Academic literature on the topic 'Hamiltonian equivalence'
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Journal articles on the topic "Hamiltonian equivalence"
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Qian, Jing, Yun Zeng, Li Xiang Zhang, and Tian Mao Xu. "Analysis on Equivalence between Transfer Function and Equivalent Circuit Simulation in General Hamiltonian Modeling." Applied Mechanics and Materials 204-208 (October 2012): 4896–99. http://dx.doi.org/10.4028/www.scientific.net/amm.204-208.4896.
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Take generator system included AVR (automatic voltage regulator) and PSS (power system stabilizer) as an example, Using the time simulation method, Study the equivalence between the transfer function model and the equivalent circuit simulation, and establish the corresponding relations between the circuit structures, internal parameters and transfer function parameters, based on the energy of equivalent circuit, the Hamiltonian function of transfer function is derived indirectly, and the Hamiltonian model is established. The study in this paper provides a new way to establish generalized Hamiltonian model for linear system based on transfer function.
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Nikitin, A. G., and V. V. Tretynyk. "Parasupersymmetries and Non-Lie Constants of Motion for Two-Particle Equations." International Journal of Modern Physics A 12, no. 24 (September 30, 1997): 4369–86. http://dx.doi.org/10.1142/s0217751x97002371.
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We search for hidden symmetries of two-particle equations with oscillator-equivalent potential, proposed by Moshinsky with collaborators. We proved that these equations admit hidden symmetries and parasupersymmetries which enable one to easily find the Hamiltonian spectra using algebraic methods and to construct exact Foldy–Wouthuysen transformations. Moreover, we demonstrate that these equations are reducible and generate Hamiltonians for pararelativistic or Kemmer oscillators. We also establish equivalence relations between different approaches to Kemmer oscillator and propose new one- and two-particle equations with oscillator-equivalent potentials.
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DERIGLAZOV, A. A., W. OLIVEIRA, and G. OLIVEIRA-NETO. "EQUIVALENCE BETWEEN DIFFERENT CLASSICAL TREATMENTS OF THE O(N) NONLINEAR SIGMA MODEL AND THEIR FUNCTIONAL SCHRÖDINGER EQUATIONS." International Journal of Modern Physics A 18, no. 05 (February 20, 2003): 755–66. http://dx.doi.org/10.1142/s0217751x03013867.
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In this work we derive the Hamiltonian formalism of the O(N) nonlinear sigma model in its original version as a second-class constrained field theory and then as a first-class constrained field theory. We treat the model as a second-class constrained field theory by two different methods: the unconstrained and the Dirac second-class formalisms. We show that the Hamiltonians for all these versions of the model are equivalent. Then, for a particular factor-ordering choice, we write the functional Schrödinger equation for each derived Hamiltonian. We show that they are all identical which justifies our factor-ordering choice and opens the way for a future quantization of the model via the functional Schrödinger representation.
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Balajany, Hamideh, and Mohammad Mehrafarin. "Geometric phase of cosmological scalar and tensor perturbations in f(R) gravity." Modern Physics Letters A 33, no. 14 (May 10, 2018): 1850077. http://dx.doi.org/10.1142/s0217732318500773.
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By using the conformal equivalence of f(R) gravity in vacuum and the usual Einstein theory with scalar-field matter, we derive the Hamiltonian of the linear cosmological scalar and tensor perturbations in f(R) gravity in the form of time-dependent harmonic oscillator Hamiltonians. We find the invariant operators of the resulting Hamiltonians and use their eigenstates to calculate the adiabatic Berry phase for sub-horizon modes as a Lewis–Riesenfeld phase.
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M, Nandakumar, and K. S. Subrahamanian Moosath. "Rough Liouville Equivalence of Integrable Hamiltonian Systems." Advances in Dynamical Systems and Applications 15, no. 2 (December 22, 2020): 153–69. http://dx.doi.org/10.37622/adsa/15.2.2020.153-169.
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Nirov, Kh S., and A. V. Razumov. "Equivalence between Lagrangian and Hamiltonian BRST formalisms." Journal of Mathematical Physics 34, no. 9 (September 1993): 3933–53. http://dx.doi.org/10.1063/1.530410.
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Martynchuk, N. N. "Semi-local Liouville equivalence of complex Hamiltonian systems defined by rational Hamiltonian." Topology and its Applications 191 (August 2015): 119–30. http://dx.doi.org/10.1016/j.topol.2015.05.090.
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AMICO, LUIGI. "ALGEBRAIC EQUIVALENCE BETWEEN CERTAIN MODELS FOR SUPERFLUID–INSULATOR TRANSITION." Modern Physics Letters B 14, no. 21 (September 10, 2000): 759–66. http://dx.doi.org/10.1142/s0217984900000963.
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Algebraic contraction is proposed to realize mappings between Hamiltonian models. This transformation contracts the algebra of the degrees of freedom underlying the Hamiltonian. The rigorous mapping between the anisotropic XXZ Heisenberg model, the quantum phase model and the Bose Hubbard model is established as the contractions of the algebra u(2) underlying the dynamics of the XXZ Heisenberg model.
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Cheng, Daizhan, Alessandro Astolfi, and Romeo Ortega. "On feedback equivalence to port controlled Hamiltonian systems." Systems & Control Letters 54, no. 9 (September 2005): 911–17. http://dx.doi.org/10.1016/j.sysconle.2005.02.005.
