-01-01
Liner shipping networks are the backbone of international trade providing low transportation cost, which is a major driver of globalization. These networks are under constant pressure to deliver capacity, cost effectiveness and environmentally conscious transport solutions. This article proposes a new path based MIP model for the Liner shipping Network Design Problem minimizing the cost of vessels and their fuel consumption facilitating a green network. The proposed model reduces problem size...
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
V.PURUSHOTHAM REDDY
2011-02-01
Full Text Available In computer networks the routing is based on shortest path routing algorithms. Based on its advantages, an alternative method is used known as Genetic Algorithm based routing algorithm, which is highly scalable and insensitive to variations in network topology. Here we propose a coarse-grained parallel genetic algorithm to solve the shortest path routing problem with the primary goal of computation time reduction along with the use of migration scheme. This algorithm is developed and implemented on an MPI cluster. The effects of migration and its performance is studied in this paper.
A Bio-Inspired Method for the Constrained Shortest Path Problem
Hongping Wang
2014-01-01
optimization, crew scheduling, network routing and so on. It is an open issue since it is a NP-hard problem. In this paper, we propose an innovative method which is based on the internal mechanism of the adaptive amoeba algorithm. The proposed method is divided into two parts. In the first part, we employ the original amoeba algorithm to solve the shortest path problem in directed networks. In the second part, we combine the Physarum algorithm with a bio-inspired rule to deal with the CSP. Finally, by comparing the results with other method using an examples in DCLC problem, we demonstrate the accuracy of the proposed method.
The Shortest Path Problems in Battery-Electric Vehicle Dispatching with Battery Renewal
Minfang Huang
2016-06-01
Full Text Available Electric vehicles play a key role for developing an eco-sustainable transport system. One critical component of an electric vehicle is its battery, which can be quickly charged or exchanged before it runs out. The problem of electric vehicle dispatching falls into the category of the shortest path problem with resource renewal. In this paper, we study the shortest path problems in (1 electric transit bus scheduling and (2 electric truck routing with time windows. In these applications, a fully-charged battery allows running a limited operational distance, and the battery before depletion needs to be quickly charged or exchanged with a fully-charged one at a battery management facility. The limited distance and battery renewal result in a shortest path problem with resource renewal. We develop a label-correcting algorithm with state space relaxation to find optimal solutions. In the computational experiments, real-world road geometry data are used to generate realistic travel distances, and other types of data are obtained from the real world or randomly generated. The computational results show that the label-correcting algorithm performs very well.
Evolutionary path control strategy for solving many-objective optimization problem.
Roy, Proteek Chandan; Islam, Md Monirul; Murase, Kazuyuki; Yao, Xin
2015-04-01
The number of objectives in many-objective optimization problems (MaOPs) is typically high and evolutionary algorithms face severe difficulties in solving such problems. In this paper, we propose a new scalable evolutionary algorithm, called evolutionary path control strategy (EPCS), for solving MaOPs. The central component of our algorithm is the use of a reference vector that helps simultaneously minimizing all the objectives of an MaOP. In doing so, EPCS employs a new fitness assignment strategy for survival selection. This strategy consists of two procedures and our algorithm applies them sequentially. It encourages a population of solutions to follow a certain path reaching toward the Pareto optimal front. The essence of our strategy is that it reduces the number of nondominated solutions to increase selection pressure in evolution. Furthermore, unlike previous work, EPCS is able to apply the classical Pareto-dominance relation with the new fitness assignment strategy. Our algorithm has been tested extensively on several scalable test problems, namely five DTLZ problems with 5 to 40 objectives and six WFG problems with 2 to 13 objectives. Furthermore, the algorithm has been tested on six CEC09 problems having 2 or 3 objectives. The experimental results show that EPCS is capable of finding better solutions compared to other existing algorithms for problems with an increasing number of objectives.
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.
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.
Efficient algorithms for the reverse shortest path problem on trees under the hamming distance
Tayyebi Javad
2017-01-01
Full Text Available Given a network G(V,A,c and a collection of origin-destination pairs with prescribed values, the reverse shortest path problem is to modify the arc length vector c as little as possible under some bound constraints such that the shortest distance between each origin-destination pair is upper bounded by the corresponding prescribed value. It is known that the reverse shortest path problem is NP-hard even on trees when the arc length modifications are measured by the weighted sum-type Hamming distance. In this paper, we consider two special cases of this problem which are polynomially solvable. The first is the case with uniform lengths. It is shown that this case transforms to a minimum cost flow problem on an auxiliary network. An efficient algorithm is also proposed for solving this case under the unit sum-type Hamming distance. The second case considered is the problem without bound constraints. It is shown that this case is reduced to a minimum cut problem on a tree-like network. Therefore, both cases studied can be solved in strongly polynomial time.
The d-edge shortest-path problem for a Monge graph
Bein, W.W. [New Mexico Univ., Albuquerque, NM (United States). Dept. of Computer Science; Larmore, L.L. [California Univ., Riverside, CA (United States). Dept. of Computer Science; Park, J.K. [Sandia National Labs.,Albuquerque, NM (United States)
1992-07-14
A complete edge-weighted directed graph on vertices 1,2,...,n that assigns cost c(i,j) to the edge (i,j) is called Monge if its edge costs form a Monge array, i.e., for all i < k and j < l, c[i, j]+c[k,l]{le} < c[i,l]+c[k,j]. One reason Monge graphs are interesting is that shortest paths can be computed quite quickly in such graphs. In particular, Wilber showed that the shortest path from vertex 1 to vertex n of a Monge graph can be computed in O(n) time, and Aggarwal, Klawe, Moran, Shor, and Wilber showed that the shortest d-edge 1-to-n path (i.e., the shortest path among all 1-to-n paths with exactly d edges) can be computed in O(dn) time. This paper`s contribution is a new algorithm for the latter problem. Assuming 0 {le} c[i,j] {le} U and c[i,j + 1] + c[i + 1,j] {minus} c[i,j] {minus} c[i + 1, j + 1] {ge} L > 0 for all i and j, our algorithm runs in O(n(1 + 1g(U/L))) time. Thus, when d {much_gt} 1 + 1g(U/L), our algorithm represents a significant improvement over Aggarwal et al.`s O(dn)-time algorithm. We also present several applications of our algorithm; they include length-limited Huffman coding, finding the maximum-perimeter d-gon inscribed in a given convex n-gon, and a digital-signal-compression problem.
HAMILTONIAN DECOMPOSITION OF COMPLETE BIPARTITE r-HYPERGRAPHS
吉日木图; 王建方
2001-01-01
In [1] the concepts of paths and cycles of a hypergraph were introduced. In this paper, we give the concepts for bipartite hypergraph and Hamiltonian paths and cycles of a hypergraph,and prove that the complete bipartite 3-hypergraph with q vertices in each part is Hamiltonian decomposable where q is a prime.
A path based model for a green liner shipping network design problem
Jepsen, Mads Kehlet; Brouer, Berit Dangaard; Plum, Christian Edinger Munk
2011-01-01
Liner shipping networks are the backbone of international trade providing low transportation cost, which is a major driver of globalization. These networks are under constant pressure to deliver capacity, cost effectiveness and environmentally conscious transport solutions. This article proposes...... a new path based MIP model for the Liner shipping Network Design Problem minimizing the cost of vessels and their fuel consumption facilitating a green network. The proposed model reduces problem size using a novel aggregation of demands. A decomposition method enabling delayed column generation...
A minimum resource neural network framework for solving multiconstraint shortest path problems.
Zhang, Junying; Zhao, Xiaoxue; He, Xiaotao
2014-08-01
Characterized by using minimum hard (structural) and soft (computational) resources, a novel parameter-free minimal resource neural network (MRNN) framework is proposed for solving a wide range of single-source shortest path (SP) problems for various graph types. The problems are the k-shortest time path problems with any combination of three constraints: time, hop, and label constraints, and the graphs can be directed, undirected, or bidirected with symmetric and/or asymmetric traversal time, which can be real and time dependent. Isomorphic to the graph where the SP is to be sought, the network is activated by generating autowave at source neuron and the autowave travels automatically along the paths with the speed of a hop in an iteration. Properties of the network are studied, algorithms are presented, and computation complexity is analyzed. The framework guarantees globally optimal solutions of a series of problems during the iteration process of the network, which provides insight into why even the SP is still too long to be satisfied. The network facilitates very large scale integrated circuit implementation and adapt to very large scale problems due to its massively parallel processing and minimum resource utilization. When implemented in a sequentially processing computer, experiments on synthetic graphs, road maps of cities of the USA, and vehicle routing with time windows indicate that the MRNN is especially efficient for large scale sparse graphs and even dense graphs with some constraints, e.g., the CPU time taken and the iteration number used for the road maps of cities of the USA is even less than ∼ 2% and 0.5% that of the Dijkstra's algorithm.
Nair, T R Gopalakrishnan; Yashoda, M B
2011-01-01
In Internet Routing, the static shortest path (SP) problem has been addressed using well known intelligent optimization techniques like artificial neural networks, genetic algorithms (GAs) and particle swarm optimization. Advancement in wireless communication lead more and more mobile wireless networks, such as mobile networks [mobile ad hoc networks (MANETs)] and wireless sensor networks. Dynamic nature of the network is the main characteristic of MANET. Therefore, the SP routing problem in MANET turns into dynamic optimization problem (DOP). Here the nodes ae made aware of the environmental condition, thereby making it intelligent, which goes as the input for GA. The implementation then uses GAs with immigrants and memory schemes to solve the dynamic SP routing problem (DSPRP) in MANETS. In our paper, once the network topology changes, the optimal solutions in the new environment can be searched using the new immigrants or the useful information stored in the memory. Results shows GA with new immigrants sho...
Plum, Christian Edinger Munk; Pisinger, David; Salazar-González, Juan-José
2012-01-01
commercial constraints. Inspiration for formulation and solution method is taken from the rich research done within pickup and delivery problems. The problem, the multicommodity one-toone pickup and delivery traveling salesman problem with path duration limits is, to the best of out knowledge, considered...... for the first time. An arc flow and a path flow model are presented. A Branch and Cut and Price solution method is proposed and implemented....
Momentum and hamiltonian in complex action theory
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...
Cutting path as a Rural Postman Problem: solutions by Memetic Algorithms
Ana Maria Rodrigues
2012-01-01
Full Text Available The Rural Postman Problem (RPP is a particular Arc Routing Problem (ARP which consists of determining a minimum cost circuit on a graph so that a given subset of required edges is traversed. The RPP is an NP-hard problem with significant real-life applications. This paper introduces an original approach based on Memetic Algorithms - the MARP algorithm - to solve the RPP and, also deals with an interesting Industrial Application, which focuses on the path optimization for component cutting operations. Memetic Algorithms are a class of Metaheuristics which may be seen as a population strategy that involves cooperation and competition processes between population elements and integrates “social knowledge”, using a local search procedure. The MARP algorithm is tested with different groups of instances and the results are compared with those gathered from other publications. MARP is also used in the context of various real-life applications.
A decomposition based on path sets for the Multi-Commodity k-splittable Maximum Flow Problem
Gamst, Mette
Switching. In the literature, the problem is solved to optimality using branch-and-price algorithms built on path-based Dantzig-Wolfe decompositions. This paper proposes a new branch-and-price algorithm built on a path set-based Dantzig-Wolfe decomposition. A path set consists of up to k paths, each...... carrying a certain amount of flow. The new branch-and-price algorithm is implemented and compared to the leading algorithms in the literature. Results for the proposed method are competitive and the method even has best performance on some instances. However, the results also indicate some scaling issues....
A genetic algorithm for the pareto optimal solution set of multi-objective shortest path problem
HU Shi-cheng; XU Xiao-fei; ZHAN De-chen
2005-01-01
Unlike the shortest path problem that has only one optimal solution and can be solved in polynomial time, the multi-objective shortest path problem (MSPP) has a set of pareto optimal solutions and cannot be solved in polynomial time. The present algorithms focused mainly on how to obtain a precisely pareto optimal solution for MSPP resulting in a long time to obtain multiple pareto optimal solutions with them. In order to obtain a set of satisfied solutions for MSPP in reasonable time to meet the demand of a decision maker, a genetic algorithm MSPP-GA is presented to solve the MSPP with typically competing objectives, cost and time, in this paper. The encoding of the solution and the operators such as crossover, mutation and selection are developed.The algorithm introduced pareto domination tournament and sharing based selection operator, which can not only directly search the pareto optimal frontier but also maintain the diversity of populations in the process of evolutionary computation. Experimental results show that MSPP-GA can obtain most efficient solutions distributed all along the pareto frontier in less time than an exact algorithm. The algorithm proposed in this paper provides a new and effective method of how to obtain the set of pareto optimal solutions for other multiple objective optimization problems in a short time.
An efficient algorithm for the vertex-disjoint paths problem in random graphs
Broder, A.Z. [Digital Systems Research Center, Palo Alto, CA (United States); Frieze, A.M.; Suen, S. [Carnegie-Mellon Univ., Pittsburgh, PA (United States); Upfal, E. [IBM Almaden Research Center, San Jose, CA (United States)
1996-12-31
Given a graph G = (V, E) and a set of pairs of vertices in V, we are interested in finding for each pair (a{sub i}, b{sub i}) a path connecting a{sub i} to b{sub i}, such that the set of paths so found is vertex-disjoint. (The problem is NP-complete for general graphs as well as for planar graphs. It is in P if the number of pairs is fixed.) Our model is that the graph is chosen first, then an adversary chooses the pairs of endpoints, subject only to obvious feasibility constraints, namely, all pairs must be disjoint, no more than a constant fraction of the vertices could be required for the paths, and not {open_quotes}too many{close_quotes} neighbors of a vertex can be endpoints. We present a randomized polynomial time algorithm that works for almost all graphs; more precisely in the G{sub n,m} or G{sub n,p} models, the algorithm succeeds with high probability for all edge densities above the connectivity threshold. The set of pairs that can be accommodated is optimal up to constant factors. Although the analysis is intricate, the algorithm itself is quite simple and suggests a practical heuristic. We include two applications of the main result, one in the context of circuit switching communication, the other in the context of topological embeddings of graphs.
Wiener, J M; Ehbauer, N N; Mallot, H A
2009-09-01
For large numbers of targets, path planning is a complex and computationally expensive task. Humans, however, usually solve such tasks quickly and efficiently. We present experiments studying human path planning performance and the cognitive processes and heuristics involved. Twenty-five places were arranged on a regular grid in a large room. Participants were repeatedly asked to solve traveling salesman problems (TSP), i.e., to find the shortest closed loop connecting a start location with multiple target locations. In Experiment 1, we tested whether humans employed the nearest neighbor (NN) strategy when solving the TSP. Results showed that subjects outperform the NN-strategy, suggesting that it is not sufficient to explain human route planning behavior. As a second possible strategy we tested a hierarchical planning heuristic in Experiment 2, demonstrating that participants first plan a coarse route on the region level that is refined during navigation. To test for the relevance of spatial working memory (SWM) and spatial long-term memory (LTM) for planning performance and the planning heuristics applied, we varied the memory demands between conditions in Experiment 2. In one condition the target locations were directly marked, such that no memory was required; a second condition required participants to memorize the target locations during path planning (SWM); in a third condition, additionally, the locations of targets had to retrieved from LTM (SWM and LTM). Results showed that navigation performance decreased with increasing memory demands while the dependence on the hierarchical planning heuristic increased.
Jean Chamberlain Chedjou
2015-01-01
Full Text Available This paper develops a flexible analytical concept for robust shortest path detection in dynamically reconfigurable graphs. The concept is expressed by a mathematical model representing the shortest path problem solver. The proposed mathematical model is characterized by three fundamental parameters expressing (a the graph topology (through the “incidence matrix”, (b the edge weights (with dynamic external weights’ setting capability, and (c the dynamic reconfigurability through external input(s of the source-destination nodes pair. In order to demonstrate the universality of the developed concept, a general algorithm is proposed to determine the three fundamental parameters (of the mathematical model developed for all types of graphs regardless of their topology, magnitude, and size. It is demonstrated that the main advantage of the developed concept is that arc costs, the origin-destination pair setting, and the graph topology are dynamically provided by external commands, which are inputs of the shortest path solver model. This enables high flexibility and full reconfigurability of the developed concept, without any retraining need. To validate the concept developed, benchmarking is performed leading to a comparison of its performance with the performances of two well-known concepts based on neural networks.
An anticipation mechanism for the shortest path problem based on Physarum polycephalum
Wang, Qing; Lu, Xi; Zhang, Xiaoge; Deng, Yong; Xiao, Can
2015-04-01
In this paper, we put forward an anticipation mechanism for the existing Physarum-inspired shortest path finding method. The Physarum-based shortest path finding model can be implemented by an iterative algorithm and has wide applications in many fundamental network optimization problems. In this paper, we mainly focus on the Physarum-inspired shortest path tree model. Normally, we stop the program when the difference between two consecutive iterations is less than a predefined threshold. However, we do not know how to set the specific value for the threshold variable. In order to find out the optimal solution, we need to set the threshold as a very small number. This in turn will consume a lot of time. From this point of view, this algorithm lacks an efficient and reliable mechanism to judge when the optimal solution will be found. In this paper, we introduce an anticipation mechanism to address this issue. Numerical examples are used to demonstrate its reliability and efficiency.
Runtime analysis of ant colony optimization on dynamic shortest path problems
Lissovoi, Andrei; Witt, Carsten
2015-01-01
A simple ACO algorithm called lambda-MMAS for dynamic variants of the single-destination shortest paths problem is studied by rigorous runtime analyses. Building upon previous results for the special case of 1-MMAS, it is studied to what extent an enlarged colony using lambda ants per vertex helps...... in tracking an oscillating optimum. It is shown that easy cases of oscillations can be tracked by a constant number of ants. However, the paper also identifies more involved oscillations that with overwhelming probability cannot be tracked with any polynomial-size colony. Finally, parameters of dynamic...
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...
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.
An Investigation of Using Parallel Genetic Algorithm for Solving the Shortest Path Routing Problem
Salman Yussof
2011-01-01
Full Text Available Problem statement: Shortest path routing is the type of routing widely used in computer network nowadays. Even though shortest path routing algorithms are well established, other alternative methods may have their own advantages. One such alternative is to use a GA-based routing algorithm. According to previous researches, GA-based routing algorithm has been found to be more scalable and insensitive to variations in network topologies. However, it is also known that GA-based routing algorithm is not fast enough for real-time computation. Approach: To improve the computation time of GA-based routing algorithm, this study proposes a coarse-grained parallel GA routing algorithm for solving the shortest path routing problem. The proposed algorithm is evaluated using simulation where the proposed algorithm is executed on networks with various topologies and sizes. The parallel computation is performed using an MPI cluster. Three different experiments were conducted to identify the best value for the migration rate, the accuracy and execution time with respect to the number of computing nodes and speedup achieved as compared to the serial version of the same algorithm. Results: The result of the simulation shows that the best result is achieved for a migration rate around 0.1 and 0.2. The experiments also show that with larger number of computing nodes, accuracy decreases linearly, but computation time decreases exponentially, which justifies the use parallel implementation of GA to improve the speed of GA-based routing algorithm. Finally, the experiments also show that the proposed algorithm is able to achieve a speedup of up to 818.11% on the MPI cluster used to run the simulation. Conclusion/Recommendations: We have successfully shown that the performance of GA-based shortest path routing algorithm can be improved by using a coarse-grained parallel GA implementation. Even though in this study the proposed algorithm is executed
Rahul Sharma; Subbajit Nandy; S P Bhattacharyya
2006-06-01
An energy-dependent partitioning scheme is explored for extracting a small number of eigenvalues of a real symmetric matrix with the help of genetic algorithm. The proposed method is tested with matrices of different sizes (30 × 30 to 1000 × 1000). Comparison is made with Löwdin's strategy for solving the problem. The relative advantages and disadvantages of the GA-based method are analyzed.
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.
Dynamical stability of Hamiltonian systems
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.
Hamiltonian systems as selfdual equations
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.
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.
