Relevant bibliographies by topics / Polynomial Hamiltonians

Academic literature on the topic 'Polynomial Hamiltonians'

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Published: 14 March 2023

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Journal articles on the topic "Polynomial Hamiltonians"

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SILVER, R. N., and H. RÖDER. "DENSITIES OF STATES OF MEGA-DIMENSIONAL HAMILTONIAN MATRICES." International Journal of Modern Physics C 05, no. 04 (August 1994): 735–53. http://dx.doi.org/10.1142/s0129183194000842.

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We propose a statistical method to estimate densities of states (DOS) and thermodynamic functions of very large Hamiltonian matrices. Orthogonal polynomials are defined on the interval between lower and upper energy bounds. The DOS is represented by a kernel polynomial constructed out of polynomial moments of the DOS and modified to damp the Gibbs phenomenon. The moments are stochastically evaluated using matrixvector multiplications on Gaussian random vectors and the polynomial recurrence relations. The resulting kernel estimate is a controlled approximation to the true DOS, because it also provides estimates of statistical and systematic errors. For a given fractional energy resolution and statistical accuracy, the required cpu time and memory scale linearly in the number of states for sparse Hamiltonians. The method is demonstrated for the two-dimensional Heisenberg anti-ferromagnet with the number of states as large as 226. Results are compared to exact diagonalization where available.
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RÜHL, WERNER, and ALEXANDER TURBINER. "EXACT SOLVABILITY OF THE CALOGERO AND SUTHERLAND MODELS." Modern Physics Letters A 10, no. 29 (September 21, 1995): 2213–21. http://dx.doi.org/10.1142/s0217732395002374.

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Translationally invariant symmetric polynomials as coordinates for N-body problems with identical particles are proposed. It is shown that in those coordinates the Calogero and Sutherland N-body Hamiltonians, after appropriate gauge transformations, can be presented as a quadratic polynomial in the generators of the algebra sl N in finitedimensional degenerate representation. The exact solvability of these models follows from the existence of the infinite flag of such representation spaces, preserved by the above Hamiltonians. A connection with Jack polynomials is discussed.
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Sokolov, A. V. "Polynomial supersymmetry for matrix Hamiltonians." Physics Letters A 377, no. 9 (March 2013): 655–62. http://dx.doi.org/10.1016/j.physleta.2013.01.012.

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Gosset, David, Jenish C. Mehta, and Thomas Vidick. "QCMA hardness of ground space connectivity for commuting Hamiltonians." Quantum 1 (July 14, 2017): 16. http://dx.doi.org/10.22331/q-2017-07-14-16.

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In this work we consider the ground space connectivity problem for commuting local Hamiltonians. The ground space connectivity problem asks whether it is possible to go from one (efficiently preparable) state to another by applying a polynomial length sequence of 2-qubit unitaries while remaining at all times in a state with low energy for a given HamiltonianH. It was shown in [Gharibian and Sikora, ICALP15] that this problem is QCMA-complete for general local Hamiltonians, where QCMA is defined as QMA with a classical witness and BQP verifier. Here we show that the commuting version of the problem is also QCMA-complete. This provides one of the first examples where commuting local Hamiltonians exhibit complexity theoretic hardness equivalent to general local Hamiltonians.
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Lu, Kang. "Completeness of Bethe Ansatz for Gaudin Models with gl(1|1) Symmetry and Diagonal Twists." Symmetry 15, no. 1 (December 21, 2022): 9. http://dx.doi.org/10.3390/sym15010009.

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We studied the Gaudin models with gl(1|1) symmetry that are twisted by a diagonal matrix and defined on tensor products of polynomial evaluation gl(1|1)[t]-modules. Namely, we gave an explicit description of the algebra of Hamiltonians (Gaudin Hamiltonians) acting on tensor products of polynomial evaluation gl(1|1)[t]-modules and showed that a bijection exists between common eigenvectors (up to proportionality) of the algebra of Hamiltonians and monic divisors of an explicit polynomial written in terms of the highest weights and evaluation parameters. In particular, our result implies that each common eigenspace of the algebra of Hamiltonians has dimension one. We also gave dimensions of the generalized eigenspaces.
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UENO, YUICHI. "POLYNOMIAL HAMILTONIANS FOR QUANTUM PAINLEVÉ EQUATIONS." International Journal of Mathematics 20, no. 11 (November 2009): 1335–45. http://dx.doi.org/10.1142/s0129167x09005789.

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Recently, a quantum version of Painlevé equations from the point of view of their symmetries was proposed by Nagoya. These quantum Painlevé equations can be written as Hamiltonian systems with a (noncommutative) polynomial Hamiltonian H J . We give a characterization of the quantum Painlevé equations by certain holomorphic properties. Namely, we introduce canonical transformations such that the Painlevé Hamiltonian system is again transformed into a polynomial Hamiltonian system, and we show that the Hamiltonian can be uniquely characterized through this holomorphic property.
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Aharonov, Dorit, Michael Ben-Or, Fernando G. S. L. Brandão, and Or Sattath. "The Pursuit of Uniqueness: Extending Valiant-Vazirani Theorem to the Probabilistic and Quantum Settings." Quantum 6 (March 17, 2022): 668. http://dx.doi.org/10.22331/q-2022-03-17-668.