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Salat, A. "Hamiltonian Approach to Magnetic Fields with Toroidal Surfaces." Zeitschrift für Naturforschung A 40, no. 10 (October 1, 1985): 959–67. http://dx.doi.org/10.1515/zna-1985-1001.
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The equivalence of magnetic field line equations to a one-dimensional time-dependent Hamiltonian system is used to construct magnetic fields with arbitrary toroidal magnetic surfaces I = const. For this purpose Hamiltonians H which together with their invariants satisfy periodicity constraints have to be known. The choice of H fixes the rotational transform η(I). Arbitrary axisymmetric fields, and nonaxisymmetric fields with constant η(I) are considered in detail.Configurations with coinciding magnetic and current density surfaces are obtained. The approach used is not well suited, however, to satisfying the additional MHD equilibrium condition of constant pressure on magnetic surfaces.
Dissertations / Theses on the topic "Hamiltonian equivalence"
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Bergougnoux, Benjamin. "Matrix decompositions and algorithmic applications to (hyper)graphs." Thesis, Université Clermont Auvergne (2017-2020), 2019. http://www.theses.fr/2019CLFAC025/document.
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Durant ces dernières décennies, d'importants efforts et beaucoup de café ont été dépensés en vue de caractériser les instances faciles des problèmes NP-difficiles. Dans ce domaine de recherche, une approche s'avère être redoutablement efficace : la théorie de la complexité paramétrée introduite par Downey et Fellows dans les années 90.Dans cette théorie, la complexité d'un problème n'est plus mesurée uniquement en fonction de la taille de l'instance, mais aussi en fonction d'un paramètre .Dans cette boite à outils, la largeur arborescente est sans nul doute un des paramètres de graphe les plus étudiés.Ce paramètre mesure à quel point un graphe est proche de la structure topologique d'un arbre.La largeur arborescente a de nombreuses propriétés algorithmiques et structurelles.Néanmoins, malgré l'immense intérêt suscité par la largeur arborescente, seules les classes de graphes peu denses peuvent avoir une largeur arborescente bornée.Mais, de nombreux problèmes NP-difficiles s'avèrent faciles dans des classes de graphes denses.La plupart du temps, cela peut s'expliquer par l'aptitude de ces graphes à se décomposer récursivement en bipartitions de sommets $(A,B)$ où le voisinage entre $A$ et $B$ possède une structure simple.De nombreux paramètres -- appelés largeurs -- ont été introduits pour caractériser cette aptitude, les plus remarquables sont certainement la largeur de clique , la largeur de rang , la largeur booléenne et la largeur de couplage induit .Dans cette thèse, nous étudions les propriétés algorithmiques de ces largeurs.Nous proposons une méthode qui généralise et simplifie les outils développés pour la largeur arborescente et les problèmes admettant une contrainte d'acyclicité ou de connexité tel que Couverture Connexe , Dominant Connexe , Coupe Cycle , etc.Pour tous ces problèmes, nous obtenons des algorithmes s'exécutant en temps $2^{O(k)}\cdot n^{O(1)}$, $2^{O(k \log(k))}\cdot n^{O(1)}$, $2^{O(k^2)}\cdot n^{O(1)}$ et $n^{O(k)}$ avec $k$ étant, respectivement, la largeur de clique, la largeur de Q-rang, la larguer de rang et la largueur de couplage induit.On prouve aussi qu'il existe un algorithme pour Cycle Hamiltonien s'exécutant en temps $n^{O(k)}$ quand une décomposition de largeur de clique $k$ est donné en entrée.Finalement, nous prouvons qu'on peut compter en temps polynomial le nombre de transversaux minimaux d'hypergraphes $\beta$-acyclique ainsi que le nombre de dominants minimaux de graphes fortement triangulés.Tous ces résultats offrent des pistes prometteuses en vue d'une généralisation des largeurs et de leurs applications algorithmiquesIn the last decades, considerable efforts have been spent to characterize what makes NP-hard problems tractable. A successful approach in this line of research is the theory of parameterized complexity introduced by Downey and Fellows in the nineties.In this framework, the complexity of a problem is not measured only in terms of the input size, but also in terms of a parameter on the input.One of the most well-studied parameters is tree-width, a graph parameter which measures how close a graph is to the topological structure of a tree.It appears that tree-width has numerous structural properties and algorithmic applications.However, only sparse graph classes can have bounded tree-width.But, many NP-hard problems are tractable on dense graph classes.Most of the time, this tractability can be explained by the ability of these graphs to be recursively decomposable along vertex bipartitions $(A,B)$ where the adjacency between $A$ and $B$ is simple to describe.A lot of graph parameters -- called width measures -- have been defined to characterize this ability, the most remarkable ones are certainly clique-width, rank-width, and mim-width.In this thesis, we study the algorithmic properties of these width measures.We provide a framework that generalizes and simplifies the tools developed for tree-width and for problems with a constraint of acyclicity or connectivity such as Connected Vertex Cover, Connected Dominating Set, Feedback Vertex Set, etc.For all these problems, we obtain $2^{O(k)}\cdot n^{O(1)}$, $2^{O(k \log(k))}\cdot n^{O(1)}$, $2^{O(k^2)}\cdot n^{O(1)}$ and $n^{O(k)}$ time algorithms parameterized respectively by clique-width, Q-rank-width, rank-width and mim-width.We also prove that there exists an algorithm solving Hamiltonian Cycle in time $n^{O(k)}$, when a clique-width decomposition of width $k$ is given.Finally, we prove that we can count in polynomial time the minimal transversals of $\beta$-acyclic hypergraphs and the minimal dominating sets of strongly chordal graphs.All these results offer promising perspectives towards a generalization of width measures and their algorithmic applications
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Seewald, Nadiane Cristina Cassol [UNESP]. "Método do hamiltoniano termodinamicamente equivalente para sistemas de muitos corpos." Universidade Estadual Paulista (UNESP), 2012. http://hdl.handle.net/11449/102540.