Numerical continuation methods for dynamical systems path following and boundary value problems
Krauskopf, Bernd; Galan-Vioque, Jorge
2007-01-01
Path following in combination with boundary value problem solvers has emerged as a continuing and strong influence in the development of dynamical systems theory and its application. It is widely acknowledged that the software package AUTO - developed by Eusebius J. Doedel about thirty years ago and further expanded and developed ever since - plays a central role in the brief history of numerical continuation. This book has been compiled on the occasion of Sebius Doedel''s 60th birthday. Bringing together for the first time a large amount of material in a single, accessible source, it is hoped that the book will become the natural entry point for researchers in diverse disciplines who wish to learn what numerical continuation techniques can achieve. The book opens with a foreword by Herbert B. Keller and lecture notes by Sebius Doedel himself that introduce the basic concepts of numerical bifurcation analysis. The other chapters by leading experts discuss continuation for various types of systems and objects ...
Solving the replacement paths problem for planar directed graphs in O(n logn) time
Wulff-Nilsen, Christian
2010-01-01
In a graph G with non-negative edge lengths, let P be a shortest path from a vertex s to a vertex t. We consider the problem of computing, for each edge e on P, the length of a shortest path in G from s to t that avoids e. This is known as the replacement paths problem. We give a linearspace algo...
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.
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...
Wan-Yu Liu
2014-07-01
Full Text Available Torespondto the reduction of greenhouse gas emissions and global warming, this paper investigates the minimal-carbon-footprint time-dependent heterogeneous-fleet vehicle routing problem with alternative paths (MTHVRPP. This finds a route with the smallestcarbon footprint, instead of the shortestroute distance, which is the conventional approach, to serve a number of customers with a heterogeneous fleet of vehicles in cases wherethere may not be only one path between each pair of customers, and the vehicle speed differs at different times of the day. Inheriting from the NP-hardness of the vehicle routing problem, the MTHVRPP is also NP-hard. This paper further proposes a genetic algorithm (GA to solve this problem. The solution representedbyour GA determines the customer serving ordering of each vehicle type. Then, the capacity check is used to classify multiple routes of each vehicle type, and the path selection determines the detailed paths of each route. Additionally, this paper improves the energy consumption model used for calculating the carbon footprint amount more precisely. Compared with the results without alternative paths, our experimental results show that the alternative path in this experimenthas a significant impact on the experimental results in terms of carbon footprint.
Subbaraj Potti
2011-01-01
Full Text Available Problem statement: A new multi-objective approach, Strength Pareto Evolutionary Algorithm (SPEA, is presented in this paper to solve the shortest path routing problem. The routing problem is formulated as a multi-objective mathematical programming problem which attempts to minimize both cost and delay objectives simultaneously. Approach: SPEA handles the shortest path routing problem as a true multi-objective optimization problem with competing and noncommensurable objectives. Results: SPEA combines several features of previous multi-objective evolutionary algorithms in a unique manner. SPEA stores nondominated solutions externally in another continuously-updated population and uses a hierarchical clustering algorithm to provide the decision maker with a manageable pareto-optimal set. SPEA is applied to a 20 node network as well as to large size networks ranging from 50-200 nodes. Conclusion: The results demonstrate the capabilities of the proposed approach to generate true and well distributed pareto-optimal nondominated solutions.
EXTENDED CASIMIR APPROACH TO CONTROLLED HAMILTONIAN SYSTEMS
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.
Rudowicz, Czesław, E-mail: crudowicz@zut.edu.pl [Institute of Physics, West Pomeranian University of Technology, Al. Piastów 17, 70-310 Szczecin (Poland); Karbowiak, Mirosław [Faculty of Chemistry, University of Wrocław, ul. F. Joliot-Curie 14, 50-383 Wrocław (Poland)
2014-10-15
The single transition ions in various crystals or molecules as well as the exchange coupled systems (ECS) of transition ions, especially the single molecule magnets (SMM) or molecular nanomagnets (MNM), have been extensively studied in recent decades using electron magnetic resonance (EMR), optical spectroscopy, and magnetic measurements. Interpretation of magnetic and spectroscopic properties of transition ions is based on two physically distinct types of Hamiltonians: the physical crystal field (CF), or equivalently ligand field (LF), Hamiltonians and the effective spin Hamiltonians (SH), which include the zero-field splitting (ZFS) Hamiltonians. Survey of recent literature has revealed a number of terminological confusions and specific problems occurring at the interface between these Hamiltonians (denoted CF (LF)↔SH (ZFS)). Elucidation of sloppy or incorrect usage of crucial notions, especially those describing or parameterizing crystal fields and zero field splittings, is a very challenging task that requires several reviews. Here we focus on the prevailing confusion between the CF (LF) and SH (ZFS) quantities, denoted as the CF=ZFS confusion, which consists in referring to the parameters (or Hamiltonians), which are the true ZFS (or SH) quantities, as purportedly the CF (LF) quantities. The inverse ZFS=CF confusion, which pertains to the cases of labeling the true CF (LF) quantities as purportedly the ZFS quantities, is considered in a follow-up paper. The two reviews prepare grounds for a systematization of nomenclature aimed at bringing order to the zoo of different Hamiltonians. Specific cases of the CF=ZFS confusion identified in the recent textbooks, review articles, and SMM (MNM)- and EMR-related papers are surveyed and the pertinent misconceptions are outlined. The consequences of the terminological confusions go far beyond simple semantic issues or misleading keyword classifications of papers in journals and scientific databases. Serious
On the direct path problem of s-elementary frame wavelets
无
2010-01-01
In this paper, we discuss the path-connectivity between two s-elementary normalized tight frame wavelets via the so-called direct paths. We show that the existence of such a direct path is equivalent to the non-existence of an atom of a σ-algebra defined over the defining sets of the corresponding frame wavelets, using a mapping defined by the natural translation and dilation operations between the sets. In particular, this gives an equivalent condition for the existence of a direct path between two s-elementary wavelets.
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....
MULTICRITERIА PROBLEM OF FINDING THE OPTIMAL PATHS FOR LARGE-SCALE TRANSPORT SYSTEM
Pavlov D. A.
2015-11-01
Full Text Available This article explores the multicriteria problems arise in the organization of routes in large-scale transport management system. As a mathematical tool for constructing a model, we were using the prefractal graphs. Prefractal graphs naturally reflect structure of the device of communications of transport system, reflecting its important features – locality and differentiation. Locality is provided with creation of internal routes (city, raionwide, etc.. Differentiation is understood as division of routes on intra regional, interregional and international. The objective is reduced to a covering of prefractal graphs by the simple paths which are crossed on edges and nodes. On the set of feasible solutions, vector criterion function with certain criteria is based. In concepts of transport system, the given criteria have concrete substantial interpretation, the transport routes allowing to design considering features of system. In this article, we construct polynomial algorithms for finding optimal according to certain criteria decision. By the criteria which aren't optimizing the allocated routes their estimates of the lower and upper bounds are given. On all given algorithms the estimates of computing complexity confirming advantage of use of methods of prefractal and fractal graphs before classical methods of the theory of graphs are constructed and proved
Families of graph-different Hamilton paths
Körner, János; Simonyi, Gábor
2011-01-01
Let D be an arbitrary subset of the natural numbers. For every n, let M(n;D) be the maximum of the cardinality of a set of Hamiltonian paths in the complete graph K_n such that the union of any two paths from the family contains a not necessarily induced cycle of some length from D. We determine or bound the asymptotics of M(n;D) in various special cases. This problem is closely related to that of the permutation capacity of graphs and constitutes a further extension of the problem area around Shannon capacity. We also discuss how to generalize our cycle-difference problems and present an example where cycles are replaced by 4-cliques. These problems are in a natural duality to those of graph intersection, initiated by Erd\\"os, Simonovits and S\\'os. The lack of kernel structure as a natural candidate for optimum makes our problems quite challenging.
Output-threshold coupled neural network for solving the shortest path problems
ZHANG Junying; WANG Defeng; SHI Meihong; WANG Joseph Yue
2004-01-01
This paper presents a coupled neural network, called output-threshold coupled neural network (OTCNN), which can mimic the autowaves in the present pulsed coupled neural networks (PCNNs), by the construction of mutual coupling between neuron outputs and the threshold of a neuron. Based on its autowaves, this paper presents a method for finding the shortest path in shortest time with OTCNNs. The method presented here features much fewer neurons needed, simplicity of the structure of the neurons and the networks, and large scale of parallel computation. It is shown that OTCNN is very effective in finding the shortest paths from a single start node to multiple destination nodes for asymmetric weighted graph, with a number of iterations proportional only to the length of the shortest paths, but independent of the complexity of the graph and the total number of existing paths in the graph. Finally, examples for finding the shortest path are presented.
Harmonic bath averaged Hamiltonian: an efficient tool to capture quantum effects of large systems.
Yang, Yonggang; Liu, Xiaomeng; Meuwly, Markus; Xiao, Liantuan; Jia, Suotang
2012-11-26
Starting from a reaction path Hamiltonian, a suitably reduced harmonic bath averaged Hamiltonian is derived by averaging over all the normal mode coordinates. Generalization of the harmonic bath averaged Hamiltonian to any dimensions are performed and the feasibility to use a linear reaction path/surface are investigated and discussed. By use of a harmonic bath averaged Hamiltonian, the tunneling splitting and proton transfer dynamics of malonaldehyde is briefly discussed and shows that the harmonic bath averaged Hamiltonian is an efficient tool to capture quantum effects in larger systems.
Reaction Path Optimization with Holonomic Constraints and Kinetic Energy Potentials.
Brokaw, Jason B; Haas, Kevin R; Chu, Jhih-Wei
2009-08-11
Two methods are developed to enhance the stability, efficiency, and robustness of reaction path optimization using a chain of replicas. First, distances between replicas are kept equal during path optimization via holonomic constraints. Finding a reaction path is, thus, transformed into a constrained optimization problem. This approach avoids force projections for finding minimum energy paths (MEPs), and fast-converging schemes such as quasi-Newton methods can be readily applied. Second, we define a new objective function - the total Hamiltonian - for reaction path optimization, by combining the kinetic energy potential of each replica with its potential energy function. Minimizing the total Hamiltonian of a chain determines a minimum Hamiltonian path (MHP). If the distances between replicas are kept equal and a consistent force constant is used, then the kinetic energy potentials of all replicas have the same value. The MHP in this case is the most probable isokinetic path. Our results indicate that low-temperature kinetic energy potentials (optimization and can significantly reduce the required steps of minimization by 2-3 times without causing noticeable differences between a MHP and MEP. These methods are applied to three test cases, the C7eq-to-Cax isomerization of an alanine dipeptide, the (4)C1-to-(1)C4 transition of an α-d-glucopyranose, and the helix-to-sheet transition of a GNNQQNY heptapeptide. By applying the methods developed in this work, convergence of reaction path optimization can be achieved for these complex transitions, involving full atomic details and a large number of replicas (>100). For the case of helix-to-sheet transition, we identify pathways whose energy barriers are consistent with experimental measurements. Further, we develop a method based on the work energy theorem to quantify the accuracy of reaction paths and to determine whether the atoms used to define a path are enough to provide quantitative estimation of energy barriers.
Yunjuan WANG; Detong ZHU
2008-01-01
Based on a differentiable merit function proposed by Taji et al.in "Math.Prog. Stud.,58,1993,369-383",the authors propose an affine scaling interior trust region strategy via optimal path to modify Newton method for the strictly monotone variational inequality problem subject to linear equality and inequality constraints.By using the eigensystem decomposition and affine scaling mapping,the authors form an affine scaling optimal curvilinear path very easily in order to approximately solve the trust region subproblem.Theoretical analysis is given which shows that the proposed algorithm is globally convergent and has a local quadratic convergence rate under some reasonable conditions.
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.
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.
Indirect quantum tomography of quadratic Hamiltonians
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.
Dicycle Cover of Hamiltonian Oriented Graphs
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.
Pizzini, Edward L.; Shepardson, Daniel P.
The classroom dynamics (class setting, lesson structure, student interactions, and student behaviors) of a traditional laboratory and a problem-solving Search, Solve, Create, and Share (SSCS) model of instruction were compared using path analysis. Class setting was based on small-group/large-group settings. Lesson structure variables were problem finding/refining, research designing, data collecting, data analyzing, and evaluating. The student-student interactions variable was determined by student-student responding, student-student initiating, and student (self-) interaction; while the teacher-student interaction variable was based on teacher-student initiating and teacher-student responding. The dependent variables of student behavior consisted of attending, responding, following, soliciting, and giving. A causal model was hypothesized for both instructional models based on the independent and dependent variables. The hypothesized causal model was tested using path-analysis procedures described by Pedhazur (1982). The hypothesized causal models were adjusted based on path coefficients with levels of significance greater than p = 0.05. While the descriptive data indicated a similarity in the classroom dynamics of the two instructional models, path analysis indicated a difference in the classroom dynamics. In the traditional laboratory model, student behaviors did not correlate to lesson structure, class setting, or student interactions, whereas in the SSCS problem-solving model student behaviors correlated to aspects of the lesson structure, class setting, and student interactions.
Maslov P-Index Theory for a Symplectic Path with Applications
Chungen LIU
2006-01-01
The Maslov P-index theory for a symplectic path is defined. Various properties of this index theory such as homotopy invariant, symplectic additivity and the relations with other Morse indices are studied. As an application, the non-periodic problem for some asymptotically linear Hamiltonian systems is considered.
Coherent-state path integrals in the continuum: The SU(2) case
Kordas, G.; Kalantzis, D.; Karanikas, A. I.
2016-09-01
We define the time-continuous spin coherent-state path integral in a way that is free from inconsistencies. The proposed definition is used to reproduce known exact results. Such a formalism opens new possibilities for applying approximations with improved accuracy and can be proven useful in a great variety of problems where spin Hamiltonians are used.
AN AUTOMATED REFERENCE POINT-LIKE APPROACH FOR MULTICRITERIA SHORTEST PATH PROBLEMS
Jo(a)o C. N. CL(I)ACO; José M. F. CRAVEIRINHA; Marta M. B. PASCOAL
2006-01-01
In this paper we introduce a method of analysis for the automated ordering and selection of solutions of a multicriteria shortest path model. The method is based on a reference point approach, where the paths in a specific priority region are ranked by non-decreasing order of a Chebyshev metric.In order to list paths according with this objective function a labelling algorithm is proposed. The developed method is applied in a video-traffic routing context. Computational results are presented and analysed, for randomly generated networks of significant dimension.
Reliable Path Selection Problem in Uncertain Traffic Network after Natural Disaster
Jing Wang
2013-01-01
Full Text Available After natural disaster, especially for large-scale disasters and affected areas, vast relief materials are often needed. In the meantime, the traffic networks are always of uncertainty because of the disaster. In this paper, we assume that the edges in the network are either connected or blocked, and the connection probability of each edge is known. In order to ensure the arrival of these supplies at the affected areas, it is important to select a reliable path. A reliable path selection model is formulated, and two algorithms for solving this model are presented. Then, adjustable reliable path selection model is proposed when the edge of the selected reliable path is broken. And the corresponding algorithms are shown to be efficient both theoretically and numerically.
Partial path column generation for the vehicle routing problem with time windows
Petersen, Bjørn; Jepsen, Mads Kehlet
2009-01-01
number of customers. We suggest to relax that ‘each column is a route’ into ‘each column is a part of the giant tour’; a so-called partial path, i.e., not necessarily starting and ending in the depot. This way, the length of the partial path can be bounded and a better control of the size of the solution...
A linear programming formulation of Mader's edge-disjoint paths problem
Keijsper, J.C.M.; Pendavingh, R.A.; Stougie, L.
2006-01-01
We give a dual pair of linear programs for a minâ€“max result of Mader describing the maximum number of edge-disjoint T-paths in a graph G=(V,E) with TV. We conclude that there exists a polynomial-time algorithm (based on the ellipsoid method) for finding the maximum number of T-paths in a
Diagonalization of Hamiltonian; Diagonalization of Hamiltonian
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.
Shek, Daniel T L; Yu, Lu
2011-03-07
The present study attempts to examine the longitudinal impact of a curriculum-based positive youth development program, entitled the Project P.A.T.H.S. (Positive Adolescent Training through Holistic Social Programmes), on adolescent problem behavior in Hong Kong. Using a longitudinal randomized group design, six waves of data were collected from 19 experimental schools (n = 3,797 at Wave 1) in which students participated in the Project P.A.T.H.S. and 24 control schools (n = 4,049 at Wave 1). At each wave, students responded to questions asking about their current problem behaviors, including delinquency and use of different types of drugs, and their intentions of engaging in such behaviors in the future. Results based on individual growth curve modeling generally showed that the participants displayed lower levels of substance abuse and delinquent behavior than did the control students. Participants who regarded the program to be helpful also showed lower levels of problem behavior than did the control students. The present findings suggest that the Project P.A.T.H.S. is effective in preventing adolescent problem behavior in the junior secondary school years.
Daniel T. L. Shek
2011-01-01
Full Text Available The present study attempts to examine the longitudinal impact of a curriculum-based positive youth development program, entitled the Project P.A.T.H.S. (Positive Adolescent Training through Holistic Social Programmes, on adolescent problem behavior in Hong Kong. Using a longitudinal randomized group design, six waves of data were collected from 19 experimental schools (n = 3,797 at Wave 1 in which students participated in the Project P.A.T.H.S. and 24 control schools (n = 4,049 at Wave 1. At each wave, students responded to questions asking about their current problem behaviors, including delinquency and use of different types of drugs, and their intentions of engaging in such behaviors in the future. Results based on individual growth curve modeling generally showed that the participants displayed lower levels of substance abuse and delinquent behavior than did the control students. Participants who regarded the program to be helpful also showed lower levels of problem behavior than did the control students. The present findings suggest that the Project P.A.T.H.S. is effective in preventing adolescent problem behavior in the junior secondary school years.
A Hamiltonian approach to Thermodynamics
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.
CAI Liang; ZHANG Ping; YANG Tao; PAN Xiao-Yin
2011-01-01
By using the path integral approach, we investigate the problem of Hooke's atom (two electrons interacting with Coulomb potential in an external harmonic-oscillator potential) in an arbitrary time-dependent electric field. For a certain infinite set of discrete oscillator frequencies, we obtain the analytical solutions. The ground state polarization of the atom is then calculated. The same result is also obtained through linear response theory.
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 ...
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.
A Quantum Algorithm for the Hamiltonian NAND Tree
Farhi, E; Gutmann, S
2007-01-01
We give a quantum algorithm for the NAND tree problem in the Hamiltonian oracle model. The algorithm uses a continuous time quantum walk with a run time proportional to sqrt(N)*sqrt(logN). We also show a lower bound of sqrt(N) for the NAND tree problem in the Hamiltonian oracle model.
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.
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 ...
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.
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
New approaches to generalized Hamiltonian realization of autonomous nonlinear systems
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.
2014-06-19
research advisor, Dr. Gilbert Peterson, for agreeing to take on this work so late in the game and providing the necessary support and guidance. Patrick...partitioning the state, the algorithm starts the worker processes using the Java Pathfinder Framework (JPF) [29], which includes a symbolic execution...DOI: 10.1145/2090147.2094081 [29] W. Visser, C. S. Pǎsǎreanu, and S. Khurshid, “Test input generation with Java PathFinder ,” in Proceedings of the
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.
On Hamiltonian realization of time-varying nonlinear systems
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.
FEEDBACK REALIZATION OF HAMILTONIAN SYSTEMS
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
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 HAMILTONIAN SYSTEMS OF THE LCZ HIERARCHY BY NONLINEARIZATION
Li Lu
2000-01-01
In this paper, we first search for the Hamiltonian structure of LCZ hierarchy by use of a trace identity. Then we determine a higher-order constraint condition between the potentials and the eigenfunctions of the LCZ spectral problem, and under this constraint condition, the Lax pairs of LCZ hierarchy are all nonlinearized into the finite-dimensional integrable Hamiltonian systems in Liouville sense.
Square-root actions, metric signature, and the path-integral of quantum gravity
Carlini, A; Carlini, A; Greensite, J
1995-01-01
We consider quantization of the Baierlein-Sharp-Wheeler form of the gravitational action, in which the lapse function is determined from the Hamiltonian constraint. This action has a square root form, analogous to the actions of the relativistic particle and Nambu string. We argue that path-integral quantization of the gravitational action should be based on a path integrand \\exp[ \\sqrt{i} S ] rather than the familiar Feynman expression \\exp[ i S ], and that unitarity requires integration over manifolds of both Euclidean and Lorentzian signature. We discuss the relation of this path integral to our previous considerations regarding the problem of time, and extend our approach to include fermions.
Square-root actions, metric signature, and the path integral of quantum gravity
Carlini, A.; Greensite, J.
1995-12-01
We consider quantization of the Baierlein-Sharp-Wheeler form of the gravitational action, in which the lapse function is determined from the Hamiltonian constraint. This action has a square root form, analogous to the actions of the relativistic particle and Nambu string. We argue that path-integral quantization of the gravitational action should be based on a path integrand exp[ √i S] rather than the familiar Feynman expression exp[iS], and that unitarity requires integration over manifolds of both Euclidean and Lorentzian signature. We discuss the relation of this path integral to our previous considerations regarding the problem of time, and extend our approach to include fermions.
Remarks on hamiltonian digraphs
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.
Edge-disjoint Hamiltonian cycles in hypertournaments
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...
Discrete variable representation for singular Hamiltonians
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...
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.
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
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.
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.
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.
GRASP with path-relinking for the selective pickup and delivery problem
Ho, Sin C.; Szeto, W. Y.
2016-01-01
Bike sharing systems are very popular nowadays. One of the characteristics is that bikes are picked up from some surplus bike stations and transported to all deficit bike stations by a repositioning vehicle with limited capacity to satisfy the demand of deficit bike stations. Motivated by this real...... world bicycle repositioning problem, we study the selective pickup and delivery problem, where demand at every delivery node has to be satisfied by the supply collected from a subset of pickup nodes. The objective is to minimize the total travel cost incurred from visiting the nodes. We present a GRASP...
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.
Study on the stability of switched dissipative Hamiltonian systems
ZHU Liying; WANG Yuzhen
2006-01-01
The hybrid Hamiltonian system is a kind of important nonlinear hybrid systems. Such a system not only plays an important role in the development of hybrid control theory, but also finds many applications in practical control designs for obtaining better control performances. This paper investigates the stability of switched dissipative Hamiltonian systems under arbitrary switching paths. Under a realistic assumption, it is shown that the Hamiltonian functions of all the subsystems can be used as the multiple-Lyapunov functions for the switched dissipative Hamiltonian system. Based on this and using the dissipative Hamiltonian structural properties, this paper then proves that the P-norm of the state of switched dissipative Hamiltonian system converges to zero with the time increasing, and presents two sufficient conditions for the asymptotical stability under arbitrary switching paths. Utilizing these new results, this paper also obtains two useful corollaries for the asymptotical stability of switched nonlinear time-invariant systems. Finally, two examples are studied by using the new results proposed in this paper, and some numerical simulations are carried out to support our new results.
Constraint-based solver for the Military unit path finding problem
Leenen, L
2010-04-01
Full Text Available -based approach because it requires flexibility in modelling. The authors formulate the MUPFP as a constraint satisfaction problem and a constraint-based extension of the search algorithm. The concept demonstrator uses a provided map, for example taken from Google...
Lagrangian and Hamiltonian Geometries. Applications to Analytical Mechanics
Miron, Radu
2012-01-01
The aim of the present text is twofold: to provide a compendium of Lagrangian and Hamiltonian geometries and to introduce and investigate new analytical Mechanics: Finslerian, Lagrangian and Hamiltonian. The fundamental equations (or evolution equations) of these Mechanics are derived from the variational calculus applied to the integral of action and these can be studied by using the methods of Lagrangian or Hamiltonian geometries. More general, the notions of higher order Lagrange or Hamilton spaces have been introduced and developed by the present author. The applications led to the notions of Lagrangian or Hamiltonian Analytical Mechanics of higher order. For short, in this text we aim to solve some difficult problems: The problem of geometrization of classical non conservative mechanical systems; The foundations of geometrical theory of new mechanics: Finslerian, Lagrangian and Hamiltonian;To determine the evolution equations of the classical mechanical systems for whose external forces depend on the hig...
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.
Sunil Kumar,
2010-12-01
Full Text Available Wireless sensor network is tremendously being used in different environments to perform various monitoring task such as search, rescue, disaster relief, target tracking and a number of tasks in smart environment. In this paper a unique localization algorithm is proposed that gives the high accuracy in wireless sensor network. We propose amobile beacon algorithm and then merge it with DV- hop algorithm to introduce a unique approach which solves the localization problem in wireless sensor network.
On the Edge-Hyper-Hamiltonian Laceability of Balanced Hypercubes
Cao Jianxiang
2016-11-01
Full Text Available The balanced hypercube BHn, defined by Wu and Huang, is a variant of the hypercube network Qn, and has been proved to have better properties than Qn with the same number of links and processors. For a bipartite graph G = (V0 ∪ V1,E, we say G is edge-hyper-Hamiltonian laceable if it is Hamiltonian laceable, and for any vertex v ∈ Vi, i ∈ {0, 1}, any edge e ∈ E(G − v, there is a Hamiltonian path containing e in G − v between any two vertices of V1−i. In this paper, we prove that BHn is edge-hy per- Hamiltonian laceable.
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.
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.
Chao Zhang
2016-06-01
Full Text Available An improved ant colony optimization (ACO combined with immunosuppression and parameters switching strategy is proposed in this paper. In this algorithm, a novel judgment criterion for immunosuppression is introduced, that is, if the optimum solution has not changed for default iteration number, the immunosuppressive strategy is carried out. Moreover, two groups of parameters in ACO are switched back and forth according to the change of optimum solution as well. Therefore, the search space is expanded greatly and the problem of the traditional ACO such as falling into local minima easily is avoided effectively. The comparative simulation studies for path planning of landfill inspection robots in Asahikawa, Japan are executed, and the results show that the proposed algorithm has better performance characterized by higher search quality and faster search speed.
The Problems and Path Thinking of China’s Rural Logistics Development
2011-01-01
This paper introduces seasonal characteristic,scattered characteristic and diversified characteristic of rural logistics in China,developing rural logistics is significant to increasing farmers’ income,promoting life quality,reducing cost of agricultural products,increasing job opportunities and quickening the process of urbanization.This paper also analyzes the status quo and existing problems of China’s rural logistics as follows.China’s rural logistics,with late start and great logistics aggregate,develops rapidly;the main body of rural logistics has a trend of diversification;the informatization develops rapidly.But there are some problems,for example,the infrastructure of rural logistics is backward;the informatization level is low;the development degree of main body of market is low;there is a shortage of talents;the technological level is low.The countermeasures are put forward to promote the development of rural logistics in China as follows:strengthen infrastructure construction of rural logistics in China;reinforce the construction of rural informatization;foster the main body of market of rural logistics in China;vigorously foster talents of modern rural logistics;promote technological level of rural logistics.
Resing, Wilma C M; Bakker, Merel; Pronk, Christine M E; Elliott, Julian G
2017-01-01
The current study investigated developmental trajectories of analogical reasoning performance of 104 7- and 8-year-old children. We employed a microgenetic research method and multilevel analysis to examine the influence of several background variables and experimental treatment on the children's developmental trajectories. Our participants were divided into two treatment groups: repeated practice alone and repeated practice with training. Each child received an initial working memory assessment and was subsequently asked to solve figural analogies on each of several sessions. We examined children's analogical problem-solving behavior and their subsequent verbal accounts of their employed solving processes. We also investigated the influence of verbal and visual-spatial working memory capacity and initial variability in strategy use on analogical reasoning development. Results indicated that children in both treatment groups improved but that gains were greater for those who had received training. Training also reduced the influence of children's initial variability in the use of analogical strategies with the degree of improvement in reasoning largely unrelated to working memory capacity. Findings from this study demonstrate the value of a microgenetic research method and the use of multilevel analysis to examine inter- and intra-individual change in problem-solving processes. Copyright © 2016 Elsevier Inc. All rights reserved.
Sentse, Miranda; Prinzie, Peter; Salmivalli, Christina
2017-07-01
The transition to secondary school is accompanied by the fragmentation of peer groups, while adolescents are also confronted with heightened incidents of bullying and increased levels of internalizing problems. Victimization, peer rejection, and internalizing problems are known to be interrelated, but how they influence each other over time remains unclear. We tested the direction of these associations by applying a cross-lagged path model among a large sample of Finnish adolescents (N = 5645; 49.1 % boys; M age at T1 = 14.0 years) after they transitioned to secondary school (grades 7-9). Self-reported depression, anxiety, and victimization and peer-reported rejection were measured 3 times over the course of 1 year. Results showed that depression was predictive of subsequent victimization for both boys and girls, in line with a symptoms-driven model; for girls, anxiety was reciprocally related to victimization, in line with a transactional model; for boys, victimization was related to subsequent anxiety, in line with an interpersonal risk model. Peer rejection was not directly related to depression or anxiety, but among girls peer rejection was bi-directionally related to victimization. Overall, our results suggest that associations between internalizing problems and peer relations differ between depression and anxiety and between genders. Implications for practice and directions for future research are discussed.
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.
Wen-Xiang Wu
2014-01-01
Full Text Available The cost-based system optimum problem in networks with continuously distributed value of time is formulated as a path-based form, which cannot be solved by the Frank-Wolfe algorithm. In light of magnitude improvement in the availability of computer memory in recent years, path-based algorithms have been regarded as a viable approach for traffic assignment problems with reasonably large network sizes. We develop a path-based gradient projection algorithm for solving the cost-based system optimum model, based on Goldstein-Levitin-Polyak method which has been successfully applied to solve standard user equilibrium and system optimum problems. The Sioux Falls network tested is used to verify the effectiveness of the algorithm.
A Novel Solution to the ATT48 Benchmark Problem
Ruffa, Anthony A
2007-01-01
A solution to the benchmark ATT48 Traveling Salesman Problem (from the TSPLIB95 library) results from isolating the set of vertices into ten open-ended zones with nine lengthwise boundaries. In each zone, a minimum-length Hamiltonian Path (HP) is found for each combination of boundary vertices, leading to an approximation for the minimum-length Hamiltonian Cycle (HC). Determination of the optimal HPs for subsequent zones has the effect of automatically filtering out non-optimal HPs from earlier zones. Although the optimal HC for ATT48 involves only two crossing edges between all zones (with one exception), adding inter-zone edges can accommodate more complex problems.
Uecker, Hannes
2015-01-01
p2pOC is an add-on toolbox to the Matlab package pde2path. It is aimed at the numerical solution of optimal control (OC) problems with an infinite time horizon for parabolic systems of PDE over 1D or 2D spatial domains. The basic idea is to treat the OC problem via the associated canonical system in two steps. First we use pde2path to find branches of stationary solutions of the canonical system, also called canonical steady states (CSS). In a second step we use the results and the spatial di...
Path-Based Supports for Hypergraphs
Brandes, Ulrik; Cornelsen, Sabine; Pampel, Barbara; Sallaberry, Arnaud
A path-based support of a hypergraph H is a graph with the same vertex set as H in which each hyperedge induces a Hamiltonian subgraph. While it is NP-complete to compute a path-based support with the minimum number of edges or to decide whether there is a planar path-based support, we show that a path-based tree support can be computed in polynomial time if it exists.
Solving the Traveling Salesman Problem Using New Operators in Genetic Algorithms
Naef T. Al Rahedi; Jalal Atoum
2009-01-01
Problem statement: Genetic Algorithms (GAs) have been used as search algorithms to find near-optimal solutions for many NP problems. GAs require effective chromosome representations as well as carefully designed crossover and mutation operators to achieve an efficient search. The Traveling Salesman Problem (TSP), as an NP search problem, involves finding the shortest Hamiltonian Path or Cycle in a graph of N cities. The main objective of this study was to propose a new representation method o...
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
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.
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.
Monte Carlo Hamiltonian:Inverse Potential
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.
An alternative Hamiltonian formulation for the Pais-Uhlenbeck oscillator
Masterov, Ivan
2015-01-01
Ostrogradsky's method allows one to construct Hamiltonian formulation for a higher derivative system. An application of this approach to the Pais-Uhlenbeck oscillator yields the Hamiltonian which is unbounded from below. This leads to the ghost problem in quantum theory. In order to avoid this nasty feature, the technique previously developed in [Acta Phys. Polon. B 36 (2005) 2115] is used to construct an alternative Hamiltonian formulation for the multidimensional Pais-Uhlenbeck oscillator of arbitrary even order with distinct frequencies of oscillation. This construction is also generalized to the case of an N=2 supersymmetric Pais-Uhlenbeck oscillator.
An alternative Hamiltonian formulation for the Pais-Uhlenbeck oscillator
Masterov, Ivan
2016-01-01
Ostrogradsky's method allows one to construct Hamiltonian formulation for a higher derivative system. An application of this approach to the Pais-Uhlenbeck oscillator yields the Hamiltonian which is unbounded from below. This leads to the ghost problem in quantum theory. In order to avoid this nasty feature, the technique previously developed in [7] is used to construct an alternative Hamiltonian formulation for the multidimensional Pais-Uhlenbeck oscillator of arbitrary even order with distinct frequencies of oscillation. This construction is also generalized to the case of an N = 2 supersymmetric Pais-Uhlenbeck oscillator.
Robust H∞ Control of Hamiltonian System with Uncertainty
薛安成; 梅生伟; 胡伟; 周原
2003-01-01
This paper investigates the robust H∞ problem for a class of generalized forced Hamiltonian systems with uncertainties. The robust L2-gain was proved for the Hamiltonian with a sufficient condition for stable control of multimachine power systems expressed as a matrix algebraic inequality. A similar sufficient condition was then extended to the robust H∞ control of Hamiltonian systems to construct the state feedback H∞ control law. A numerical example is given to verify the validity of the proposed control scheme, which shows the effectiveness and promising application of the method.
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...
The Existence of Homoclinic Solutions for Second Order Hamiltonian System
Jie Gao
2011-10-01
Full Text Available The research of homoclinic orbits for Hamiltonian system is a classical problem, it has valuable applications in celestial mechanics, plasma physis, and biological engineering. For example, homoclinic orbits rupture can yield chaos lead to more complex dynamics behaviour. This paper studies the existence of homoclinic solutions for a class of second order Hamiltonian system, we will prove this system exists at least one nontrivial homoclinic solution.
Hamiltonian Forms for a Hierarchy of Discrete Integrable Coupling Systems
XU Xi-Xiang; YANG Hong-Xiang; LU Rong-Wu
2008-01-01
A semi-direct sum of two Lie algebras of four-by-four matrices is presented, and a discrete four-by-fore matrix spectral problem is introduced. A hierarchy of discrete integrable coupling systems is derived. The obtained integrable coupling systems are all written in their Hamiltonian forms by the discrete variational identity. Finally, we prove that the lattice equations in the obtained integrable coupling systems are all Liouville integrable discrete Hamiltonian systems.
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 Models of Nonlinear Evolution Paths in Adiabatic Quantum Algorithms
SUN Jie; LU Song-Feng; Samuel L.Braunstein
2013-01-01
In this paper,we study two different nonlinear interpolating paths in adiabatic evolution algorithms for solving a particular class of quantum search problems where both the initial and final Hamiltonian are one-dimensional projector Hamiltonians on the corresponding ground state.If the overlap between the initial state and final state of the quantum system is not equal to zero,both of these models can provide a constant time speedup over the usual adiabatic algorithms by increasing some another corresponding "complexity".But when the initial state has a zero overlap with the solution state in the problem,the second model leads to an infinite time complexity of the algorithm for whatever interpolating functions being applied while the first one can still provide a constant running time.However,inspired by a related reference,a variant of the first model can be constructed which also fails for the problem when the overlap is exactly equal to zero if we want to make up the "intrinsic" fault of the second model — an increase in energy.Two concrete theorems are given to serve as explanations why neither of these two models can improve the usual adiabatic evolution algorithms for the phenomenon above.These just tell us what should be noted when using certain nonlinear evolution paths in adiabatic quantum algorithms for some special kind of problems.
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...
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.
NATO Advanced Study Institute on Hamiltonian Dynamical Systems and Applications
2008-01-01
Physical laws are for the most part expressed in terms of differential equations, and natural classes of these are in the form of conservation laws or of problems of the calculus of variations for an action functional. These problems can generally be posed as Hamiltonian systems, whether dynamical systems on finite dimensional phase space as in classical mechanics, or partial differential equations (PDE) which are naturally of infinitely many degrees of freedom. This volume is the collected and extended notes from the lectures on Hamiltonian dynamical systems and their applications that were given at the NATO Advanced Study Institute in Montreal in 2007. Many aspects of the modern theory of the subject were covered at this event, including low dimensional problems as well as the theory of Hamiltonian systems in infinite dimensional phase space; these are described in depth in this volume. Applications are also presented to several important areas of research, including problems in classical mechanics, continu...
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
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
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
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.
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.
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.
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
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.
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.
Recent advances in the numerical solution of Hamiltonian partial differential equations
Barletti, Luigi; Brugnano, Luigi; Caccia, Gianluca Frasca; Iavernaro, Felice
2016-10-01
In this paper, we study recent results in the numerical solution of Hamiltonian partial differential equations (PDEs), by means of energy-conserving methods in the class of Line Integral Methods, in particular, the Runge-Kutta methods named Hamiltonian Boundary Value Methods (HBVMs). We show that the use of energy-conserving methods, able to conserve a discrete counterpart of the Hamiltonian functional (which derives from a proper space semi-discretization), confers more robustness to the numerical solution of such problems.
Continuation of periodic orbits in symmetric Hamiltonian and conservative systems
Galan-Vioque, J.; Almaraz, F. J. M.; Macías, E. F.
2014-12-01
We present and review results on the continuation and bifurcation of periodic solutions in conservative, reversible and Hamiltonian systems in the presence of symmetries. In particular we show how two-point boundary value problem continuation software can be used to compute families of periodic solutions of symmetric Hamiltonian systems. The technique is introduced with a very simple model example (the mathematical pendulum), justified with a theoretical continuation result and then applied to two non trivial examples: the non integrable spring pendulum and the continuation of the figure eight solution of the three body problem.
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
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.
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.
无
2000-01-01
A new algorithm called homotopy iteration method based on the homotopy function is studied and improved. By the improved homotopy iteration method, polynomial systems with high order and deficient can be solved fast and efficiently comparing to the original homotopy iteration method. Numerical examples for the ninepoint path synthesis of four-bar linkages show the advantages and efficiency of the improved homotopy iteration method.
A Class of Asymmetric Gapped Hamiltonians on Quantum Spin Chains and its Characterization II
Ogata, Yoshiko
2016-12-01
We give a characterization of the class of gapped Hamiltonians introduced in Part I (Ogata, A class of asymmetric gapped Hamiltonians on quantum spin chains and its classification I, 2015). The Hamiltonians in this class are given as MPS (Matrix product state) Hamiltonians. In Ogata (A class of asymmetric gapped Hamiltonians on quantum spin chains and its classification I, 2015), we list up properties of ground state structures of Hamiltonians in this class. In this Part II, we show the converse. Namely, if a (not necessarily MPS) Hamiltonian H satisfies five of the listed properties, there is a Hamiltonian H' from the class by Ogata (A class of asymmetric gapped Hamiltonians on quantum spin chains and its classification I, 2015), satisfying the following: The ground state spaces of the two Hamiltonians on the infinite interval coincide. The spectral projections onto the ground state space of H on each finite intervals are approximated by that of H' exponentially well, with respect to the interval size. The latter property has an application to the classification problem with open boundary conditions.