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seewald_ncc_dr_ift.pdf: 980110 bytes, checksum: a8da01736f6d240fb7a6880d23b95d14 (MD5)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
O objetivo da Tese é investigar a aplicabilidade e propor extensões do método do hamiltoniano termodinamicamente equivalente (MHTE) para sistemas de muitos corpos descritos por uma teoria de campos. Historicamente, o MHTE tem sua origem na teoria quântica de muitos corpos para descrever o fenômeno da supercondutividade. O método consiste na observação de que o hamiltoniano de um sistema pode ser diagonalizado exatamente através de uma transformação unitária quando um número finito de momentos transferidos que contribuem para a interação é levado em conta no limite termodinâmico. Essa transformação unitária depende explicitamente de funções de gap que podem ser determinadas através do método variacional de Gibbs. Na presente Tese, extensões do método são feitas visando aplicações em sistemas de muitos corpos em diferentes situações, tais como: transições de fase estáaticas, evolução temporal de parâmetros de ordem descrita por equações dinâmicas estocásticas do tipo Ginzburg-Landau-Langevin (GLL), teorias quânticas de campos escalares relativísticos e teorias de muitos corpos para sistemas fermiônicos não relativísticos. Mostra-se, em particular, que o MHTE é um esquema de aproximação sistemático e controlável que permite incorporar acoplamentos de componentes de Fourier de parâmetros de ordem além do modo zero, da mesma forma que em teorias quânticas relativísticas ou não relativísticas ele incorpora correlações não perturbativas entre as partículas além daquelas levadas em conta pelas tradicionais aproximações de campo médio. Métodos são desenvolvidos para obtermos soluções numéricas explícitas com o objetivo de avaliar a aplicabilidade do MHTE em alguns casos específicos. Particular atenção é dedicada ao controle de divergências de Rayleigh-Jeans nas simulações numéricas de equações de GLL
The general objective of the Thesis is to apply the Method of the Thermodynamically Equivalent Hamiltonian (MTEH) to many-body systems described by a field theory. Historically, the MTEH has its origins in the quantum theory of manybody systems to describe the phenomenon of superconductivity. The method is based on the observation that the Hamiltonian of the system can be diagonalized exactly with a unitary transformation when a finite number of transfer momenta of the interaction are taken into account in the thermodynamic limit. This unitary transformation depends explicitly on gap functions that can be determined with the use of the Gibbs variational principle. In the present Thesis, extensions of the method are made envisaging applications in many-body systems in different situations, like: static phase transitions, time evolution of order parameters described by dynamic stochastic Ginzburg-Landau-Langevin equations, relativistic quantum scalar field theories, and many-body theories for nonrelativistic fermionic systems. It is shown that the MTEH is a systematic and controllable approximation scheme that in the theory of phase transitions allows to incorporate Fourier modes of the order parameter beyond the zero mode, in the same way that in the relativistic and nonrelativistic theories it incorporates particle nonperturbative correlations beyond those taken into account by the traditional mean field approximation. Methods are developed to obtain explicit numerical solutions with the aim to assess the applicability of the MTEH in specific situations. Particular attention is devoted to the control of Rayleigh-Jeans ultraviolet divergences in the numerical simulations of Ginzburg-Landau-Langevin equations
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Seewald, Nadiane Cristina Cassol. "Método do hamiltoniano termodinamicamente equivalente para sistemas de muitos corpos /." São Paulo, 2012. http://hdl.handle.net/11449/102540.