A Class of Asymmetric Gapped Hamiltonians on Quantum Spin Chains and its Characterization II
Ogata, Yoshiko
2016-06-01
We give a characterization of the class of gapped Hamiltonians introduced in Part I (Ogata, A class of asymmetric gapped Hamiltonians on quantum spin chains and its classification I, 2015). The Hamiltonians in this class are given as MPS (Matrix product state) Hamiltonians. In Ogata (A class of asymmetric gapped Hamiltonians on quantum spin chains and its classification I, 2015), we list up properties of ground state structures of Hamiltonians in this class. In this Part II, we show the converse. Namely, if a (not necessarily MPS) Hamiltonian H satisfies five of the listed properties, there is a Hamiltonian H' from the class by Ogata (A class of asymmetric gapped Hamiltonians on quantum spin chains and its classification I, 2015), satisfying the following: The ground state spaces of the two Hamiltonians on the infinite interval coincide. The spectral projections onto the ground state space of H on each finite intervals are approximated by that of H' exponentially well, with respect to the interval size. The latter property has an application to the classification problem with open boundary conditions.
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.
Cluster expansion for ground states of local Hamiltonians
Bastianello, Alvise; Sotiriadis, Spyros
2016-08-01
A central problem in many-body quantum physics is the determination of the ground state of a thermodynamically large physical system. We construct a cluster expansion for ground states of local Hamiltonians, which naturally incorporates physical requirements inherited by locality as conditions on its cluster amplitudes. Applying a diagrammatic technique we derive the relation of these amplitudes to thermodynamic quantities and local observables. Moreover we derive a set of functional equations that determine the cluster amplitudes for a general Hamiltonian, verify the consistency with perturbation theory and discuss non-perturbative approaches. Lastly we verify the persistence of locality features of the cluster expansion under unitary evolution with a local Hamiltonian and provide applications to out-of-equilibrium problems: a simplified proof of equilibration to the GGE and a cumulant expansion for the statistics of work, for an interacting-to-free quantum quench.
Cluster expansion for ground states of local Hamiltonians
Alvise Bastianello
2016-08-01
Full Text Available A central problem in many-body quantum physics is the determination of the ground state of a thermodynamically large physical system. We construct a cluster expansion for ground states of local Hamiltonians, which naturally incorporates physical requirements inherited by locality as conditions on its cluster amplitudes. Applying a diagrammatic technique we derive the relation of these amplitudes to thermodynamic quantities and local observables. Moreover we derive a set of functional equations that determine the cluster amplitudes for a general Hamiltonian, verify the consistency with perturbation theory and discuss non-perturbative approaches. Lastly we verify the persistence of locality features of the cluster expansion under unitary evolution with a local Hamiltonian and provide applications to out-of-equilibrium problems: a simplified proof of equilibration to the GGE and a cumulant expansion for the statistics of work, for an interacting-to-free quantum quench.
Cluster expansion for ground states of local Hamiltonians
Bastianello, Alvise, E-mail: abastia@sissa.it [SISSA, via Bonomea 265, 34136 Trieste (Italy); INFN, Sezione di Trieste (Italy); Sotiriadis, Spyros [SISSA, via Bonomea 265, 34136 Trieste (Italy); INFN, Sezione di Trieste (Italy); Institut de Mathématiques de Marseille (I2M), Aix Marseille Université, CNRS, Centrale Marseille, UMR 7373, 39, rue F. Joliot Curie, 13453, Marseille (France); University of Roma Tre, Department of Mathematics and Physics, L.go S.L. Murialdo 1, 00146 Roma (Italy)
2016-08-15
A central problem in many-body quantum physics is the determination of the ground state of a thermodynamically large physical system. We construct a cluster expansion for ground states of local Hamiltonians, which naturally incorporates physical requirements inherited by locality as conditions on its cluster amplitudes. Applying a diagrammatic technique we derive the relation of these amplitudes to thermodynamic quantities and local observables. Moreover we derive a set of functional equations that determine the cluster amplitudes for a general Hamiltonian, verify the consistency with perturbation theory and discuss non-perturbative approaches. Lastly we verify the persistence of locality features of the cluster expansion under unitary evolution with a local Hamiltonian and provide applications to out-of-equilibrium problems: a simplified proof of equilibration to the GGE and a cumulant expansion for the statistics of work, for an interacting-to-free quantum quench.
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.
Multivector field formulation of Hamiltonian field theories: equations and symmetries
Echeverria-Enriquez, A.; Munoz-Lecanda, M.C.; Roman-Roy, N. [Departamento de Matematica Aplicada y Telematica, Edificio C-3, Campus Norte UPC, Barcelona (Spain)
1999-12-03
We state the intrinsic form of the Hamiltonian equations of first-order classical field theories in three equivalent geometrical ways: using multivector fields, jet fields and connections. Thus, these equations are given in a form similar to that in which the Hamiltonian equations of mechanics are usually given. Then, using multivector fields, we study several aspects of these equations, such as the existence and non-uniqueness of solutions, and the integrability problem. In particular, these problems are analysed for the case of Hamiltonian systems defined in a submanifold of the multimomentum bundle. Furthermore, the existence of first integrals of these Hamiltonian equations is considered, and the relation between Cartan-Noether symmetries and general symmetries of the system is discussed. Noether's theorem is also stated in this context, both the 'classical' version and its generalization to include higher-order Cartan-Noether symmetries. Finally, the equivalence between the Lagrangian and Hamiltonian formalisms is also discussed. (author)
Port-Hamiltonian Formulation of the Gradient Method Applied to Smart Grids
Stegink, Tjerk; De Persis, Claudio; van der Schaft, Arjan
2015-01-01
The gradient method is a well-known tool for solving convex optimization problems. This paper shows that the gradient method admits a Brayton-Moser and a port-Hamiltonian representation. In fact, its dynamics can be interpreted as a interconnection of multiple (port-Hamiltonian) passive systems, whi
A Hamiltonian method for finding broadband modal eigenvalues.
Wang, Haozhong; Wang, Ning; Gao, Dazhi
2012-02-01
For shallow water waveguides over a layered elastic bottom, modal eigenvalues can be determined by searching the locations in the complex plane of the horizontal wave number at which the complex phase function is a multiple of π [C. T. Tindle and N. R. Chapman, J. Acoust. Soc. Am. 96, 1777-1782 (1994)]. In this paper, a Hamiltonian method is introduced for tracing the path in the complex plane along which the phase function keeps real. The Hamiltonian method can also be extended to compute the broadband modal eigenvalues or the modal dispersion curves in the Pekeris waveguide with fluid/elastic bottoms. For each proper or leaky normal mode, a different Hamiltonian is constructed in the complex plane and used to trace automatically the complex dispersion curve with the eigenvalue in a reference frequency as the initial value. In contrast to the usual methods, the dispersion curve for each mode is determined individually. The Hamiltonian method shows good performance by comparing with KRAKEN.
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...
Moeller, Scott J; Crocker, Jennifer
2009-06-01
Coping motives for drinking initiate alcohol-related problems. Interpersonal goals, which powerfully influence affect, could provide a starting point for this relation. Here we tested effects of self-image goals (which aim to construct and defend desired self-views) and compassionate goals (which aim to support others) on heavy-episodic drinking and alcohol-related problems. Undergraduate drinkers (N=258) completed measures of self-image and compassionate goals in academics and friendships, coping and enhancement drinking motives, heavy-episodic drinking, and alcohol-related problems in a cross-sectional design. As predicted, self-image goals, but not compassionate goals, positively related to alcohol-related problems. Path models showed that self-image goals relate to coping motives, but not enhancement motives; coping motives then relate to heavy-episodic drinking, which in turn relate to alcohol-related problems. Self-image goals remained a significant predictor in the final model, which accounted for 34% of the variance in alcohol-related problems. These findings indicate that self-image goals contribute to alcohol-related problems in college students both independently and through coping motives. Interventions can center on reducing self-image goals and their attendant negative affect.
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…
Maslov index for Hamiltonian systems
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.
Derivation of Hamiltonians for accelerators
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
Mark Setterfield
2015-01-01
Path dependency is defined, and three different specific concepts of path dependency – cumulative causation, lock in, and hysteresis – are analyzed. The relationships between path dependency and equilibrium, and path dependency and fundamental uncertainty are also discussed. Finally, a typology of dynamical systems is developed to clarify these relationships.
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
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.
An integrable Hamiltonian hierarchy and associated integrable couplings system
Chen Xiao-Hong; Xia Tie-Cheng; Zhu Lian-Cheng
2007-01-01
This paper establishes a new isospectral problem. By making use of the Tu scheme, a new integrable system is obtained. It gives integrable couplings of the system obtained. Finally, the Hamiltonian form of a binary symmetric constrained flow of the system obtained is presented.
Dual partitioning for effective Hamiltonians to avoid intruders
Ten-no, Seiichiro
2015-01-01
We present a new Hamiltonian partitioning which converges an arbitrary number of states of interest in the effective Hamiltonian to the full configuration interaction limits simultaneously. This feature is quite useful for the recently developed model space quantum Monte Carlo. A dual partitioning (DP) technique is introduced to avoid the intruder state problem present in the previous eigenvalue independent partitioning of Coope. The new approach is computationally efficient and applicable to general excited states involving conical intersections. We present a preliminary application of the method to model systems to investigate the performance.
Nonclassical degrees of freedom in the Riemann Hamiltonian.
Srednicki, Mark
2011-09-02
The Hilbert-Pólya conjecture states that the imaginary parts of the zeros of the Riemann zeta function are eigenvalues of a quantum Hamiltonian. If so, conjectures by Katz and Sarnak put this Hamiltonian in the Altland-Zirnbauer universality class C. This implies that the system must have a nonclassical two-valued degree of freedom. In such a system, the dominant primitive periodic orbits contribute to the density of states with a phase factor of -1. This resolves a previously mysterious sign problem with the oscillatory contributions to the density of the Riemann zeros.
Average quantum dynamics of closed systems over stochastic Hamiltonians
Yu, Li
2011-01-01
We develop a master equation formalism to describe the evolution of the average density matrix of a closed quantum system driven by a stochastic Hamiltonian. The average over random processes generally results in decoherence effects in closed system dynamics, in addition to the usual unitary evolution. We then show that, for an important class of problems in which the Hamiltonian is proportional to a Gaussian random process, the 2nd-order master equation yields exact dynamics. The general formalism is applied to study the examples of a two-level system, two atoms in a stochastic magnetic field and the heating of a trapped ion.
M. Sentse (Miranda); P.J. Prinzie (Peter); C. Salmivalli (Christina)
2016-01-01
textabstractThe transition to secondary school is accompanied by the fragmentation of peer groups, while adolescents are also confronted with heightened incidents of bullying and increased levels of internalizing problems. Victimization, peer rejection, and internalizing problems are known to be int
Least-Squares Solutions of the Equation AX = B Over Anti-Hermitian Generalized Hamiltonian Matrices
无
2006-01-01
Upon using the denotative theorem of anti-Hermitian generalized Hamiltonian matrices, we solve effectively the least-squares problem min ‖AX - B‖ over anti-Hermitian generalized Hamiltonian matrices. We derive some necessary and sufficient conditions for solvability of the problem and an expression for general solution of the matrix equation AX = B. In addition, we also obtain the expression for the solution of a relevant optimal approximate problem.
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
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
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.
Fourier series expansion for nonlinear Hamiltonian oscillators.
Méndez, Vicenç; Sans, Cristina; Campos, Daniel; Llopis, Isaac
2010-06-01
The problem of nonlinear Hamiltonian oscillators is one of the classical questions in physics. When an analytic solution is not possible, one can resort to obtaining a numerical solution or using perturbation theory around the linear problem. We apply the Fourier series expansion to find approximate solutions to the oscillator position as a function of time as well as the period-amplitude relationship. We compare our results with other recent approaches such as variational methods or heuristic approximations, in particular the Ren-He's method. Based on its application to the Duffing oscillator, the nonlinear pendulum and the eardrum equation, it is shown that the Fourier series expansion method is the most accurate.
PLANE INFINITE ANALYTICAL ELEMENT AND HAMILTONIAN SYSTEM
孙雁; 周钢; 刘正兴
2003-01-01
It is not convenient to solve those engineering problems defined in an infinitefield by using FEM. An infinite area can be divided into a regular infinite external area anda finite internal area. The finite internal area was dealt with by the FEM and the regularinfinite external area was settled in a polar coordinate. All governing equations weretransformed into the Hamiltonian system. The methods of variable separation andeigenfunction expansion were used to derive the stiffness matrix of a new infinite analyticalelement. This new element, like a super finite element, can be combined with commonlyused finite elements. The proposed method was verified by numerical case studies. Theresults show that the preparation work is very simple, the infinite analytical element has ahigh precision, and it can be used conveniently. The method can also be easily extended to a three-dimensional problem.
Quantum Adiabatic Algorithms, Small Gaps, and Different Paths
Farhi, Edward; Gosset, David; Gutmann, Sam; Meyer, Harvey B; Shor, Peter
2011-01-01
We construct a set of instances of 3SAT which are not solved efficiently using the simplest quantum adiabatic algorithm. These instances are obtained by picking random clauses all consistent with two disparate planted solutions and then penalizing one of them with a single additional clause. We argue that by randomly modifying the beginning Hamiltonian, one obtains (with substantial probability) an adiabatic path that removes this difficulty. This suggests that the quantum adiabatic algorithm should in general be run on each instance with many different random paths leading to the problem Hamiltonian. We do not know whether this trick will help for a random instance of 3SAT (as opposed to an instance from the particular set we consider), especially if the instance has an exponential number of disparate assignments that violate few clauses. We use a continuous imaginary time Quantum Monte Carlo algorithm in a novel way to numerically investigate the ground state as well as the first excited state of our system...
Lie transforms and their use in Hamiltonian perturbation theory
Cary, J.R.
1978-06-01
A review is presented of the theory of Lie transforms as applied to Hamiltonian systems. We begin by presenting some general background on the Hamiltonian formalism and by introducing the operator notation for canonical transformations. We then derive the general theory of Lie transforms. We derive the formula for the new Hamiltonian when one uses a Lie transform to effect a canonical transformation, and we use Lie transforms to prove a very general version of Noether's theorem, or the symmetry-equals-invariant theorem. Next we use the general Lie transform theory to derive Deprit's perturbation theory. We illustrate this perturbation theory by application to two well-known problems in classical mechanics. Finally we present a chapter on conventions. There are many ways to develop Lie transforms. The last chapter explains the reasons for the choices made here.
Barnow, Sven; Schuckit, Marc A; Lucht, Michael; John, Ulrich; Freyberger, Harald J
2002-05-01
The purpose of this study was to test a hypothetical model of alcohol problems in German adolescents. Among 180 offspring, family history of alcoholism, parenting styles, behavioral and emotional problems, peer-group characteristics, feelings of self-esteem, behavioral problems and psychiatric comorbidity of the parents were examined. Data were generated from the Study of Health in Pomerania (SHIP), in which families were randomly selected if 12-18 year old biological offspring were members of the household; a smaller group of subjects was selected from local outpatient treatment centers. Members of 133 families, including 180 (50.6% male) offspring who were appropriate for the current analyses, received personal semistructured diagnostic interviews and several self-rating questionnaires. Analyses compared offspring with alcohol problems (AP; n = 40) and with no alcohol problems (NAP; n = 140), and used structural equation modeling to test a hypothetical model. The comparisons revealed that the AP group had significantly more behavioral problems (e.g., aggression/delinquency), more perceived parental rejection and less emotional warmth, a higher amount of alcohol consumption, were more likely to associate with substance-using peers and more often received a diagnosis of conduct disorder or antisocial personality disorder. Whereas the family history of alcoholism did not differ significantly between groups, parents of offspring with an alcohol use disorder had significantly more additional diagnoses on DSM-IV Axis I. The evaluation of the model supported the importance of aggression/delinquency and association with substance-using peers for alcohol problems in people. An additional diagnosis in the parents was directly and indirectly (through aggression/delinquency) related to alcohol problems of the adolescents. The data indicate that alcohol problems in the offspring are associated with several domains of influence in their environment. Prospective studies
Tan, Hong
2014-01-01
The new curriculum, new ideas and new requirements concerning English teaching have made the rural English teaching face unprecedented challenges. There are many problems contributing to the poor effect of rural English teaching, such as outdated teaching equipment, unreasonable curriculum design, insufficient teaching staff, asymmetrical teaching content, family education and students' personal problems. Based on the Chinese General Social Survey data, it is found that in terms of English re...
Improving Christofides' Algorithm for the s-t Path TSP
An, Hyung-Chan; Shmoys, David B
2011-01-01
We present a deterministic (1+sqrt(5))/2-approximation algorithm for the s-t path TSP. Given a symmetric metric cost between n vertices including two prespecified endpoints, the problem is to find a shortest Hamiltonian path between the two endpoints; Hoogeveen showed that the natural variant of Christofides' algorithm is a 5/3-approximation algorithm for this problem, and this asymptotically tight bound in fact has been the best approximation ratio known until now. We modify this algorithm so that it chooses the initial spanning tree based on an optimal solution to the Held-Karp relaxation rather than a minimum spanning tree; we prove this simple but crucial modification leads to an improved approximation ratio, surpassing the 20-year-old barrier set by the natural Christofides' algorithm variant. Our algorithm also proves an upper bound of (1+sqrt(5))/2 on the integrality gap of the path-variant Held-Karp relaxation. The techniques devised in this paper can be applied to other optimization problems over s-t...
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.
Hamiltonian dynamics of extended objects
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.
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.
On Hamiltonian formulation of cosmologies
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.
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.
Kosaka, Shinya; Saji, Etsuro [In-Core Fuel Management System Department, Toden Software, Inc., Tokyo (Japan)
2000-12-01
A characteristics transport theory code, CHAPLET, has been developed for the purpose of making it practical to perform a whole LWR core calculation with the same level of calculational model and accuracy as that of an ordinary single assembly calculation. The characteristics routine employs the CACTUS algorithm for drawing ray tracing lines, which assists the two key features of the flux solution in the CHAPLET code. One is the direct neutron path linking (DNPL) technique which strictly connects angular fluxes at each assembly interface in the flux solution separated between assemblies. Another is to reduce the required memory storage by sharing the data related to ray tracing among assemblies with the same configuration. For faster computation, the coarse mesh rebalance (CMR) method and the Aitken method were incorporated in the code and the combined use of both methods showed the most promising acceleration performance among the trials. In addition, the parallelization of the flux solution was attempted, resulting in a significant reduction in the wall-clock time of the calculation. By all these efforts, coupled with the results of many verification studies, a whole LWR core heterogeneous transport theory calculation finally became practical. CHAPLET is thought to be a useful tool which can produce the reference solutions for analyses of an LWR (author)
When a local Hamiltonian must be frustration-free.
Sattath, Or; Morampudi, Siddhardh C; Laumann, Chris R; Moessner, Roderich
2016-06-07
A broad range of quantum optimization problems can be phrased as the question of whether a specific system has a ground state at zero energy, i.e., whether its Hamiltonian is frustration-free. Frustration-free Hamiltonians, in turn, play a central role for constructing and understanding new phases of matter in quantum many-body physics. Unfortunately, determining whether this is the case is known to be a complexity-theoretically intractable problem. This makes it highly desirable to search for efficient heuristics and algorithms to, at least, partially answer this question. Here we prove a general criterion-a sufficient condition-under which a local Hamiltonian is guaranteed to be frustration-free by lifting Shearer's theorem from classical probability theory to the quantum world. Remarkably, evaluating this condition proceeds via a fully classical analysis of a hardcore lattice gas at negative fugacity on the Hamiltonian's interaction graph, which, as a statistical mechanics problem, is of interest in its own right. We concretely apply this criterion to local Hamiltonians on various regular lattices, while bringing to bear the tools of spin glass physics that permit us to obtain new bounds on the satisfiable to unsatisfiable transition in random quantum satisfiability. We are then led to natural conjectures for when such bounds will be tight, as well as to a novel notion of universality for these computer science problems. Besides providing concrete algorithms leading to detailed and quantitative insights, this work underscores the power of marrying classical statistical mechanics with quantum computation and complexity theory.
Coupled Hamiltonians and Three Dimensional Short-Range Wetting Transitions
Parry, A. O.; Swain, P S
1997-01-01
We address three problems faced by effective interfacial Hamiltonian models of wetting based on a single collective coordinate \\ell representing the position of the unbinding fluid interface. Problems (P1) and (P2) refer to the predictions of non-universality at the upper critical dimension d=3 at critical and complete wetting respectively which are not borne out by Ising model simulation studies. (P3) relates to mean-field correlation function structure in the underlying continuum Landau mod...
Monte Carlo methods in continuous time for lattice Hamiltonians
Huffman, Emilie
2016-01-01
We solve a variety of sign problems for models in lattice field theory using the Hamiltonian formulation, including Yukawa models and simple lattice gauge theories. The solutions emerge naturally in continuous time and use the dual representation for the bosonic fields. These solutions allow us to construct quantum Monte Carlo methods for these problems. The methods could provide an alternative approach to understanding non-perturbative dynamics of some lattice field theories.
Wilson, Helen W.; Widom, Cathy Spatz
2010-01-01
Behaviors beginning in childhood or adolescence may mediate the relationship between childhood maltreatment and involvement in prostitution. This paper examines 5 potential mediators: early sexual initiation, running away, juvenile crime, school problems, and early drug use. Using a prospective cohort design, abused and neglected children (ages…
Walwyn, Amy L.; Navarro, Daniel J.
2010-01-01
An experiment is reported comparing human performance on two kinds of visually presented traveling salesperson problems (TSPs), those reliant on Euclidean geometry and those reliant on city block geometry. Across multiple array sizes, human performance was near-optimal in both geometries, but was slightly better in the Euclidean format. Even so,…
Walwyn, Amy L.; Navarro, Daniel J.
2010-01-01
An experiment is reported comparing human performance on two kinds of visually presented traveling salesperson problems (TSPs), those reliant on Euclidean geometry and those reliant on city block geometry. Across multiple array sizes, human performance was near-optimal in both geometries, but was slightly better in the Euclidean format. Even so,…
Rehmat, Abeera Parvaiz
As we progress into the 21st century, higher-order thinking skills and achievement in science and math are essential to meet the educational requirement of STEM careers. Educators need to think of innovative ways to engage and prepare students for current and future challenges while cultivating an interest among students in STEM disciplines. An instructional pedagogy that can capture students' attention, support interdisciplinary STEM practices, and foster higher-order thinking skills is problem-based learning. Problem-based learning embedded in the social constructivist view of teaching and learning (Savery & Duffy, 1995) promotes self-regulated learning that is enhanced through exploration, cooperative social activity, and discourse (Fosnot, 1996). This quasi-experimental mixed methods study was conducted with 98 fourth grade students. The study utilized STEM content assessments, a standardized critical thinking test, STEM attitude survey, PBL questionnaire, and field notes from classroom observations to investigate the impact of problem-based learning on students' content knowledge, critical thinking, and their attitude towards STEM. Subsequently, it explored students' experiences of STEM integration in a PBL environment. The quantitative results revealed a significant difference between groups in regards to their content knowledge, critical thinking skills, and STEM attitude. From the qualitative results, three themes emerged: learning approaches, increased interaction, and design and engineering implementation. From the overall data set, students described the PBL environment to be highly interactive that prompted them to employ multiple approaches, including design and engineering to solve the problem.
Wilson, Helen W.; Widom, Cathy Spatz
2010-01-01
Behaviors beginning in childhood or adolescence may mediate the relationship between childhood maltreatment and involvement in prostitution. This paper examines 5 potential mediators: early sexual initiation, running away, juvenile crime, school problems, and early drug use. Using a prospective cohort design, abused and neglected children (ages…
Law, Richard; Waters, Dave; Morgan, Sven; Stahr, Don; Francsis, Matthew; Ashley, Kyle; Kronenberg, Andreas; Thomas, Jay; Mazza, Sarah; Heaverlo, Nicholas
2013-04-01
The quartz c-axis fabric opening-angle thermometer proposed by Kruhl (1998) offers a potential analytical technique for estimating deformation temperatures in rocks deformed by crystal plastic flow. However, in addition to deformation temperature, opening-angle is also sensitive to other variables such as strain rate, degree of hydrolytic weakening, and 3D strain type. Unless the influence of these individual variables can be quantified, use of fabric opening-angle as a deformation thermometer remains problematic and controversial. Over the last decade close correlations between: a) deformation temperatures indicated by fabric opening-angles and, b) temperatures of metamorphism indicated by trace element and mineral phase equilibria analyses, have been reported from a range of different tectonic settings, thereby arguably giving support to the use of opening-angles as a deformation thermometer. However, it needs to be demonstrated that the similar temperatures estimated by the different methods are related to the same geologic event, and therefore occupy at least a similar position on the PTt path - something that is in practice difficult to achieve for an individual rock sample. In cases where temperatures indicated by opening angles and mineral assemblages are markedly different, these differences could, for example, be explained by penetrative deformation and mineral growth/diffusion occurring at different times. Alternatively, when apparent deformation temperatures based on quartz fabrics are significantly greater than temperatures indicated by synchronous metamorphic mineral assemblages, this might be due to extreme hydrolytic weakening of quartz. We illustrate this talk on the pros and cons of using fabric opening-angles as a deformation thermometer with examples from: a) Aureoles of forcibly emplaced plutons in the White-Inyo Range of eastern California where crystal-plastic deformation and recrystallization was short-lived and synchronous with contact
Ohzeki, Masayuki
2017-01-01
Quantum annealing is a generic solver of the optimization problem that uses fictitious quantum fluctuation. Its simulation in classical computing is often performed using the quantum Monte Carlo simulation via the Suzuki–Trotter decomposition. However, the negative sign problem sometimes emerges in the simulation of quantum annealing with an elaborate driver Hamiltonian, since it belongs to a class of non-stoquastic Hamiltonians. In the present study, we propose an alternative way to avoid the negative sign problem involved in a particular class of the non-stoquastic Hamiltonians. To check the validity of the method, we demonstrate our method by applying it to a simple problem that includes the anti-ferromagnetic XX interaction, which is a typical instance of the non-stoquastic Hamiltonians. PMID:28112244
Universal localizing bounds for compact invariant sets of natural polynomial Hamiltonian systems
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.
A systematic study of finite BRST-BFV transformations in generalized Hamiltonian formalism
Batalin, Igor A.; Lavrov, Peter M.; Tyutin, Igor V.
2014-09-01
We study systematically finite BRST-BFV transformations in the generalized Hamiltonian formalism. We present explicitly their Jacobians and the form of a solution to the compensation equation determining the functional field dependence of finite Fermionic parameters, necessary to generate an arbitrary finite change of gauge-fixing functions in the path integral.
A systematic study of finite BRST-BFV transformations in generalized Hamiltonian formalism
Batalin, Igor A; Tyutin, Igor V
2014-01-01
We study systematically finite BRST-BFV transformations in the generalized Hamiltonian formalism. We present explicitly their Jacobians and the form of a solution to the compensation equation determining the functional field dependence of finite Fermionic parameters, necessary to generate arbitrary finite change of gauge-fixing functions in the path integral.
Batalin, Igor A; Tyutin, Igor V
2014-01-01
We study systematically finite BRST-BFV transformations in $Sp(2)$-extended generalized Hamiltonian formalism. We present explicitly their Jacobians and the form of a solution to the compensation equation determining the functional field dependence of finite Fermionic parameters, necessary to generate arbitrary finite change of gauge-fixing functions in the path integral.
Batalin, Igor A.; Lavrov, Peter M.; Tyutin, Igor V.
2014-09-01
We study systematically finite BRST-BFV transformations in Sp(2)-extended generalized Hamiltonian formalism. We present explicitly their Jacobians and the form of a solution to the compensation equation determining the functional field dependence of finite Fermionic parameters, necessary to generate arbitrary finite change of gauge-fixing functions in the path integral.
Protein-Ligand Binding from Distancefield Distances and Hamiltonian Replica Exchange Simulations.
de Ruiter, Anita; Oostenbrink, Chris
2013-02-12
The calculation of protein-ligand binding free energies is an important goal in the field of computational chemistry. Applying path-sampling methods for this purpose involves calculating the associated potential of mean force (PMF) and gives insight into the binding free energy along the binding process. Without a priori knowledge about the binding path, sampling reversible binding can be difficult to achieve. To alleviate this problem, we introduce the distancefield (DF) as a reaction coordinate for such calculations. DF is a grid-based method in which the shortest distance between the binding site and a ligand is determined avoiding routes that pass through the protein. Combining this reaction coordinate with Hamiltonian replica exchange molecular dynamics (HREMD) allows for the reversible binding of the ligand to the protein. A comparison is made between umbrella sampling using regular distance restraints and HREMD with DF restraints to study aspirin binding to the protein phospholipase A2. Although the free energies of binding are similar for both methods, the increased sampling with HREMD has a significant influence on the shape of the PMF. A remarkable agreement between the calculated binding free energies from the PMF and the experimental estimate is obtained.
Path planning in dynamic environments
Berg, J.P. van den
2007-01-01
Path planning plays an important role in various fields of application, such as CAD design, computer games and virtual environments, molecular biology, and robotics. In its most general form, the path planning problem is formulated as finding a collision-free path for a moving entity between a start
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 ...
Maxwell consideration of polaritonic quasi-particle Hamiltonians in multi-level systems
Richter, Steffen; Michalsky, Tom; Fricke, Lennart; Sturm, Chris; Franke, Helena; Grundmann, Marius; Schmidt-Grund, Rüdiger [Institut für Experimentelle Physik II, Universität Leipzig, Linnéstr. 5, 04103 Leipzig (Germany)
2015-12-07
We address the problem of the correct description of light-matter coupling for excitons and cavity photons in the case of systems with multiple photon modes or excitons, respectively. In the literature, two different approaches for the phenomenological coupling Hamiltonian can be found: Either one single Hamiltonian with a basis whose dimension equals the sum of photonic modes and excitonic resonances is used. Or a set of independent Hamiltonians, one for each photon mode, is chosen. Both are usually used equivalently for the same kind of multi-photonic systems which cannot be correct. However, identifying the suitable Hamiltonian is difficult when modeling experimental data. By means of numerical transfer matrix calculations, we demonstrate the scope of application of each approach: The first one holds only for the coupling of a single photon state to several excitons, while in the case of multiple photon modes, separate Hamiltonians must be used for each photon mode.
(Anti-Hermitian Generalized (Anti-Hamiltonian Solution to a System of Matrix Equations
Juan Yu
2014-01-01
Full Text Available We mainly solve three problems. Firstly, by the decomposition of the (anti-Hermitian generalized (anti-Hamiltonian matrices, the necessary and sufficient conditions for the existence of and the expression for the (anti-Hermitian generalized (anti-Hamiltonian solutions to the system of matrix equations AX=B,XC=D are derived, respectively. Secondly, the optimal approximation solution minX∈K∥X^-X∥ is obtained, where K is the (anti-Hermitian generalized (anti-Hamiltonian solution set of the above system and X^ is the given matrix. Thirdly, the least squares (anti-Hermitian generalized (anti-Hamiltonian solutions are considered. In addition, algorithms about computing the least squares (anti-Hermitian generalized (anti-Hamiltonian solution and the corresponding numerical examples are presented.
Quantum Calisthenics: Gaussians, The Path Integral and Guided Numerical Approximations
Weinstein, Marvin; /SLAC
2009-02-12
It is apparent to anyone who thinks about it that, to a large degree, the basic concepts of Newtonian physics are quite intuitive, but quantum mechanics is not. My purpose in this talk is to introduce you to a new, much more intuitive way to understand how quantum mechanics works. I begin with an incredibly easy way to derive the time evolution of a Gaussian wave-packet for the case free and harmonic motion without any need to know the eigenstates of the Hamiltonian. This discussion is completely analytic and I will later use it to relate the solution for the behavior of the Gaussian packet to the Feynman path-integral and stationary phase approximation. It will be clear that using the information about the evolution of the Gaussian in this way goes far beyond what the stationary phase approximation tells us. Next, I introduce the concept of the bucket brigade approach to dealing with problems that cannot be handled totally analytically. This approach combines the intuition obtained in the initial discussion, as well as the intuition obtained from the path-integral, with simple numerical tools. My goal is to show that, for any specific process, there is a simple Hilbert space interpretation of the stationary phase approximation. I will then argue that, from the point of view of numerical approximations, the trajectory obtained from my generalization of the stationary phase approximation specifies that subspace of the full Hilbert space that is needed to compute the time evolution of the particular state under the full Hamiltonian. The prescription I will give is totally non-perturbative and we will see, by the grace of Maple animations computed for the case of the anharmonic oscillator Hamiltonian, that this approach allows surprisingly accurate computations to be performed with very little work. I think of this approach to the path-integral as defining what I call a guided numerical approximation scheme. After the discussion of the anharmonic oscillator I will
Hong; TAN
2014-01-01
The new curriculum,new ideas and new requirements concerning English teaching have made the rural English teaching face unprecedented challenges. There are many problems contributing to the poor effect of rural English teaching,such as outdated teaching equipment,unreasonable curriculum design,insufficient teaching staff,asymmetrical teaching content,family education and students’ personal problems. Based on the Chinese General Social Survey data,it is found that in terms of English reading,English speaking or English writing,the current English level of China’s rural residents is lagging behind. From the average,the reading level of rural residents is better than the speaking and writing level,but the paired T-test results show that there are no significant differences between them,suggesting that under the current system of rural English teaching,the English level of rural residents is constrained to a low level. To improve the rural English teaching in the future,it is necessary to pay close attention to the following aspects: stabilizing the investment in rural education; optimizing the English teaching content; converting the philosophy of education; increasing teacher training; establishing the new linkage system.
Monte Carlo Hamiltonian: Linear Potentials
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
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.
Stochastic optimal control of partially observable nonlinear quasi-integrable Hamiltonian systems
无
2010-01-01
The stochastic optimal control of partially observable nonlinear quasi-integrable Hamiltonian systems is investigated. First, the stochastic optimal control problem of a partially observable nonlinear quasi-integrable Hamiltonian system is converted into that of a completely observable linear system based on a theorem due to Charalambous and Elliot. Then, the converted stochastic optimal control problem is solved by applying the stochastic averaging method and the stochastic dynamical programming principle. The response of the controlled quasi Hamiltonian system is predicted by solving the averaged Fokker-Planck-Kolmogorov equation and the Riccati equation for the estimated error of system states. As an example to illustrate the procedure and effectiveness of the proposed method, the stochastic optimal control problem of a partially observable two-degree-of-freedom quasi-integrable Hamiltonian system is worked out in detail.
Fluctuating paths and fields Festschrift Kleinert (Hagen)
Bachmann, M; Schmidt, H J; Janke, W
2001-01-01
This volume covers the following fields: path integrals, quantum field theory, variational perturbation theory, phase transitions and critical phenomena, topological defects, strings and membranes, gravitation and cosmology. Contents: Path Integrals and Quantum Mechanics: Semiclassical Quantum Mechanics: A Path-Integral Approach (B R Holstein); Conjecture on the Reality of Spectra of Non-Hermitian Hamiltonians (C M Bender et al.); Time-Transformation Approach to q -Deformed Objects (A Inomata); Characterizing Volume Forms (P Cartier et al.); Vassiliev Invariants and Functional Integration (L H
Hamiltonian formulation of time-dependent plausible inference
Davis, Sergio
2014-01-01
Maximization of the path information entropy is a clear prescription for performing time-dependent plausible inference. Here it is shown that, following this prescription under the assumption of arbitrary instantaneous constraints on position and velocity, a Lagrangian emerges which determines the most probable trajectory. Deviations from the probability maximum can be consistently described as slices in time by a Hamiltonian, according to a nonlinear Langevin equation and its associated Fokker-Planck equation. The connections unveiled between the maximization of path entropy and the Langevin/Fokker-Planck equations imply that missing information about the phase space coordinate never decreases in time, a purely information-theoretical version of the Second Law of Thermodynamics. All of these results are independent of any physical assumptions, and thus valid for any generalized coordinate as a function of time, or any other parameter. This reinforces the view that the Second Law is a fundamental property of ...
Stochastic averaging of quasi-Hamiltonian systems
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.
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.
An Effective-Hamiltonian Approach to CH5+, Using Ideas from Atomic Spectroscopy
Hougen, Jon T.
2016-06-01
In this talk we present the first steps in the design of an effective Hamiltonian for the vibration-rotation energy levels of CH5+. Such a Hamiltonian would allow calculation of energy level patterns anywhere along the path travelled by a hypothetical CH5+ (or CD5+) molecule as it passes through various coupling cases, and might thus provide some hints for assigning the observed high-resolution spectra. The steps discussed here, which have not yet addressed computational problems, focus on mapping the vibration-rotation problem in CH5+ onto the five-electron problem in the boron atom, using ideas and mathematical machinery from Condon and Shortley's book on atomic spectroscopy. The mapping ideas are divided into: (i) a mapping of particles, (ii) a mapping of coordinates (i.e., mathematical degrees of freedom), and (iii) a mapping of quantum mechanical interaction terms. The various coupling cases along the path correspond conceptually to: (i) the analog of a free-rotor limit, where the H atoms see the central C atom but do not see each other, (ii) the low-barrier and high-barrier tunneling regimes, and (iii) the rigid-molecule limit, where the H atoms remain locked in some fixed molecular geometry. Since the mappings considered here often involve significant changes in mathematics, a number of interesting qualitative changes occur in the basic ideas when passing from B to CH5+, particularly in discussions of: (i) antisymmetrization and symmetrization ideas, (ii) n,l,ml,ms or n,l,j,mj quantum numbers, and (iii) Russell-Saunders computations and energy level patterns. Some of the mappings from B to CH5+ to be discussed are as follows. Particles: the atomic nucleus is replaced by the C atom, the electrons are replaced by protons, and the empty space between particles is replaced by an "electron soup." Coordinates: the radial coordinates of the electrons map onto the five local C-H stretching modes, the angular coordinates of the electrons map onto three rotational
Liu, Jian
2017-01-01
We introduce the isomorphism between an multi-state Hamiltonian and the second-quantized many-electron Hamiltonian (with only 1-electron interactions). This suggests that all methods developed for the former can be employed for the latter, and vice versa. The resonant level (Landauer) model for nonequilibrium quantum transport is used as a proof-of-concept example. Such as the classical mapping models for the multi-state Hamiltonian proposed in our previous work [J. Liu, J. Chem. Phys. 145, 204105 (2016)] lead to exact results for this model problem. We further demonstrate how these methods can also be applied to the second-quantized many-electron Hamiltonian even when 2-electron interactions are included.
Liu, Jian
2016-01-01
We introduce the isomorphism between the multi-state Hamiltonian and the second-quantized many-electron Hamiltonian (with only 1-electron interactions). This suggests that all methods developed for the former can be employed for the latter, and vice versa. The resonant level (Landauer) model for nonequilibrium quantum transport is used as a proof-of-concept example. Such as the classical mapping models for the multi-state Hamiltonian proposed in our previous work [J. Chem. Phys. (submitted)] lead to exact results for this model problem. We further demonstrate how these methods can also be applied to the second-quantized many-electron Hamiltonian even when 2-electron interactions are included.
Non-Hamiltonian perturbations of integrable systems and resonance trapping
Ghil, M.; Wolansky, G.
1992-01-01
This paper studies general, non-Hamiltonian perturbations of integrable systems with two degrees of freedom and derives conditions for temporary and permanent resonance trapping. The analysis involves a noncanonical transformation of variables near the resonant manifold and averaging with respect to the fast phase to investigate oscillatory behavior on the intermediate timescale. The resulting reduced system is Hamiltonian to leading order and permits, after averaging on the intermediate, or libration, timescale, a canonical transformation to action-angle variables in the oscillation zone. The final system so obtained reveals the possible existence of two- and three-dimensional invariant tori in the vicinity of the resonant manifold. An explicit divergence condition for general perturbations to be dissipative on the slow timescale follows from the analysis. An application of this approach to the problem of resonant trapping and escape is outlined for the restricted problem of three bodies subject to dissipative perturbations with a radial symmetry.