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Orientador: Gastão Inácio KreinBanca: Marcus Benghi Pinto
Banca: Ney Lemke
Banca: Sandra dos Santos Padula
Banca: Yogiro Hama
Resumo: O objetivo da Tese é investigar a aplicabilidade e propor extensões do método do hamiltoniano termodinamicamente equivalente (MHTE) para sistemas de muitos corpos descritos por uma teoria de campos. Historicamente, o MHTE tem sua origem na teoria quântica de muitos corpos para descrever o fenômeno da supercondutividade. O método consiste na observação de que o hamiltoniano de um sistema pode ser diagonalizado exatamente através de uma transformação unitária quando um número finito de momentos transferidos que contribuem para a interação é levado em conta no limite termodinâmico. Essa transformação unitária depende explicitamente de funções de gap que podem ser determinadas através do método variacional de Gibbs. Na presente Tese, extensões do método são feitas visando aplicações em sistemas de muitos corpos em diferentes situações, tais como: transições de fase estáaticas, evolução temporal de parâmetros de ordem descrita por equações dinâmicas estocásticas do tipo Ginzburg-Landau-Langevin (GLL), teorias quânticas de campos escalares relativísticos e teorias de muitos corpos para sistemas fermiônicos não relativísticos. Mostra-se, em particular, que o MHTE é um esquema de aproximação sistemático e controlável que permite incorporar acoplamentos de componentes de Fourier de parâmetros de ordem além do modo zero, da mesma forma que em teorias quânticas relativísticas ou não relativísticas ele incorpora correlações não perturbativas entre as partículas além daquelas levadas em conta pelas tradicionais aproximações de campo médio. Métodos são desenvolvidos para obtermos soluções numéricas explícitas com o objetivo de avaliar a aplicabilidade do MHTE em alguns casos específicos. Particular atenção é dedicada ao controle de divergências de Rayleigh-Jeans nas simulações numéricas de equações de GLL
Abstract: The general objective of the Thesis is to apply the Method of the Thermodynamically Equivalent Hamiltonian (MTEH) to many-body systems described by a field theory. Historically, the MTEH has its origins in the quantum theory of manybody systems to describe the phenomenon of superconductivity. The method is based on the observation that the Hamiltonian of the system can be diagonalized exactly with a unitary transformation when a finite number of transfer momenta of the interaction are taken into account in the thermodynamic limit. This unitary transformation depends explicitly on gap functions that can be determined with the use of the Gibbs variational principle. In the present Thesis, extensions of the method are made envisaging applications in many-body systems in different situations, like: static phase transitions, time evolution of order parameters described by dynamic stochastic Ginzburg-Landau-Langevin equations, relativistic quantum scalar field theories, and many-body theories for nonrelativistic fermionic systems. It is shown that the MTEH is a systematic and controllable approximation scheme that in the theory of phase transitions allows to incorporate Fourier modes of the order parameter beyond the zero mode, in the same way that in the relativistic and nonrelativistic theories it incorporates particle nonperturbative correlations beyond those taken into account by the traditional mean field approximation. Methods are developed to obtain explicit numerical solutions with the aim to assess the applicability of the MTEH in specific situations. Particular attention is devoted to the control of Rayleigh-Jeans ultraviolet divergences in the numerical simulations of Ginzburg-Landau-Langevin equations
Doutor
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Veglia, Luca. "Multisymplectic formalism for theories of super-fields and non-equivalent symplectic structures on the covariant phase space." Thesis, Sorbonne Paris Cité, 2016. http://www.theses.fr/2016USPCC303/document.
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Le Calcul des Variations et son interprétation géométrique ont toujours joué un rôle crucial en Physique Mathématique, que ce soit par le formalisme lagrangien, ou à travers les équations hamiltoniennes.Le formalisme multisymplectique permet une description géométrique de dimension finie des théories de champ classiques (qui correspondent à des problèmes variationnels avec plusieurs variables spatio-temporelles) vues d’un point de vue hamiltonien. La géométrie multisymplectique joue un rôle similaire à celui de la géométrie symplectique dans la description de la mécanique hamiltonienne classique. De plus, l’approche multisymplectique fournit un outil pour construire une structure symplectique sur l’espace des solutions de la théorie des champs et pour l’étudier.Dans cette thèse, je m’intéresse principalement au formalisme multisymplectique pour construire des théories de champs de premier ordre et j’espère pouvoir donner deux principales contributions originales :– Je montre que, dans certaines situations, la structure symplectique de l’espace des phases covariant peut en effet dépendre du choix de la topologie du découpage de l’espace-temps en l’espace et en le temps;– Je construis une extension du formalisme multisymplectique aux théories de super-champs. En tant que «sous-produit», je présente une autre contribution que j’espère intéressante :– Je définie des formes fractionnaires sur des supervariétés avec leur calcul de Cartan. Ces formes fractionnaires se révèlent utiles pour construire le formalisme multisymplectique pour les théories de super-champs.Les ingrédients principaux du formalisme que j'utilise sont : l’espace des multimoments de dimension finie P et son extension aux théories de super-champs que je définie ; la superforme lagrangienne, le superhamiltonien et la superforme multisymplectique. Dans la thèse je montre aussi un théorème de comparaison qui permets de clarifier les relations existant entre les théories dites en composantes et les théories de superchamps. J’explique comment le formalisme supermultisymplectique peut être utilisé pour définir des super crochets de Poisson pour les superchamps. Je donne une version "super" du premier théorème de Noether valable pour l'action de supergroupes de symétrie et je propose une extension « super » de l'application multimoment. Enfin je présente quelques exemples montrant comment toute la théorie peut être mise en œuvre : en particulier j'étudie la superparticule libre et le modèle sigma 3-dimensionnelThe Calculus of Variations and its geometric interpretation always played a key role in Mathematical Physics, either through the Lagrangian formalism, or through the Hamiltonian equations.The multisymplectic formalism allows a finite dimensional geometric description of classical field theories seen from an Hamiltonian point of view. Multisymplectic geometry plays the same role played by symplectic geometry in the description of classical Hamiltonian mechanics. Moreover the multisymplectic approach provides a tool for building a symplectic structure on the space of solutions of the field theory and for investigating it.In this thesis I use the multisymplectic formalism to build first order field theories and I hope to give two main original contributions:– I show that, in some situations, the symplectic structure on the covariant phase space may indeed depend from the choice of splitting of spacetime in space and time;– I extend the multisymplectic formalism to superfield theories.As a "byproduct", I present another contribution:– I define fractional forms on supermanifolds with their relative Cartan Calculus. These fractional forms are useful to build the multisymplectic formalism for superfield theories.The main ingredients of the formalism I use are: the finite dimensional multimomenta phase space P and its extension to super field theories, which I give; the Lagrangian superform; the super-Hamiltonian, the multisymplectic superform.In my thesis I also prove a Comparison Theorem which allows to clarify the relations existing between the so called components theories and the so called superfield theories. I explain how the supermultisymplectic formalism can be used to define super Poisson brackets for super fields. I give a "super" version of the first Noether theorem valid for the action of supergroups of symmetry and I propose a “super” extension of the multimomentum map.Finally I present some examples showing how all the theory can be implemented: I study the free superparticle and the 3-dimensional sigma-model
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Cochran, Caroline. "THE EQUIVALENCE PROBLEM FOR ORTHOGONALLY SEPARABLE WEBS ON SPACES OF CONSTANT CURVATURE." 2011. http://hdl.handle.net/10222/14191.
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This thesis is devoted to creating a systematic way of determining all inequivalent
orthogonal coordinate systems which separate the Hamilton-Jacobi equation for a
given natural Hamiltonian defined on three-dimensional spaces of constant, non-zero
curvature. To achieve this, we represent the problem with Killing tensors and employ
the recently developed invariant theory of Killing tensors.
Killing tensors on the model spaces of spherical and hyperbolic space enjoy a
remarkably simple form; even more striking is the fact that their parameter tensors
admit the same symmetries as the Riemann curvature tensor, and thus can be
considered algebraic curvature tensors. Using this property to obtain invariants and
covariants of Killing tensors, together with the web symmetries of the associated orthogonal
coordinate webs, we establish an equivalence criterion for each space. In
the case of three-dimensional spherical space, we demonstrate the surprising result
that these webs can be distinguished purely by the symmetries of the web. In the
case of three-dimensional hyperbolic space, we use a combination of web symmetries,
invariants and covariants to achieve an equivalence criterion. To completely solve the
equivalence problem in each case, we develop a method for determining the moving
frame map for an arbitrary Killing tensor of the space. This is achieved by defining
an algebraic Ricci tensor.
Solutions to equivalence problems of Killing tensors are particularly useful in the
areas of multiseparability and superintegrability. This is evidenced by our analysis
of symmetric potentials defined on three-dimensional spherical and hyperbolic space.
Using the most general Killing tensor of a symmetry subspace, we derive the most
general potential “compatible” with this Killing tensor. As a further example, we
introduce the notion of a joint invariant in the vector space of Killing tensors and use
them to characterize a well-known superintegrable potential in the plane.
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TORTORELLA, ALFONSO GIUSEPPE. "Deformations of coisotropic submanifolds in Jacobi manifolds." Doctoral thesis, 2017. http://hdl.handle.net/2158/1077777.
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In this thesis, we investigate deformation theory and moduli theory of coisotropic submanifolds in Jacobi manifolds. Originally introduced by Kirillov as local Lie algebras with one dimensional fibers, Jacobi manifolds encompass, unifying and generalizing, locally conformal symplectic manifolds, locally conformal Poisson manifolds, and non-necessarily coorientable contact manifolds.
We attach an L-infinity-algebra to any coisotropic submanifold in a Jacobi manifold. Our construction generalizes and unifies analogous constructions by Oh-Park (symplectic case), Cattaneo-Felder (Poisson case), and Le-Oh (locally conformal symplectic case). As a completely new case we also associate an L-infinity-algebra with any coisotropic submanifold in a contact manifold. The L-infinity-algebra of a coisotropic submanifold S controls the formal coisotropic deformation problem of S, even under Hamiltonian equivalence, and provides criteria both for the obstructedness and for the unobstructedness at the formal level. Additionally we prove that if a certain condition ("fiberwise entireness") is satisfied then the L-infinity-algebra controls the non-formal coisotropic deformation problem, even under Hamiltonian equivalence.
We associate a BFV-complex with any coisotropic submanifold in a Jacobi manifold. Our construction extends an analogous construction by Schatz in the Poisson setting, and in particular it also applies in the locally conformal symplectic/Poisson setting and the contact setting. Unlike the L-infinity-algebra, we prove that, with no need of any restrictive hypothesis, the BFV-complex of a coisotropic submanifold S controls the non-formal coisotropic deformation problem of S, even under both Hamiltonian equivalence and Jacobi equivalence.
Notwithstanding the differences there is a close relation between the approaches to the coisotropic deformation problem via L-infinity-algebra and via BFV-complex. Indeed both the L-infinity-algebra and the BFV-complex of a coisotropic submanifold S provide a cohomological reduction of S. Moreover they are L-infinity quasi-isomorphic and so they encode equally well the moduli space of formal coisotropic deformations of S under Hamiltonian equivalence.
In addition we exhibit two examples of coisotropic submanifolds in the contact setting whose coisotropic deformation problem is obstructed at the formal level. Further we provide a conceptual explanation of this phenomenon both in terms of the L-infinity-algebra and in terms of the BFV-complex.
Books on the topic "Hamiltonian equivalence"
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Mercati, Flavio. Hamiltonian Formulation. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198789475.003.0006.
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The Hamiltonian formulation of relational particle dynamics unveils its equivalence with modern gauge theory, which admits exactly the same canonical formulation. Both are constrained Hamiltonian systems with nonhonolomic constraints, for which Dirac’s analysis, made popular by his lectures, is necessary. Dirac’s analysis is briefly summarized in this chapter for readers unfamiliar with it. The Hamiltonian formulation of the kind of systems we’re interested in is nontrivial. In fact the standard formulation fails to be predictive, precisely because of the relational nature of our dynamics.