Deepak Goyal
2013-07-01
Full Text Available This paper addresses the malicious node detection and path optimization problem for wireless sensor networks. Malicious node detection in neighborhood is a needed because that node may cause incorrect decisions or energy depletion. In this paper APSO (combination of Artificial bee colony and particular swarm optimization is used to choose an optimized path. Through this improved version we will overcome the disadvantage of local optimal which comes when we use PSO approach.
An application of Hamiltonian neurodynamics using Pontryagin's Maximum (Minimum) Principle.
Koshizen, T; Fulcher, J
1995-12-01
Classical optimal control methods, notably Pontryagin's Maximum (Minimum) Principle (PMP) can be employed, together with Hamiltonians, to determine optimal system weights in Artificial Neural dynamical systems. A new learning rule based on weight equations derived using PMP is shown to be suitable for both discrete- and continuous-time systems, and moreover, can also be applied to feedback networks. Preliminary testing shows that this PMP learning rule compares favorably with Standard BackPropagations (SBP) on the XOR problem.
When a local Hamiltonian must be frustration-free
Sattath, Or; Morampudi, Siddhardh C.; Laumann, Chris R.; Moessner, Roderich
2016-06-01
A broad range of quantum optimization problems can be phrased as the question of whether a specific system has a ground state at zero energy, i.e., whether its Hamiltonian is frustration-free. Frustration-free Hamiltonians, in turn, play a central role for constructing and understanding new phases of matter in quantum many-body physics. Unfortunately, determining whether this is the case is known to be a complexity-theoretically intractable problem. This makes it highly desirable to search for efficient heuristics and algorithms to, at least, partially answer this question. Here we prove a general criterion—a sufficient condition—under which a local Hamiltonian is guaranteed to be frustration-free by lifting Shearer’s theorem from classical probability theory to the quantum world. Remarkably, evaluating this condition proceeds via a fully classical analysis of a hardcore lattice gas at negative fugacity on the Hamiltonian’s interaction graph, which, as a statistical mechanics problem, is of interest in its own right. We concretely apply this criterion to local Hamiltonians on various regular lattices, while bringing to bear the tools of spin glass physics that permit us to obtain new bounds on the satisfiable to unsatisfiable transition in random quantum satisfiability. We are then led to natural conjectures for when such bounds will be tight, as well as to a novel notion of universality for these computer science problems. Besides providing concrete algorithms leading to detailed and quantitative insights, this work underscores the power of marrying classical statistical mechanics with quantum computation and complexity theory.
Hamiltonian hierarchy and the Hulthén potential
Gönül, B.; Özer, O.; Cançelik, Y.; Koçak, M.
2000-10-01
We deal with the Hamiltonian hierarchy problem of the Hulthén potential within the frame of the supersymmetric quantum mechanics and find that the associated supersymmetric 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 the Hulthén potential which gives satisfactory values for the non-zero angular momentum states.
(Anti-)Hermitian Generalized (Anti-)Hamiltonian Solution to a System of Matrix Equations
Juan Yu; Qing-Wen Wang; Chang-Zhou Dong
2014-01-01
We mainly solve three problems. Firstly, by the decomposition of the (anti-)Hermitian generalized (anti-)Hamiltonian matrices, the necessary and sufficient conditions for the existence of and the expression for the (anti-)Hermitian generalized (anti-)Hamiltonian solutions to the system of matrix equations AX=B,XC=D are derived, respectively. Secondly, the optimal approximation solution minX∈K∥X^-X∥ is obtained, where K is the (anti-)Hermitian generalized (anti-)Hamiltonian solution set of t...
EIGENVALUE PROBLEM OF A LARGE SCALE INDEFINITE GYROSCOPIC DYNAMIC SYSTEM
SUI Yong-feng; ZHONG Wan-xie
2006-01-01
Gyroscopic dynamic system can be introduced to Hamiltonian system. Based on an adjoint symplectic subspace iteration method of Hamiltonian gyroscopic system,an adjoint symplectic subspace iteration method of indefinite Hamiltonian function gyroscopic system was proposed to solve the eigenvalue problem of indefinite Hamiltonian function gyroscopic system. The character that the eigenvalues of Hamiltonian gyroscopic system are only pure imaginary or zero was used. The eigenvalues that Hamiltonian function is negative can be separated so that the eigenvalue problem of positive definite Hamiltonian function system was presented, and an adjoint symplectic subspace iteration method of positive definite Hamiltonian function system was used to solve the separated eigenvalue problem. Therefore, the eigenvalue problem of indefinite Hamiltonian function gyroscopic system was solved, and two numerical examples were given to demonstrate that the eigensolutions converge exactly.
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
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
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
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
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.
Square conservation systems and Hamiltonian systems
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.
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.
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 $t\\rightarrow \\infty$.
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.
Williams, Virginia Vassilevska
2010-01-01
The replacement paths problem for directed graphs is to find for given nodes s and t and every edge e on the shortest path between them, the shortest path between s and t which avoids e. For unweighted directed graphs on n vertices, the best known algorithm runtime was \\tilde{O}(n^{2.5}) by Roditty and Zwick. For graphs with integer weights in {-M,...,M}, Weimann and Yuster recently showed that one can use fast matrix multiplication and solve the problem in O(Mn^{2.584}) time, a runtime which would be O(Mn^{2.33}) if the exponent \\omega of matrix multiplication is 2. We improve both of these algorithms. Our new algorithm also relies on fast matrix multiplication and runs in O(M n^{\\omega} polylog(n)) time if \\omega>2 and O(n^{2+\\eps}) for any \\eps>0 if \\omega=2. Our result shows that, at least for small integer weights, the replacement paths problem in directed graphs may be easier than the related all pairs shortest paths problem in directed graphs, as the current best runtime for the latter is \\Omega(n^{2.5...
Shortest Paths and Vehicle Routing
Petersen, Bjørn
This thesis presents how to parallelize a shortest path labeling algorithm. It is shown how to handle Chvátal-Gomory rank-1 cuts in a column generation context. A Branch-and-Cut algorithm is given for the Elementary Shortest Paths Problem with Capacity Constraint. A reformulation of the Vehicle R...... Routing Problem based on partial paths is presented. Finally, a practical application of finding shortest paths in the telecommunication industry is shown.......This thesis presents how to parallelize a shortest path labeling algorithm. It is shown how to handle Chvátal-Gomory rank-1 cuts in a column generation context. A Branch-and-Cut algorithm is given for the Elementary Shortest Paths Problem with Capacity Constraint. A reformulation of the Vehicle...
The Liouville integrable coupling system of the m-AKNS hierarchy and its Hamiltonian structure
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.
An optimum Hamiltonian for non-Hermitian quantum evolution and the complex Bloch sphere
Nesterov, Alexander I., E-mail: nesterov@cencar.udg.m [Departamento de Fisica, CUCEI, Universidad de Guadalajara, Av. Revolucion 1500, Guadalajara, CP 44420, Jalisco (Mexico)
2009-09-28
For a quantum system governed by a non-Hermitian Hamiltonian, we studied the problem of obtaining an optimum Hamiltonian that generates nonunitary transformations of a given initial state into a certain final state in the smallest time tau. The analysis is based on the relationship between the states of the two-dimensional subspace of the Hilbert space spanned by the initial and final states and the points of the two-dimensional complex Bloch sphere.
Asteroidal Quadruples in non Rooted Path Graphs
Gutierrez Marisa
2015-11-01
Full Text Available A directed path graph is the intersection graph of a family of directed subpaths of a directed tree. A rooted path graph is the intersection graph of a family of directed subpaths of a rooted tree. Rooted path graphs are directed path graphs. Several characterizations are known for directed path graphs: one by forbidden induced subgraphs and one by forbidden asteroids. It is an open problem to find such characterizations for rooted path graphs. For this purpose, we are studying in this paper directed path graphs that are non rooted path graphs. We prove that such graphs always contain an asteroidal quadruple.
Mireille Bousquet-Mélou
2008-04-01
Full Text Available Let a and b be two positive integers. A culminating path is a path of ℤ 2 that starts from (0,0, consists of steps (1,a and (1,-b, stays above the x-axis and ends at the highest ordinate it ever reaches. These paths were first encountered in bioinformatics, in the analysis of similarity search algorithms. They are also related to certain models of Lorentzian gravity in theoretical physics. We first show that the language on a two letter alphabet that naturally encodes culminating paths is not context-free. Then, we focus on the enumeration of culminating paths. A step by step approach, combined with the kernel method, provides a closed form expression for the generating function of culminating paths ending at a (generic height k. In the case a = b, we derive from this expression the asymptotic behaviour of the number of culminating paths of length n. When a > b, we obtain the asymptotic behaviour by a simpler argument. When a < b, we only determine the exponential growth of the number of culminating paths. Finally, we study the uniform random generation of culminating paths via various methods. The rejection approach, coupled with a symmetry argument, gives an algorithm that is linear when a ≥ b, with no precomputation stage nor non-linear storage required. The choice of the best algorithm is not as clear when a < b. An elementary recursive approach yields a linear algorithm after a precomputation stage involving O (n 3 arithmetic operations, but we also present some alternatives that may be more efficient in practice.
On the quantum mechanics of bicomplex Hamiltonian system
Banerjee, Abhijit
2017-02-01
We investigate the Schrödinger equation in the framework of bicomplex numbers, which are pairs of complex numbers making up a commutative ring with zero-divisors. We propose an analytical method to solve bicomplex-version of Schrödinger equation corresponding to the systems of Hamiltonians of both hermitian (self-adjoint) and non-hermitian PT symmetric type. In our approach we extend the existing mathematical formulation of quantum system searching for the exact or quasi-exact solution for ground state energy eigenvalues and associated wave functions acting in bicomplex Hilbert space. The model concerning hermitian Hamiltonians is then applied to the problems of two bicomplex valued polynomial oscillators one involving x2 and another of isotonic type. The ground states and associated energy values for both the oscillators are found to be hyperbolic in nature. The model in connection to the unbroken PT symmetric Hamiltonians is then applied to illustrate the problems of complex and bicomplex valued shifted oscillators.
赵著行; 闵应骅; 等
1997-01-01
For different delay models,the concept of sensitization can be very different.Traditonal concepts of sensitization cannot precisely describe circuit behavior when the input vectors change very fast.Using Boolean process aporoach,this paper presents a new definition of sensitization for arbitrary input waveforms.By this new concept it is found that if the inputs of a combinational circuit can change at any time,and each gate's delay varies within an interval (bounded gate delay model),then every path,which is not necessarily a single topological path,is sensitizable.From the experimental results it can be seen that,all nonsensitizable paths for traditional concepts actually can propagate transitions along them for some input waveforms.However,specified time between input transitions(STBIT) and minimum permissible pulse width(ε）are two major factors to make some paths non-sensitizable.
Optical waveguide Hamiltonians leading to step-2 difference equations
Rueda-Paz, Juvenal; Wolf, Kurt Bernardo, E-mail: bwolf@fis.unam.mx [Instituto de Ciencias Fisicas, Universidad Nacional Autonoma de Mexico, Av. Universidad s/n, Cuernavaca, Morelos 62251 (Mexico)
2011-03-01
We examine the evolution of an N-point signal produced and sensed at finite arrays of points transverse to a planar waveguide, within the framework of the finite quantization of geometric optics. In contradistinction to the common mechanical Hamiltonians (kinetic plus potential energy terms) the classical waveguide Hamiltonian is the square root of a difference of squares of the refractive index profile minus the optical momentum. The finitely quantized model requires the solution of the square eigenvalue and eigenfunction problem which leads to a step-two difference equation that contains two solutions and two signs of energy. We find the proper linear combinations to fit the Kravchuk functions of the finite oscillator model.
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.
The envelope Hamiltonian for electron interaction with ultrashort pulses
Toyota, Koudai; Rost, Jan M
2014-01-01
For ultrashort VUV pulses with a pulse length comparable to the orbital time of the bound electrons they couple to we propose a simplified envelope Hamiltonian. It is based on the Kramers-Henneberger representation in connection with a Floquet expansion of the strong-field dynamics but keeps the time dependence of the pulse envelope explicit. Thereby, the envelope Hamiltonian captures the essence of the physics, -- light-induced shifts of bound states, single-photon absorption, and non-adiabatic electronic transitions. It delivers quantitatively accurate ionization dynamics and allows for physical insight into the processes occurring. Its minimal requirements for construction in terms of laser parameters make it ideally suited for a large class of atomic and molecular problems.
Optical waveguide Hamiltonians leading to step-2 difference equations
Rueda-Paz, Juvenal; Wolf, Kurt Bernardo
2011-03-01
We examine the evolution of an N-point signal produced and sensed at finite arrays of points transverse to a planar waveguide, within the framework of the finite quantization of geometric optics. In contradistinction to the common mechanical Hamiltonians (kinetic plus potential energy terms) the classical waveguide Hamiltonian is the square root of a difference of squares of the refractive index profile minus the optical momentum. The finitely quantized model requires the solution of the square eigenvalue and eigenfunction problem which leads to a step-two difference equation that contains two solutions and two signs of energy. We find the proper linear combinations to fit the Kravchuk functions of the finite oscillator model.
Energy diffusion controlled reaction rate in dissipative Hamiltonian systems
Deng Mao-Lin; Zhu Wei-Qiu
2007-01-01
In this paper the energy diffusion controlled reaction rate in dissipative Hamiltonian systems is investigated by using the stochastic averaging method for quasi Hamiltonian systems. The boundary value problem of mean first-passage time (MFPT) of averaged system is formulated and the energy diffusion controlled reaction rate is obtained as the inverse of MFPT. The energy diffusion controlled reaction rate in the classical Kramers bistable potential and in a two-dimensional bistable potential with a heat bath are obtained by using the proposed approach respectively. The obtained results are then compared with those from Monte Carlo simulation of original systems and from the classical Kramers theory. It is shown that the reaction rate obtained by using the proposed approach agrees well with that from Monte Carlo simulation and is more accurate than the classical Kramers rate.
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.
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
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
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.
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
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
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.
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.
Improved Sufficient Conditions for Hamiltonian Properties
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.
Coherent discrete embeddings for Lagrangian and Hamiltonian systems
Cresson, Jacky; Pierre, Charles
2011-01-01
The general topic of the present paper is to study the conservation for some structural property of a given problem when discretising this problem. Precisely we are interested with Lagrangian or Hamiltonian structures and thus with variational problems attached to a least action principle. Considering a partial differential equation (PDE) deriving from such a variational principle, a natural question is to know whether this structure at the continuous level is preserved at the discrete level when discretising the PDE. To address this question a concept of \\textit{coherence} is introduced. Both the differential equation (the PDE translating the least action principle) and the variational structure can be embedded at the discrete level. This provides two discrete embeddings for the original problem. In case these procedures finally provide the same discrete problem we will say that the discretisation is \\textit{coherent}. Our purpose is illustrated with the Poisson problem. Coherence for discrete embeddings of ...
Hamiltonian system for orthotropic plate bending based on analogy theory
无
2001-01-01
Based on analogy between plane elasticity and plate bending as well as variational principles of mixed energy, Hamiltonian system is further led to orthotropic plate bending problems in this paper. Thus many effective methods of mathematical physics such as separation of variables and eigenfunction expansion can be employed in orthotropic plate bending problems as they are used in plane elasticity. Analytical solutions of rectangular plate are presented directly, which expands the range of analytical solutions. There is an essential distinction between this method and traditional semi-inverse method. Numerical results of orthotropic plate with two lateral sides fixed are included to demonstrate the effectiveness and accuracy of this method.
An alternative path integral for quantum gravity
Krishnan, Chethan; Kumar, K. V. Pavan; Raju, Avinash
2016-10-01
We define a (semi-classical) path integral for gravity with Neumann boundary conditions in D dimensions, and show how to relate this new partition function to the usual picture of Euclidean quantum gravity. We also write down the action in ADM Hamiltonian formulation and use it to reproduce the entropy of black holes and cosmological horizons. A comparison between the (background-subtracted) covariant and Hamiltonian ways of semi-classically evaluating this path integral in flat space reproduces the generalized Smarr formula and the first law. This "Neumann ensemble" perspective on gravitational thermodynamics is parallel to the canonical (Dirichlet) ensemble of Gibbons-Hawking and the microcanonical approach of Brown-York.
An Alternate Path Integral for Quantum Gravity
Krishnan, Chethan; Raju, Avinash
2016-01-01
We define a (semi-classical) path integral for gravity with Neumann boundary conditions in $D$ dimensions, and show how to relate this new partition function to the usual picture of Euclidean quantum gravity. We also write down the action in ADM Hamiltonian formulation and use it to reproduce the entropy of black holes and cosmological horizons. A comparison between the (background-subtracted) covariant and Hamiltonian ways of semi-classically evaluating this path integral in flat space reproduces the generalized Smarr formula and the first law. This "Neumann ensemble" perspective on gravitational thermodynamics is parallel to the canonical (Dirichlet) ensemble of Gibbons-Hawking and the microcanonical approach of Brown-York.
An alternative path integral for quantum gravity
Krishnan, Chethan; Kumar, K.V. Pavan; Raju, Avinash [Center for High Energy Physics, Indian Institute of Science,Bangalore 560012 (India)
2016-10-10
We define a (semi-classical) path integral for gravity with Neumann boundary conditions in D dimensions, and show how to relate this new partition function to the usual picture of Euclidean quantum gravity. We also write down the action in ADM Hamiltonian formulation and use it to reproduce the entropy of black holes and cosmological horizons. A comparison between the (background-subtracted) covariant and Hamiltonian ways of semi-classically evaluating this path integral in flat space reproduces the generalized Smarr formula and the first law. This “Neumann ensemble” perspective on gravitational thermodynamics is parallel to the canonical (Dirichlet) ensemble of Gibbons-Hawking and the microcanonical approach of Brown-York.
Path Integrals in Quantum Physics
Rosenfelder, R
2012-01-01
These lectures aim at giving graduate students an introduction to and a working knowledge of path integral methods in a wide variety of fields in physics. Consequently, the lecture notes are organized in three main parts dealing with non-relativistic quantum mechanics, many-body physics and field theory. In the first part the basic concepts of path integrals are developed in the usual heuristic, non-mathematical way followed by standard examples and special applications including numerical evaluation of (euclidean) path integrals by Monte-Carlo methods with a program for the anharmonic oscillator. The second part deals with the application of path integrals in statistical mechanics and many-body problems treating the polaron problem, dissipative quantum systems, path integrals over ordinary and Grassmannian coherent states and perturbation theory for both bosons and fermions. Again a simple Fortran program is included for illustrating the use of strong-coupling methods. Finally, in the third part path integra...
Hamiltonian formalism for Perturbed Black Hole Spacetimes
Mihaylov, Deyan; Gair, Jonathan
2017-01-01
Present and future gravitational wave observations provide a new mechanism to probe the predictions of general relativity. Observations of extreme mass ratio inspirals with millihertz gravitational wave detectors such as LISA will provide exquisite constraints on the spacetime structure outside astrophysical black holes, enabling tests of the no-hair property that all general relativistic black holes are described by the Kerr metric. Previous work to understand what constraints LISA observations will be able to place has focussed on specific alternative theories of gravity, or generic deviations that preserve geodesic separability. We describe an alternative approach to this problem--a technique that employs canonical perturbations of the Hamiltonian function describing motion in the Kerr metric. We derive this new approach and demonstrate its application to the cases of a slowly rotating Kerr black hole which is viewed as a perturbation of a Schwarzschild black hole, of coupled perturbations of black holes in the second-order Chern-Simons modified gravity theory, and several more indicative scenarios. Deyan Mihaylov is funded by STFC.
Effective stability for generalized Hamiltonian systems
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
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.
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
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 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.
Continuous finite element methods for Hamiltonian systems
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.
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
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.