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Mercati, Flavio. York’s Solution to the Initial-Value Problem. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198789475.003.0008.
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In this chapter I briefly review York’s method (or the conformal method) for solving the initial value problem of (GR). This method, developed initially by Lichnerowicz and then generalized by Choquet-Bruhat and York, allows to find solutions of the constraints of (GR) (in particular the Hamiltonian, or refoliation constraint) by scanning the conformal equivalence class of spatial metrics for a solution of the Hamiltonian constraint, exploiting the fact that, in a particular foliation (CMC), the transverse nature of the momentum field is preserved under conformal transformations. This method allows to transform the initial value problem into an elliptic problem for the solution for which good existence and uniqueness theorems are available. Moreover this method allows to identify the reduced phase space of (GR) with the cotangent bundle to conformal superspace (the space of conformal 3-geometries), when the CMC foliation is valid. SD essentially amounts to taking this phase space as fundamental and renouncing the spacetime description when the CMC foliation is not available.
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Zeitlin, Vladimir. Rotating Shallow-Water model with Horizontal Density and/or Temperature Gradients. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198804338.003.0014.
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The derivation of rotating shallow-water equations by vertical averaging and columnar motion hypothesis is repeated without supposing horizontal homogeneity of density/potential temperature. The so-called thermal rotating shallow-water model arises as the result. The model turns to be equivalent to gas dynamics with a specific equation of state. It is shown that it possesses Hamiltonian structure and can be derived from a variational principle. Its solution at low Rossby numbers should obey the thermo-geostrophic equilibrium, replacing the standard geostrophic equilibrium. The wave spectrum of the model is analysed, and the appearance of a whole new class of vortex instabilities of convective type, resembling asymmetric centrifugal instability and leading to a strong mixing at nonlinear stage, is demonstrated.
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Horing, Norman J. Morgenstern. Q. M. Pictures; Heisenberg Equation; Linear Response; Superoperators and Non-Markovian Equations. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0003.
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Three fundamental and equivalent mathematical frameworks (“pictures”) in which quantum theory can be lodged are exhibited and their relations and relative advantages/disadvantages are discussed: (1) The Schrödinger picture considers the dynamical development of the overall system state vector as a function of time relative to a fixed complete set of time-independent basis eigenstates; (2) The Heisenberg picture (convenient for the use of Green’s functions) embeds the dynamical development of the system in a time-dependent counter-rotation of the complete set of basis eigenstates relative to the fixed, time-independent overall system state, so that the relation of the latter fixed system state to the counter-rotating basis eigenstates is identically the same in the Heisenberg picture as it is in the Schrödinger picture; (3) the Interaction Picture addresses the situation in which a Hamiltonian, H=H0+H1, involves a part H0 whose equations are relatively easy to solve and a more complicated part, H1, treated perturbatively. The Heisenberg equation of motion for operators is discussed, and is applied to annihilation and creation operators. The S-matrix, density matrix and von Neumann equation, along with superoperators and non-Markovian kinetic equations are also addressed (e.g. the intracollisional field effect).
Book chapters on the topic "Hamiltonian equivalence"
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"Maupertuis Principle and Geodesic Equivalence." In Integrable Hamiltonian Systems. CRC Press, 2004. http://dx.doi.org/10.1201/9780203643426.ch15.
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"Maupertuis Principle and Geodesic Equivalence." In Integrable Hamiltonian Systems, 663–702. CRC Press, 2004. http://dx.doi.org/10.1201/9780203643426-19.
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"Liouville Equivalence of Integrable Systems with Two Degrees of Freedom." In Integrable Hamiltonian Systems. CRC Press, 2004. http://dx.doi.org/10.1201/9780203643426.ch4.
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"Rough Liouville Equivalence of Integrable Systems with Two Degrees of Freedom." In Integrable Hamiltonian Systems. CRC Press, 2004. http://dx.doi.org/10.1201/9780203643426.ch3.
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"Rough Liouville Equivalence of Integrable Systems with Two Degrees of Freedom." In Integrable Hamiltonian Systems, 145–74. CRC Press, 2004. http://dx.doi.org/10.1201/9780203643426-7.
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Vadim, Kaloshin, and Zhang Ke. "Forcing equivalence between kissing cylinders." In Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom, 133–44. Princeton University Press, 2020. http://dx.doi.org/10.23943/princeton/9780691202525.003.0012.
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This chapter formulates and proves the jump mechanism. It constructs a variational problem which proves forcing equivalence for the original Hamiltonian using Definition 6.18. It first constructs a special variational problem for the slow mechanical system. A solution of this variational problem is an orbit “jumping” from one homology class to the other. The chapter then modifies this variational problem for the fast time-periodic perturbation of the slow mechanical system. This is achieved by applying the perturbative results established in Chapter 7. Recall the original Hamiltonian system near a double resonance can be brought to a normal form and this normal form, in turn, is related to the perturbed slow system through coordinate change and energy reduction. The variational problem for the perturbed slow system can then be converted to a variational problem for the original.
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Iliopoulos, J., and T. N. Tomaras. "Elements of Classical Field Theory." In Elementary Particle Physics, 24–34. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780192844200.003.0003.
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The purpose of this chapter is to recall the principles of Lagrangian and Hamiltonian classical mechanics. Many results are presented without detailed proofs. We obtain the Euler–Lagrange equations of motion, and show the equivalence with Hamilton’s equations. We derive Noether’s theorem and show the connection between symmetries and conservation laws. These principles are extended to a system with an infinite number of degrees of freedom, i.e. a classical field theory. The invariance under a Lie group of transformations implies the existence of conserved currents. The corresponding charges generate, through the Poisson brackets, the infinitesimal transformations of the fields as well as the Lie algebra of the group.
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Vadim, Kaloshin, and Zhang Ke. "Perturbative weak KAM theory." In Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom, 66–76. Princeton University Press, 2020. http://dx.doi.org/10.23943/princeton/9780691202525.003.0007.
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This chapter explores perturbation aspects of the weak Kolmogorov-Arnold-Moser (KAM) theory. By perturbative weak KAM theory, we mean two things. How do the weak KAM solutions and the Mather, Aubry, and Mañé sets respond to limits of the Hamiltonian? How do the weak KAM solutions change when we perturb a system, in particular, what happens when we perturb (1) completely integrable systems, and (2) autonomous systems by a time-periodic perturbation? The chapter states and proves results in both aspects, as a technical tool for proving forcing equivalence. It derives a special Lipshitz estimate of weak KAM solutions for perturbations of autonomous systems. The proof relies on semi-concavity of weak KAM solution.
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Vadim, Kaloshin, and Zhang Ke. "Weak KAM Theory and Forcing Equivalence." In Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom, 55–65. Princeton University Press, 2020. http://dx.doi.org/10.23943/princeton/9780691202525.003.0006.
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This chapter describes weak Kolmogorov-Arnold-Moser (KAM) theory and forcing relation. One change from the standard presentation is that one needs to modify the definition of Tonelli Hamiltonians to allow different periods in the t component. The chapter points out an alternative definition of the alpha function, namely, one can replace the class of minimal measures with the class of closed measures. It then considers a dual setting which corresponds to forward dynamic. It also looks at elementary solutions, static classes, and Peierls barrier. In many parts of the proof, the chapter studies the hyperbolic property of a minimizing orbit, for which the concept of Green bundles is very useful.
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Cina, Jeffrey A. "Short-pulse electronic absorption." In Getting Started on Time-Resolved Molecular Spectroscopy, 1–10. Oxford University Press, 2022. http://dx.doi.org/10.1093/oso/9780199590315.003.0001.
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Linear absorption, by a molecule, of pulsed laser light is detailed using time-dependent perturbation theory. Pulse propagators, which describe the transfer and shaping of nuclear wave packets during laser-driven electronic transitions are introduced. The equivalence, in the long-pulse limit, to Heller’s description of linear absorption in terms of wave-packet dynamics is established. The effects of initial thermal equilibrium, spectral congestion, and finite spectral resolution are illustrated with signal calculations on model Hamiltonians.
Conference papers on the topic "Hamiltonian equivalence"
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Hudon, N., K. Hoffner, and M. Guay. "Equivalence to dissipative Hamiltonian realization." In 2008 47th IEEE Conference on Decision and Control. IEEE, 2008. http://dx.doi.org/10.1109/cdc.2008.4739446.
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Stojanović, S. D., M. V. Pavkov-Hrvojević, and M. J. Škrinjar. "The Equivalence of Transfer Matrix Method and Boson Hamiltonian Approach Calculations in Ferromagnetic Superlattices." In SIXTH INTERNATIONAL CONFERENCE OF THE BALKAN PHYSICAL UNION. AIP, 2007. http://dx.doi.org/10.1063/1.2733399.
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Bae, D. S., and Y. S. Won. "A Hamiltonian Equation of Motion for Realtime Vehicle Simulation." In ASME 1990 Design Technical Conferences. American Society of Mechanical Engineers, 1990. http://dx.doi.org/10.1115/detc1990-0062.
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Abstract A relative coordinate formulation of the Hamiltonian equation of motion is derived for realtime vehicle simulation. The Baumgarte stabilization method [1] is adopted to solve the Differential-Algebraic Equations (DAE) of motion. The stability theory of multi-step integration methods is used to determine the stabilization constant. The equations of motion are first derived in Cartesian space and are reduced to relative coordinate space using the velocity transformation method [2]. Partial derivative of the kinetic energy with respect to the relative coordinate is obtained from equivalence of the Lagrangian and the Newton-Euler formulations. Parallel processing of the formulation is also discussed. Realtime simulation of a passenger vehicle is carried out to demonstrate the efficiency of the new formulation.
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Tian, Liguang, and H. J. Carmichael. "Broadband excitation of the Jaynes–Cummings molecule." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1990. http://dx.doi.org/10.1364/oam.1990.ws3.
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When a single atom interacts with one mode of an optical cavity and the coupling to the cavity mode is sufficiently large, the spectroscopic response of the composite system to a weak probe is a doublet, with peaks located at the eigenfrequencies of the one-quantum excited states of the Jaynes–Cummings Hamiltonian. So far as these one-quantum states are concerned the spectroscopy of the Jaynes–Cummings model is the same as that of coupled, damped harmonic oscillators. This equivalence has been used to observe a doublet spectrum (the so-called "vacuum" Rabi splitting) by exciting a collective dipole oscillator inside an optical cavity.1,2 At higher levels of excitation the spectroscopy of the Jaynes–Cummings model differs markedly from that of coupled harmonic oscillators. Coupled harmonic oscillators give a doublet at all excitation levels; because of its noncommensurate excited state energies the Jaynes–Cummings model gives a multitude of additional peaks. In this paper we show how the excited states of the Jaynes–Cummings Hamiltonian can be probed by driving a cavity containing a single atom with broadband chaotic light. For a sufficiently large dipole coupling strength the spectrum of the light scattered out of the cavity mode shows peaks at the many resonance frequencies of the Jaynes–Cummings Hamiltonian. A similar multipeaked spectrum is seen in transmission. The spectrum of the light reflected from the cavity shows corresponding absorption dips superimposed on the broadband input.