Finite-time thermodynamics of port-Hamiltonian systems
Delvenne, Jean-Charles; Sandberg, Henrik
2014-01-01
In this paper, we identify a class of time-varying port-Hamiltonian systems that is suitable for studying problems at the intersection of statistical mechanics and control of physical systems. Those port-Hamiltonian systems are able to modify their internal structure as well as their interconnection with the environment over time. The framework allows us to prove the First and Second Laws of thermodynamics, but also lets us apply results from optimal and stochastic control theory to physical systems. In particular, we show how to use linear control theory to optimally extract work from a single heat source over a finite time interval in the manner of Maxwell’s demon. Furthermore, the optimal controller is a time-varying port-Hamiltonian system, which can be physically implemented as a variable linear capacitor and transformer. We also use the theory to design a heat engine operating between two heat sources in finite-time Carnot-like cycles of maximum power, and we compare those two heat engines.
Hamiltonian of a homogeneous two-component plasma.
Essén, Hanno; Nordmark, A
2004-03-01
The Hamiltonian of one- and two-component plasmas is calculated in the negligible radiation Darwin approximation. Since the Hamiltonian is the phase space energy of the system its form indicates, according to statistical mechanics, the nature of the thermal equilibrium that plasmas strive to attain. The main issue is the length scale of the magnetic interaction energy. In the past a screening length lambda=1/square root of r(e)n], with n number density and r(e) classical electron radius, has been derived. We address the question whether the corresponding longer screening range obtained from the classical proton radius is physically relevant and the answer is affirmative. Starting from the Darwin Lagrangian it is nontrivial to find the Darwin Hamiltonian of a macroscopic system. For a homogeneous system we resolve the difficulty by temporarily approximating the particle number density by a smooth constant density. This leads to Yukawa-type screened vector potential. The nontrivial problem of finding the corresponding, divergence free, Coulomb gauge version is solved.
Madsen, Mogens Ove
Begrebet Path Dependence blev oprindelig udviklet inden for New Institutionel Economics af bl.a. David, Arthur og North. Begrebet har spredt sig vidt i samfundsvidenskaberne og undergået en udvikling. Dette paper propagerer for at der er sket så en så omfattende udvikling af begrebet, at man nu kan...... tale om 1. og 2. generation af Path Dependence begrebet. Den nyeste udvikling af begrebet har relevans for metodologi-diskusionerne i relation til Keynes...
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.
Interest rates in quantum finance: the Wilson expansion and Hamiltonian.
Baaquie, Belal E
2009-10-01
Interest rate instruments form a major component of the capital markets. The Libor market model (LMM) is the finance industry standard interest rate model for both Libor and Euribor, which are the most important interest rates. The quantum finance formulation of the Libor market model is given in this paper and leads to a key generalization: all the Libors, for different future times, are imperfectly correlated. A key difference between a forward interest rate model and the LMM lies in the fact that the LMM is calibrated directly from the observed market interest rates. The short distance Wilson expansion [Phys. Rev. 179, 1499 (1969)] of a Gaussian quantum field is shown to provide the generalization of Ito calculus; in particular, the Wilson expansion of the Gaussian quantum field A(t,x) driving the Libors yields a derivation of the Libor drift term that incorporates imperfect correlations of the different Libors. The logarithm of Libor phi(t,x) is defined and provides an efficient and compact representation of the quantum field theory of the Libor market model. The Lagrangian and Feynman path integrals of the Libor market model of interest rates are obtained, as well as a derivation given by its Hamiltonian. The Hamiltonian formulation of the martingale condition provides an exact solution for the nonlinear drift of the Libor market model. The quantum finance formulation of the LMM is shown to reduce to the industry standard Bruce-Gatarek-Musiela-Jamshidian model when the forward interest rates are taken to be exactly correlated.
Evolution of Arbitrary States under Fock-Darwin Hamiltonian and a Time-Dependent Electric Field
徐晓飞; 杨涛; 翟智远; 潘孝胤
2012-01-01
The method of path integral is employed to calculate the time evolution of the eigenstates of a charged particle under the Fock-Darwin （FD） Hamiltonian subjected to a time-dependent electric field in the plane of the system. An exact analytical expression is established for the evolution of the eigenstates. This result then provides a general solution to the time-dependent Schrodinger equation.
Path Integral Approach to Atomic Collisions
Harris, Allison
2016-09-01
The Path Integral technique is an alternative formulation of quantum mechanics that is based on a Lagrangian approach. In its exact form, it is completely equivalent to the Hamiltonian-based Schrödinger equation approach. Developed by Feynman in the 1940's, following inspiration from Dirac, the path integral approach has been widely used in high energy physics, quantum field theory, and statistical mechanics. However, only in limited cases has the path integral approach been applied to quantum mechanical few-body scattering. We present a theoretical and computational development of the path integral method for use in the study of atomic collisions. Preliminary results are presented for some simple systems. Ultimately, this approach will be applied to few-body ion-atom collisions. Work supported by NSF grant PHY-1505217.
Modeling DNA Dynamics by Path Integrals
Zoli, Marco
2013-01-01
Complementary strands in DNA double helix show temporary fluctuational openings which are essential to biological functions such as transcription and replication of the genetic information. Such large amplitude fluctuations, known as the breathing of DNA, are generally localized and, microscopically, are due to the breaking of the hydrogen bonds linking the base pairs (\\emph{bps}). I apply imaginary time path integral techniques to a mesoscopic Hamiltonian which accounts for the helicoidal geometry of a short circular DNA molecule. The \\emph{bps} displacements with respect to the ground state are interpreted as time dependent paths whose amplitudes are consistent with the model potential for the hydrogen bonds. The portion of the paths configuration space contributing to the partition function is determined by selecting the ensemble of paths which fulfill the second law of thermodynamics. Computations of the thermodynamics in the denaturation range show the energetic advantage for the equilibrium helicoidal g...
Li, Fajie
2011-01-01
This unique text/reference reviews algorithms for the exact or approximate solution of shortest-path problems, with a specific focus on a class of algorithms called rubberband algorithms. Discussing each concept and algorithm in depth, the book includes mathematical proofs for many of the given statements. Topics and features: provides theoretical and programming exercises at the end of each chapter; presents a thorough introduction to shortest paths in Euclidean geometry, and the class of algorithms called rubberband algorithms; discusses algorithms for calculating exact or approximate ESPs i
Adiabatic Hamiltonian of charged particle motion in a dipole field. [geomagnetic trapping
Chen, A. J.; Stern, D. P.
1975-01-01
The Hamiltonian for a dipole field is developed, and the result is expressed by an analytic approximation accurate to within about 1%. This allows extension of results derived for equatorial particles to particles with arbitrary pitch angles; in particular, it makes available even in the presence of electric fields orthogonal to the magnetic field a function K that is preserved by the bounce-averaged motion. This function provides at once the equations of drift paths in (alpha, beta) or of their projections onto the equatorial plane; the derivation of a pacing function that times the progress of particles along such drift paths is also described.
An extended phase-space stochastic quantization of constrained Hamiltonian systems
Ter-Kazarian, G T [Byurakan Astrophysical Observatory, Byurakan 378433, Aragatsotn District (Armenia); Sobouti, Y [Institute for Advanced Studies in Basic Sciences, Gava Zang, Zanjan, PO Box 45195-159 (Iran, Islamic Republic of)], E-mail: gago-50@yahoo.com, E-mail: sobouti@iasbs.ac.ir
2008-08-08
Having gained some insight into the concept of 'actual and virtual paths' in a phase-space formalism (Sobouti and Nasiri 1993 Int. J. Mod. Phys. B 7 3255, Nasiri et al 2006 J. Math. Phys. 47 092106), in the present paper we address the question of 'extended' phase-space stochastic quantization of Hamiltonian systems with first class holonomic constraints. We present the appropriate Langevin equations, which quantize such constrained systems, and prove the equivalence of the stochastic quantization method with the conventional path-integral gauge measure of Faddeev-Popov quantization.
Lie symmetries and conserved quantities of discrete nonholonomic Hamiltonian systems
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...
Persistence of Hyperbolic Tori in Generalized Hamiltonian Systems%广义Hamilton系统中双曲环面的保持性
柳振鑫; 伊贺达赉; 黄庆道
2005-01-01
In this paper we prove the persistence of hyperbolic invariant tori in generalized Hamiltonian systems, which may admit a distinct number of action and angle variables. The systems under consideration can be odd dimensional in tangent direction. Our results generalize the well-known results of Graff and Zehnder in standard Hamiltonians. In our case the unperturbed Hamiltonian systems may be degenerate. We also consider the persistence problem of hyperbolic tori on submanifolds.
Chen, Yunjie; Kale, Seyit; Weare, Jonathan; Dinner, Aaron R; Roux, Benoît
2016-04-12
A multiple time-step integrator based on a dual Hamiltonian and a hybrid method combining molecular dynamics (MD) and Monte Carlo (MC) is proposed to sample systems in the canonical ensemble. The Dual Hamiltonian Multiple Time-Step (DHMTS) algorithm is based on two similar Hamiltonians: a computationally expensive one that serves as a reference and a computationally inexpensive one to which the workload is shifted. The central assumption is that the difference between the two Hamiltonians is slowly varying. Earlier work has shown that such dual Hamiltonian multiple time-step schemes effectively precondition nonlinear differential equations for dynamics by reformulating them into a recursive root finding problem that can be solved by propagating a correction term through an internal loop, analogous to RESPA. Of special interest in the present context, a hybrid MD-MC version of the DHMTS algorithm is introduced to enforce detailed balance via a Metropolis acceptance criterion and ensure consistency with the Boltzmann distribution. The Metropolis criterion suppresses the discretization errors normally associated with the propagation according to the computationally inexpensive Hamiltonian, treating the discretization error as an external work. Illustrative tests are carried out to demonstrate the effectiveness of the method.
Large Scale Emerging Properties from Non Hamiltonian Complex Systems
Marco Bianucci
2017-06-01
Full Text Available The concept of “large scale” depends obviously on the phenomenon we are interested in. For example, in the field of foundation of Thermodynamics from microscopic dynamics, the spatial and time large scales are order of fraction of millimetres and microseconds, respectively, or lesser, and are defined in relation to the spatial and time scales of the microscopic systems. In large scale oceanography or global climate dynamics problems the time scales of interest are order of thousands of kilometres, for space, and many years for time, and are compared to the local and daily/monthly times scales of atmosphere and ocean dynamics. In all the cases a Zwanzig projection approach is, at least in principle, an effective tool to obtain class of universal smooth “large scale” dynamics for few degrees of freedom of interest, starting from the complex dynamics of the whole (usually many degrees of freedom system. The projection approach leads to a very complex calculus with differential operators, that is drastically simplified when the basic dynamics of the system of interest is Hamiltonian, as it happens in Foundation of Thermodynamics problems. However, in geophysical Fluid Dynamics, Biology, and in most of the physical problems the building block fundamental equations of motions have a non Hamiltonian structure. Thus, to continue to apply the useful projection approach also in these cases, we exploit the generalization of the Hamiltonian formalism given by the Lie algebra of dissipative differential operators. In this way, we are able to analytically deal with the series of the differential operators stemming from the projection approach applied to these general cases. Then we shall apply this formalism to obtain some relevant results concerning the statistical properties of the El Niño Southern Oscillation (ENSO.
Rigorous KAM results around arbitrary periodic orbits for Hamiltonian systems
Kapela, Tomasz; Simó, Carles
2017-03-01
We set up a methodology for computer assisted proofs of the existence and the KAM stability of an arbitrary periodic orbit for Hamiltonian systems. We give two examples of application for systems with two and three degrees of freedom. The first example verifies the existence of tiny elliptic islands inside large chaotic domains for a quartic potential. In the 3-body problem we prove the KAM stability of the well-known figure eight orbit and two selected orbits of the so called family of rotating eights. Some additional theoretical and numerical information is also given for the dynamics of both examples.
On Critical Behaviour in Systems of Hamiltonian Partial Differential Equations
Dubrovin, Boris; Grava, Tamara; Klein, Christian; Moro, Antonio
2015-06-01
We study the critical behaviour of solutions to weakly dispersive Hamiltonian systems considered as perturbations of elliptic and hyperbolic systems of hydrodynamic type with two components. We argue that near the critical point of gradient catastrophe of the dispersionless system, the solutions to a suitable initial value problem for the perturbed equations are approximately described by particular solutions to the Painlevé-I (P) equation or its fourth-order analogue P. As concrete examples, we discuss nonlinear Schrödinger equations in the semiclassical limit. A numerical study of these cases provides strong evidence in support of the conjecture.
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.
Karnøe, Peter; Garud, Raghu
2012-01-01
This paper employs path creation as a lens to follow the emergence of the Danish wind turbine cluster. Supplier competencies, regulations, user preferences and a market for wind power did not pre-exist; all had to emerge in a tranformative manner involving multiple actors and artefacts. Competenc......This paper employs path creation as a lens to follow the emergence of the Danish wind turbine cluster. Supplier competencies, regulations, user preferences and a market for wind power did not pre-exist; all had to emerge in a tranformative manner involving multiple actors and artefacts....... Competencies emerged through processes and mechanisms such as co-creation that implicated multiple learning processes. The process was not an orderly linear one as emergent contingencies influenced the learning processes. An implication is that public policy to catalyse clusters cannot be based...
Hamiltonian replica exchange molecular dynamics using soft-core interactions.
Hritz, Jozef; Oostenbrink, Chris
2008-04-14
To overcome the problem of insufficient conformational sampling within biomolecular simulations, we have developed a novel Hamiltonian replica exchange molecular dynamics (H-REMD) scheme that uses soft-core interactions between those parts of the system that contribute most to high energy barriers. The advantage of this approach over other H-REMD schemes is the possibility to use a relatively small number of replicas with locally larger differences between the individual Hamiltonians. Because soft-core potentials are almost the same as regular ones at longer distances, most of the interactions between atoms of perturbed parts will only be slightly changed. Rather, the strong repulsion between atoms that are close in space, which in many cases results in high energy barriers, is weakened within higher replicas of our proposed scheme. In addition to the soft-core interactions, we proposed to include multiple replicas using the same Hamiltonian/level of softness. We have tested the new protocol on the GTP and 8-Br-GTP molecules, which are known to have high energy barriers between the anti and syn conformation of the base with respect to the sugar moiety. During two 25 ns MD simulations of both systems the transition from the more stable to the less stable (but still experimentally observed) conformation is not seen at all. Also temperature REMD over 50 replicas for 1 ns did not show any transition at room temperature. On the other hand, more than 20 of such transitions are observed in H-REMD using six replicas (at three different Hamiltonians) during 6.8 ns per replica for GTP and 12 replicas (at six different Hamiltonians) during 8.7 ns per replica for 8-Br-GTP. The large increase in sampling efficiency was obtained from an optimized H-REMD scheme involving soft-core potentials, with multiple simulations using the same level of softness. The optimization of the scheme was performed by fast mimicking [J. Hritz and C. Oostenbrink, J. Chem. Phys. 127, 204104 (2007)].
Equivalent Hamiltonians with additional discrete states
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
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.
Path integral approach to two-dimensional QCD in the light-front frame
Gaete, P. (Instituto de Fisica, Universidade Federal do Rio de Janeiro, C.P. 68528, BR-21945, Rio de Janeiro (Brazil)); Gamboa, J. (Fachbereich 7 Physik, Universitaet Siegen, Siegen, D-57068 (Germany)); Schmidt, I. (Departamento de Fisica, Universidad Tecnica Federico Santa Maria, Casilla 110-V, Valparaiso (Chile))
1994-05-15
Two-dimensional quantum chromodynamics in the light-front frame is studied following Hamiltonian methods. The theory is quantized using the path integral formalism and an effective theory similar to the Nambu--Jona-Lasinio model is obtained. Confinement in two dimensions is derived by analyzing directly the constraints in the path integral.
The path integral representation kernel of evolution operator in Merton-Garman model
Blazhyevskyi, L F; 10.5488/CMP.14.23001
2011-01-01
In the framework of path integral the evolution operator kernel for the Merton-Garman Hamiltonian is constructed. Based on this kernel option formula is obtained, which generalizes the well-known Black-Scholes result. Possible approximation numerical schemes for path integral calculations are proposed.
Ruby, Alan; Simons, Fran
This paper discusses the three phases of the recent and future work of the Network groups--Network 1--of the OECD/CERI International Indicators Project. Essentially, Network 1's responsibility is to develop and test "participation" indicators on enrollments, educational career paths, and school leavers at different stages of the member…
Discrete Coherent State Path Integrals
Marchioro, Thomas L., II
1990-01-01
The quantum theory provides a fundamental understanding of the physical world; however, as the number of degrees of freedom rises, the information required to specify quantum wavefunctions grows geometrically. Because basis set expansions mirror this geometric growth, a strict practical limit on quantum mechanics as a numerical tool arises, specifically, three degrees of freedom or fewer. Recent progress has been made utilizing Feynman's Path Integral formalism to bypass this geometric growth and instead calculate time -dependent correlation functions directly. The solution of the Schrodinger equation is converted into a large dimensional (formally infinite) integration, which can then be attacked with Monte Carlo techniques. To date, work in this area has concentrated on developing sophisticated mathematical algorithms for evaluating the highly oscillatory integrands occurring in Feynman Path Integrals. In an alternative approach, this work demonstrates two formulations of quantum dynamics for which the number of mathematical operations does not scale geometrically. Both methods utilize the Coherent State basis of quantum mechanics. First, a localized coherent state basis set expansion and an approximate short time propagator are developed. Iterations of the short time propagator lead to the full quantum dynamics if the coherent state basis is sufficiently dense along the classical phase space path of the system. Second, the coherent state path integral is examined in detail. For a common class of Hamiltonians, H = p^2/2 + V( x) the path integral is reformulated from a phase space-like expression into one depending on (q,dot q). It is demonstrated that this new path integral expression contains localized damping terms which can serve as a statistical weight for Monte Carlo evaluation of the integral--a process which scales approximately linearly with the number of degrees of freedom. Corrections to the traditional coherent state path integral, inspired by a
Effective Hamiltonians for phosphorene and silicene
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.
Hamiltonian theory of guiding-center motion
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.
Tokmachev, A. M.; Robb, M. A.
The spin-Hamiltonian valence bond theory relies upon covalent configurations formed by singly occupied orbitals differing by their spin counterparts. This theory has been proven to be successful in studying potential energy surfaces of the ground and lowest excited states in organic molecules when used as a part of the hybrid molecular mechanics - valence bond method. The method allows one to consider systems with large active spaces formed by n electrons in n orbitals and relies upon a specially proposed graphical unitary group approach. At the same time, the restriction of the equality of the numbers of electrons and orbitals in the active space is too severe: it excludes from the consideration a lot of interesting applications. We can mention here carbocations and systems with heteroatoms. Moreover, the structure of the method makes it difficult to study charge-transfer excited states because they are formed by ionic configurations. In the present work we tackle these problems by significant extension of the spin-Hamiltonian approach. We consider (i) more general active space formed by n ± m electrons in n orbitals and (ii) states with the charge transfer. The main problem addressed is the generation of Hamiltonian matrices for these general cases. We propose a scheme combining operators of electron exchange and hopping, generating all nonzero matrix elements step-by-step. This scheme provides a very efficient way to generate the Hamiltonians, thus extending the applicability of spin-Hamiltonian valence bond theory.
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.
A Hamiltonian Approach to Fault Isolation in a Planar Vertical Take–Off and Landing Aircraft Model
Rodriguez-Alfaro Luis H.
2015-03-01
Full Text Available The problem of fault detection and isolation in a class of nonlinear systems having a Hamiltonian representation is considered. In particular, a model of a planar vertical take-off and landing aircraft with sensor and actuator faults is studied. A Hamiltonian representation is derived from an Euler-Lagrange representation of the system model considered. In this form, nonlinear decoupling is applied in order to obtain subsystems with (as much as possible specific fault sensitivity properties. The resulting decoupled subsystem is represented as a Hamiltonian system and observer-based residual generators are designed. The results are presented through simulations to show the effectiveness of the proposed approach.
GONG Lun-Xun; CAO Jian-Li; PAN Jun-Ting; ZHANG Hua; JIAO Wan-Tang
2008-01-01
Based on the second integrable case of known two-dimensional Hamiltonian system with a quartic potential, we propose a 4×4 matrix spectral problem and derive a hierarchy of coupled KdV equations and their Hamiltonian structures. It is shown that solutions of the coupled KdV equations in the hierarchy are reduced to solving two compatible systems of ordinary differential equations. As an application, quite a few explicit solutions of the coupled KdV equations are obtained via using separability for the second integrable case of the two-dimensional Hamiltonian system.
Partial Path Column Generation for the ESPPRC
Jepsen, Mads Kehlet; Petersen, Bjørn
This talk introduces a decomposition of the Elementary Shortest Path Problem with Resource Constraints(ESPPRC), where the path is combined by smaller sub paths. We show computational result by comparing different approaches for the decomposition and compare the best of these with existing...
A SCALED CENTRAL PATH FOR LINEAR PROGRAMMING
Ya-xiang Yuan
2001-01-01
Interior point methods are very efficient methods for solving large scale linear programming problems. The central path plays a very important role in interior point methods. In this paper we propose a new central path, which scales the variables. Thus it has the advantage of forcing the path to have roughly the same distance from each active constraint boundary near the solution.
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.
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
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.
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
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
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 constants for several new entire solutions
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
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
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)
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-
The addition of the lower level to spectrums of matrix and scalar components of d=2 SUSY Hamiltonian
Leble, S B
1998-01-01
Supersymmetrical quantum--mechanical system is consider in the case of d=2. The problem of addition of the lower level to spectrums of matrix and scalar components of d=2 SUSY Hamiltonian is investigated. It is shown that in the case, the level E=0 may be degenerate. The multi--dimensional scalar Hamiltonians with energy spectra coinciding up to finite number of discrete levels are constructed.
刘萍; 高军; 丁筱玲
2012-01-01
针对工业钢构打字加工路径的组合优化目标，为尽量减少换刀次数和优化刀具移动轨迹，使走刀时间最短，提出建立基于旅行商问题（TSP）的非确定型多项式数学模型，并应用遗传算法（GA）对钢构打字刀具路径的优化问题进行分析、研究和解答。通过合理安排工序和换刀、走刀路径，在不改变机床硬件的前提下，尽可能缩短加工时间。经MATLAB工具箱仿真实验证明，该研究能很好地解决目前我国钢构打字路径寻优问题，使打字过程中的定位精度和加工效率都得到较大提高。%Industrial steel typing processing path optimization goal, to minimize the number of tool changing and optimizing tool moving trajectory, so that the tool path with the shortest time, proposed the establishment based on the traveling salesman problem （TSP） of nondeterministic polynomial mathematical models, and the application of genetic algorithms （GA） on steel typing tool path optimization of analysis, research and solve. Through reasonable arrangement of process and tool, tool path, without changing the machine hardware under the premise, as far as possible to shorten the processing time. The MATLAB toolbox simulation experiments, the study can well solve at present our country steel typing route optimization problem, so that the typing process precision and processing efficiency has been greatly improved.
Effective Hamiltonian approach to periodically perturbed quantum optical systems
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.
Integrable Coupling of KN Hierarchy and Its Hamiltonian Structure
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.
Peter Juhasz
2017-03-01
Full Text Available While risk management gained popularity during the last decades even some of the basic risk types are still far out of focus. One of these is path dependency that refers to the uncertainty of how we reach a certain level of total performance over time. While decision makers are careful in accessing how their position will look like the end of certain periods, little attention is given how they will get there through the period. The uncertainty of how a process will develop across a shorter period of time is often “eliminated” by simply choosing a longer planning time interval, what makes path dependency is one of the most often overlooked business risk types. After reviewing the origin of the problem we propose and compare seven risk measures to access path. Traditional risk measures like standard deviation of sub period cash flows fail to capture this risk type. We conclude that in most cases considering the distribution of the expected cash flow effect caused by the path dependency may offer the best method, but we may need to use several measures at the same time to include all the optimisation limits of the given firm
A Port-Hamiltonian Approach to Visual Servo Control of a Pick and Place System
Dirksz, Daniel A.; Scherpen, Jacquelien M. A.; Steinbuch, Maarten
In this paper, we take a port-Hamiltonian approach to address the problem of image-based visual servo control of a pick and place system. Through a coordinate transformation and a passive interconnection between mechanical system and camera dynamics we realize a closed-loop system that is
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.
Sturm intersection theory for periodic Jacobi matrices and linear Hamiltonian systems
Schulz-Baldes, Hermann
2011-01-01
Sturm-Liouville oscillation theory for periodic Jacobi operators with matrix entries is discussed and illustrated. The proof simplifies and clarifies the use of intersection theory of Bott, Maslov and Conley-Zehnder. It is shown that the eigenvalue problem for linear Hamiltonian systems can be dealt with by the same approach.
Path integrals, hyperbolic spaces and Selberg trace formulae
Grosche, Christian
2013-01-01
In this second edition, a comprehensive review is given for path integration in two- and three-dimensional (homogeneous) spaces of constant and non-constant curvature, including an enumeration of all the corresponding coordinate systems which allow separation of variables in the Hamiltonian and in the path integral. The corresponding path integral solutions are presented as a tabulation. Proposals concerning interbasis expansions for spheroidal coordinate systems are also given. In particular, the cases of non-constant curvature Darboux spaces are new in this edition.The volume also contains r
Nonconventional fluctuation dissipation process in non-Hamiltonian dynamical systems
Bianucci, Marco
2016-08-01
Here, we introduce a statistical approach derived from dynamics, for the study of the geophysical fluid dynamics phenomena characterized by a weak interaction among the variables of interest and the rest of the system. The approach is reminiscent of the one developed some years ago [M. Bianucci, R. Mannella, P. Grigolini and B. J. West, Phys. Rev. E 51, 3002 (1995)] to derive statistical mechanics of macroscopic variables on interest starting from Hamiltonian microscopic dynamics. However, in the present work, we are interested to generalize this approach beyond the context of the foundation of thermodynamics, in fact, we take into account the cases where the system of interest could be non-Hamiltonian (dissipative) and also the interaction with the irrelevant part can be of a more general type than Hamiltonian. As such example, we will refer to a typical case from geophysical fluid dynamics: the complex ocean-atmosphere interaction that gives rise to the El Niño Southern Oscillation (ENSO). Here, changing all the scales, the role of the “microscopic” system is played by the atmosphere, while the ocean (or some ocean variables) plays the role of the intrinsically dissipative macroscopic system of interest. Thus, the chaotic and divergent features of the fast atmosphere dynamics remains in the decaying properties of the correlation functions and of the response function of the atmosphere variables, while the exponential separation of the perturbed (or close) single trajectories does not play a direct role. In the present paper, we face this problem in the frame of a not formal Langevin approach, limiting our discussion to physically based rather than mathematics arguments. Elsewhere, we obtain these results via a much more formal procedure, using the Zwanzing projection method and some elements from the Lie Algebra field.
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.
Multi-Machine Controller Design of Permanent Magnet Wind Generators using Hamiltonian Energy Method
Bing Wang
2013-07-01
Full Text Available In this paper, the nonlinear control problem of permanent magnet wind generators is investigated based on Hamiltonian energy method. A nonlinear design method is proposed for the multi-machine system, such that the closed-loop system is stable simultaneously. Moreover, in the presence of disturbances, the closed-loop is finite–gain L2 stable under the action of the Hamiltonian controller. In order to illustrate the effectiveness of the proposed method, the simulations are performed which show that the gotten controller can improve the transient property and robustness of the system.
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.
Resolutions of Identity for Some Non-Hermitian Hamiltonians. II. Proofs
Andrey V. Sokolov
2011-12-01
Full Text Available This part is a continuation of the Part I where we built resolutions of identity for certain non-Hermitian Hamiltonians constructed of biorthogonal sets of their eigen- and associated functions for the spectral problem defined on entire axis. Non-Hermitian Hamiltonians under consideration are taken with continuous spectrum and the following cases are examined: an exceptional point of arbitrary multiplicity situated on a boundary of continuous spectrum and an exceptional point situated inside of continuous spectrum. In the present work the rigorous proofs are given for the resolutions of identity in both cases.
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.
HAMILTONIAN MECHANICS ON K(A)HLER MANIFOLDS
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.
Classical mechanics systems of particles and Hamiltonian dynamics
Greiner, Walter
2010-01-01
This textbook Classical Mechanics provides a complete survey on all aspects of classical mechanics in theoretical physics. An enormous number of worked examples and problems show students how to apply the abstract principles to realistic problems. The textbook covers Newtonian mechanics in rotating coordinate systems, mechanics of systems of point particles, vibrating systems and mechanics of rigid bodies. It thoroughly introduces and explains the Lagrange and Hamilton equations and the Hamilton-Jacobi theory. A large section on nonlinear dynamics and chaotic behavior of systems takes Classical Mechanics to newest development in physics. The new edition is completely revised and updated. New exercises and new sections in canonical transformation and Hamiltonian theory have been added.
Quasi-Hamiltonian Method for Computation of Decoherence Rates
Joynt, Robert; Wang, Qiang-Hua
2009-01-01
We present a general formalism for the dissipative dynamics of an arbitrary quantum system in the presence of a classical stochastic process. It is applicable to a wide range of physical situations, and in particular it can be used for qubit arrays in the presence of classical two-level systems (TLS). In this formalism, all decoherence rates appear as eigenvalues of an evolution matrix. Thus the method is linear, and the close analogy to Hamiltonian systems opens up a toolbox of well-developed methods such as perturbation theory and mean-field theory. We apply the method to the problem of a single qubit in the presence of TLS that give rise to pure dephasing 1/f noise and solve this problem exactly. The exact solution gives an experimentally observable improvement over the popular Gaussian approximation.
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.
Yekini Shehu
2010-01-01
real Banach space which is also uniformly smooth using the properties of generalized f-projection operator. Using this result, we discuss strong convergence theorem concerning general H-monotone mappings and system of generalized mixed equilibrium problems in Banach spaces. Our results extend many known recent results in the literature.
Generic fractal structure of finite parts of trajectories of piecewise smooth Hamiltonian systems
Hildebrand, R.; Lokutsievskiy, L. V.; Zelikin, M. I.
2013-03-01
Piecewise smooth Hamiltonian systems with tangent discontinuity are studied. A new phenomenon is discovered, namely, the generic chaotic behavior of finite parts of trajectories. The approach is to consider the evolution of Poisson brackets for smooth parts of the initial Hamiltonian system. It turns out that, near second-order singular points lying on a discontinuity stratum of codimension two, the system of Poisson brackets is reduced to the Hamiltonian system of the Pontryagin Maximum Principle. The corresponding optimization problem is studied and the topological structure of its optimal trajectories is constructed (optimal synthesis). The synthesis contains countably many periodic solutions on the quotient space by the scale group and a Cantor-like set of nonwandering points (NW) having fractal Hausdorff dimension. The dynamics of the system is described by a topological Markov chain. The entropy is evaluated, together with bounds for the Hausdorff and box dimension of (NW).
Atomic algorithm and the servers' s use to find the Hamiltonian cycles
M. Sghiar
2016-06-01
Full Text Available Inspired by the movement of the particles in the atom, I demonstrated in [5] the existence of a polynomial algorithm of the order O(n 3 for finding Hamiltonian cycles in a graph with basis E= {x0,... , xn− 1 } . In this article I will give an improvement in space and in time of the algorithm says: we know that there exist several methods to find the Hamiltonian cycles such as the Monte Carlo method, Dynamic programming, or DNA computing. Unfortunately they are either expensive or slow to execute it. Hence the idea to use multiple servers to solve this problem : Each point xi in the graph will be considered as a server, and each server xi will communicate with each other server x j with which it is connected . And finally the server x0 will receive and display the Hamiltonian cycles if they exist.
Quantum search on the two-dimensional lattice using the staggered model with Hamiltonians
Portugal, R.; Fernandes, T. D.
2017-04-01
Quantum search on the two-dimensional lattice with one marked vertex and cyclic boundary conditions is an important problem in the context of quantum algorithms with an interesting unfolding. It avails to test the ability of quantum walk models to provide efficient algorithms from the theoretical side and means to implement quantum walks in laboratories from the practical side. In this paper, we rigorously prove that the recent-proposed staggered quantum walk model provides an efficient quantum search on the two-dimensional lattice, if the reflection operators associated with the graph tessellations are used as Hamiltonians, which is an important theoretical result for validating the staggered model with Hamiltonians. Numerical results show that on the two-dimensional lattice staggered models without Hamiltonians are not as efficient as the one described in this paper and are, in fact, as slow as classical random-walk-based algorithms.
Single-valued Hamiltonian via Legendre–Fenchel transformation and time translation symmetry
Chi, Huan-Hang, E-mail: hhchi@stanford.edu [Physics Department, Stanford University, Stanford, CA 94305 (United States); Institute of Modern Physics and Center for High Energy Physics, Tsinghua University, Beijing 100084 (China); Physics Department, Tsinghua University, Beijing 100084 (China); He, Hong-Jian, E-mail: hjhe@tsinghua.edu.cn [Institute of Modern Physics and Center for High Energy Physics, Tsinghua University, Beijing 100084 (China); Physics Department, Tsinghua University, Beijing 100084 (China); Center for High Energy Physics, Peking University, Beijing 100871 (China)
2014-08-15
Under conventional Legendre transformation, systems with a non-convex Lagrangian will result in a multi-valued Hamiltonian as a function of conjugate momentum. This causes problems such as non-unitary time evolution of quantum state and non-determined motion of classical particles, and is physically unacceptable. In this work, we propose a new construction of single-valued Hamiltonian by applying Legendre–Fenchel transformation, which is a mathematically rigorous generalization of conventional Legendre transformation, valid for non-convex Lagrangian systems, but not yet widely known to the physics community. With the new single-valued Hamiltonian, we study spontaneous breaking of time translation symmetry and derive its vacuum state. Applications to theories of cosmology and gravitation are discussed.
Study of lower hybrid wave propagation in ionized gas by Hamiltonian theory
Casolari, Andrea
2013-01-01
In order to find an approximate solution to the Vlasov-Maxwell equation system describing the lower hybrid wave propagation in magnetic confined plasmas, the use of the WKB method leads to the ray tracing equations. The Hamiltonian character of the ray tracing equations is investigated analytically and numerically in order to deduce the physical properties of the wave propagating without absorption in the confined plasma. The consequences of the Hamiltonian character of the equations on the travelling wave, in particular, on the evolution of the parallel wavenumber along the propagation path have been accounted and the chaotic diffusion of the timeaveraged parallel wave-number towards higher values has been evaluated. Numerical analysis by means of a Runge-Kutta based algorithm implemented in a ray tracing code supplies the analytical considerations. A numerical tool based on the symplectic integration of the ray trajectories has been developed.
Study of lower hybrid wave propagation in ionized gas by Hamiltonian theory
Casolari, A. [Università di Pisa, Pisa (Italy); Cardinali, A. [Associazione Euratom-ENEA sulla Fusione, C.P. 65 - I-00044 - Frascati, Rome (Italy)
2014-02-12
In order to find an approximate solution to the Vlasov-Maxwell equation system describing the lower hybrid wave propagation in magnetic confined plasmas, the use of the WKB method leads to the ray tracing equations. The Hamiltonian character of the ray tracing equations is investigated analytically and numerically in order to deduce the physical properties of the wave propagating without absorption in the confined plasma. The consequences of the Hamiltonian character of the equations on the travelling wave, in particular, on the evolution of the parallel wavenumber along the propagation path have been accounted and the chaotic diffusion of the timeaveraged parallel wave-number towards higher values has been evaluated. Numerical analysis by means of a Runge-Kutta based algorithm implemented in a ray tracing code supplies the analytical considerations. A numerical tool based on the symplectic integration of the ray trajectories has been developed.
To Solve Pipeline Layout Problem with the Improved Shortest Path Model%利用改进的最短路径模型解决输油管的布置问题
余淼
2011-01-01
2010年去过数学建模大赛c题“输油管的布置”数学建模的目的是设计最优化的路线，建立一条费用最省的输油管线路，但是不同于普遍的最短路径问题，该题需要考虑多种情况，例如，城区和郊区费用的不同，采用共用管线和非公用管线价格的不同等等。我们基于最短路径模型，对于题目实际情况进行研究和分析，基于光的传播原理，设计了一种改进的最短路径模型，对问题设计了合适的数学模型并做出了相应的解答和处理。%Mathematical Modeling Contest in 2010 been to C title＂pipeline layout,＂The purpose of mathematical modeling is to design the most optimal route to establish a pipeline of least cost route,but unlike the general shortest path problem,the problem needs consider a variety of situations,for example,the cost of different urban and suburban areas,the use of shared pipeline and the price of different non-public lines and so on.On the basis of the shortest path model for the actual subject of research and analysis,based on the principle of light transmission,an improved design of the shortest path model,the appropriate design of the problem and make the corresponding mathematical model answers and treatment.
Hamiltonian and Lagrangian Dynamical Matrix Approaches Applied to Magnetic Nanostructures
Roberto Zivieri
2012-01-01
Full Text Available Two micromagnetic tools to study the spin dynamics are reviewed. Both approaches are based upon the so-called dynamical matrix method, a hybrid micromagnetic framework used to investigate the spin-wave normal modes of confined magnetic systems. The approach which was formulated first is the Hamiltonian-based dynamical matrix method. This method, used to investigate dynamic magnetic properties of conservative systems, was originally developed for studying spin excitations in isolated magnetic nanoparticles and it has been recently generalized to study the dynamics of periodic magnetic nanoparticles. The other one, the Lagrangian-based dynamical matrix method, was formulated as an extension of the previous one in order to include also dissipative effects. Such dissipative phenomena are associated not only to intrinsic but also to extrinsic damping caused by injection of a spin current in the form of spin-transfer torque. This method is very accurate in identifying spin modes that become unstable under the action of a spin current. The analytical development of the system of the linearized equations of motion leads to a complex generalized Hermitian eigenvalue problem in the Hamiltonian dynamical matrix method and to a non-Hermitian one in the Lagrangian approach. In both cases, such systems have to be solved numerically.
Path Minima Queries in Dynamic Weighted Trees
Davoodi, Pooya; Brodal, Gerth Stølting; Satti, Srinivasa Rao
2011-01-01
In the path minima problem on a tree, each edge is assigned a weight and a query asks for the edge with minimum weight on a path between two nodes. For the dynamic version of the problem, where the edge weights can be updated, we give data structures that achieve optimal query time\\todo{what about...
Hamiltonian[k,k+1]-因子%Hamiltonian [k, k + 1]-Factor
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.
Spreading paths in partially observed social networks
Onnela, Jukka-Pekka
2011-01-01
Understanding how far information, behaviors, or pathogens spread in social networks is an important problem, having implications for both predicting the size of epidemics, as well as for planning effective interventions. There are, however, two main challenges for inferring spreading path lengths in real-world networks. One is the practical difficulty of observing a dynamic process on a network, and the other is the typical constraint of only partially observing a network. Using a static, structurally realistic social network as a platform for simulations, we juxtapose three distinct paths: (1) the stochastic path taken by a simulated spreading process from source to target; (2) the topologically shortest path in the fully observed network, and hence the single most likely stochastic path, between the two nodes; and (3) the topologically shortest path in a partially observed network. In a sampled network, how closely does the partially observed shortest path (3) emulate the unobserved spreading path (1)? Alt...
Time optimal paths for high speed maneuvering
Reister, D.B.; Lenhart, S.M.
1993-01-01
Recent theoretical results have completely solved the problem of determining the minimum length path for a vehicle with a minimum turning radius moving from an initial configuration to a final configuration. Time optimal paths for a constant speed vehicle are a subset of the minimum length paths. This paper uses the Pontryagin maximum principle to find time optimal paths for a constant speed vehicle. The time optimal paths consist of sequences of axes of circles and straight lines. The maximum principle introduces concepts (dual variables, bang-bang solutions, singular solutions, and transversality conditions) that provide important insight into the nature of the time optimal paths. We explore the properties of the optimal paths and present some experimental results for a mobile robot following an optimal path.