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Petrzela, Jiri. "Equivalent circuit realizations of fourth-order chaotic Hamiltonian system." In 2016 26th International Conference Radioelektronika (RADIOELEKTRONIKA). IEEE, 2016. http://dx.doi.org/10.1109/radioelek.2016.7477353.
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Butcher, Eric A., and S. C. Sinha. "Canonical Perturbation of a Fast Time-Periodic Hamiltonian via Liapunov-Floquet Transformation." In ASME 1997 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/detc97/vib-4107.
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Abstract In this study a possible application of time-dependent canonical perturbation theory to a fast nonlinear time-periodic Hamiltonian with strong internal excitation is considered. It is shown that if the time-periodic unperturbed part is quadratic, the Hamiltonian may be canonically transformed to an equivalent form in which the new unperturbed part is time-invariant so that the time-dependent canonical perturbation theory may be successfully applied. For this purpose, the Liapunov-Floquet (L-F) transformation and its inverse associated with the unperturbed time-periodic quadratic Hamiltonian are computed using a recently developed technique. Action-angle variables and time-dependent canonical perturbation theory are then utilized to find the solution in the original coordinates. The results are compared for accuracy with solutions obtained by both numerical integration and by the classical method of directly applying the time-dependent perturbation theory in which the time-periodic quadratic part is treated as another perturbation term. A strongly excited Mathieu-Hill quadratic Hamiltonian with a cubic perturbation and a nonlinear time-periodic Hamiltonian without a constant quadratic part serve as illustrative examples. It is shown that, unlike the classical method in which the internal excitation must be weak, the proposed formulation provides accurate solutions for an arbitrarily large internal excitation.
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Jannson, Tomasz, and Joel Ng. "Nonimaging optics and the Liouville theorem in the XUV region." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1987. http://dx.doi.org/10.1364/oam.1987.thpo24.
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In general, Liouville's theorem holds for any time-reversible Hamiltonian system including the geometrical optics (both imaging and nonimaging1,2) model of monochromatic rays, where, in Hamiltonian formulation,2 the z-coordinate is treated as a parameter equivalent to the time variable in statistical classical mechanics. Thus the so-called ideal nonimaging optical elements, well known in the IR/VIS/UV region,1,3 can also be introduced to the collimation and concentration of XUV electromagnetic radiation (1–100 nm). Contrary to the IR/VIS/UV region, where the nonimagng elements are based on either metallic reflection or dielectric total internal reflection, the XUV concentrators/collimators are based on grazing incidence total external reflection, since the refractive index of all optical materials is smaller than 1 in the XUV region.
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Robinett, Rush D., and David G. Wilson. "Decentralized Exergy/Entropy Thermodynamic Control for Collective Robotic Systems." In ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-43691.
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This paper develops a distributed decentralized control law for collective robotic systems. The control laws are developed based on exergy/entropy thermodynamic concepts and information theory. The source field is characterized through second-order accuracy. The proposed feedback control law stability for both the collective and individual robots are demonstrated by selecting a general Hamiltonian based solution developed as Fisher Information Equivalency as the vector Lyapunov function. Stability boundaries and system performance are then determined with Lyapunov’s direct method. A robot collective plume tracing numerical simulation example demonstrates this decentralized exergy/entropy collective control architecture.
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Groner, Peter. "THE INTRIGUING Fbc(PbPc+PcPb) TERM IN THE INTERACTION HAMILTONIAN FOR TUNNELING BETWEEN EQUIVALENT GAUCHE CONFORMERS." In 2022 International Symposium on Molecular Spectroscopy. Urbana, Illinois: University of Illinois at Urbana-Champaign, 2022. http://dx.doi.org/10.15278/isms.2022.tf01.
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Orth, K., G. Grad, and J. Friedrich. "Nuclear spin conversion relaxation processes in dimethyl-s-tetrazine doped n-octane measured by spectral hole burning techniques." In Spectral Hole-Burning and Luminescence Line Narrowing: Science and Applications. Washington, D.C.: Optica Publishing Group, 1992. http://dx.doi.org/10.1364/shbl.1992.wa5.
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Rotational tunnel systems provide deep insight into the basic laws of quantum mechanics. For a review, see [1]. Let us take the -CH3 entity as a prototype. A rotation by 2π/3 around the symmetry axis perpendicular to the plane of the protons leaves the relevant Hamiltonian invariant. The spatial wave functions have A- and E-type symmetries. Since such a rotation is equivalent with a double permutation of two protons, the total wave function (space ⊗ spin) has to be totally symmetric because of Pauli’s principle. That is, the Pauli principle puts a strong symmetry restriction onto the wave function of the -CH3-rotor: In the E-type states, the total nuclear spin is 1/2, in the A-type states it is 3/2. As a consequence, a relaxation of the total spin in these kind of quantum rotors is always connected with a change of the rotational or librational wavefunction. The corresponding overall process is called spin conversion relaxation.