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Valiant-Vazirani showed in 1985 \cite{VV85} that solving NP with the promise that "yes" instances have only one witness is powerful enough to solve the entire NP class (under randomized reductions).We are interested in extending this result to the quantum setting. We prove extensions to the classes Merlin-Arthur MA and Quantum-Classical-Merlin-Arthur QCMA \cite{AN02}. Our results have implications for the complexity of approximating the ground state energy of a quantum local Hamiltonian with a unique ground state and an inverse polynomial spectral gap. We show that the estimation (to within polynomial accuracy) of the ground state energy of poly-gapped 1-D local Hamiltonians is QCMA-hard, under randomized reductions. This is in stark contrast to the case of constant gapped 1-D Hamiltonians, which is in NP \cite{Has07}. Moreover, it shows that unless QCMA can be reduced to NP by randomized reductions, there is no classical description of the ground state of every poly-gapped local Hamiltonian that allows efficient calculation of expectation values.Finally, we discuss a few of the obstacles to the establishment of an analogous result to the class Quantum-Merlin-Arthur (QMA). In particular, we show that random projections fail to provide a polynomial gap between two witnesses.
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Bravyi, S., D. P. DiVincenzo, R. Oliveira, and B. M. Terhal. "The complexity of stoquastic local Hamiltonian problems." Quantum Information and Computation 8, no. 5 (May 2008): 361–85. http://dx.doi.org/10.26421/qic8.5-1.

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We study the complexity of the Local Hamiltonian Problem (denoted as LH-MIN) in the special case when a Hamiltonian obeys the condition that all off-diagonal matrix elements in the standard basis are real and non-positive. We will call such Hamiltonians, which are common in the natural world, stoquastic. An equivalent characterization of stoquastic Hamiltonians is that they have an entry-wise non-negative Gibbs density matrix for any temperature. We prove that LH-MIN for stoquastic Hamiltonians belongs to the complexity class \AM{}--- a probabilistic version of \NP{} with two rounds of communication between the prover and the verifier. We also show that $2$-local stoquastic LH-MIN is hard for the class \MA. With the additional promise of having a polynomial spectral gap, we show that stoquastic LH-MIN belongs to the class \POSTBPP=\BPPpath --- a generalization of \BPP{} in which a post-selective readout is allowed. This last result also shows that any problem solved by adiabatic quantum computation using stoquastic Hamiltonians is in PostBPP.
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Vigo-Aguiar, M. I., M. E. Sansaturio, and J. M. Ferrándiz. "Integrability of Hamiltonians with polynomial potentials." Journal of Computational and Applied Mathematics 158, no. 1 (September 2003): 213–24. http://dx.doi.org/10.1016/s0377-0427(03)00467-9.

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Mingalev, Oleg V., Yurii N. Orlov, and Victor V. Vedenyapin. "Conservation laws for polynomial quantum Hamiltonians." Physics Letters A 223, no. 4 (December 1996): 246–50. http://dx.doi.org/10.1016/s0375-9601(96)00680-9.

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Dissertations / Theses on the topic "Polynomial Hamiltonians"

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ABENDA, SIMONETTA. "Analysis of Singularity Structures for Quasi-Integrable Hamiltonian Systems." Doctoral thesis, SISSA, 1994. http://hdl.handle.net/20.500.11767/4499.

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Hyder, Asif M. "Green's operator for Hamiltonians with Coulomb plus polynomial potentials." California State University, Long Beach, 2013.

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Evrim, Colak Ilker. "Hamiltonian linear type centers and nilpotent centers of linear plus cubic polynomial vector fields." Doctoral thesis, Universitat Autònoma de Barcelona, 2014. http://hdl.handle.net/10803/283528.

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En este trabajo proporcionamos doce formas normales para todos los campos vectoriales polinomiales Hamiltonianos en el plano que tienen términos lineales más cúbicos homogéneos y que poseen en el origen un centro de tipo lineal o un centro nilpotente. Para estos sistemas caracterizamos sus retratos de fase globales en el disco de Poincaré y describimos sus diagramas de bifurcación. Las formas normales de estos sistemas las obtenemos utilizando las formas normales de los sistemas cúbicos homogéneos dados en [1], y añadiendo a estos los términos lineales de manera que el origen sea un centro de tipo lineal o un centro nilpotente. Luego describimos los retratos de fase globales en el disco de Poincaré de estas doce familias de sistemas. Para ello en primer lugar encontramos los retratos de fase en el infinito de esos sistemas, y luego encontramos los retratos de fase locales en los puntos singulares finitos. Usando estos dos resultados determinamos los posibles retratos de fase globales de cada familia. Para algunas familias los puntos singulares finitos son demasiado complicados para estudiar sus retratos de fase local, y en algunos otros casos ni siquiera podemos calcular los puntos singulares finitos. En estas situaciones primero determinamos el número máximo de puntos singulares finitos que los sistemas pueden tener, a continuación utilizando el hecho de que el índice total de todos los puntos singulares de un campo vectorial en la esfera de Poincaré con un número finito de puntos singulares es 2 (este resultado se conoce como el teorema de Poincaré–Hopf) determinamos el número posible de puntos singulares finitos y sus posibles retratos fase locales posibles. Para determinar los posibles retratos de fase globales posibles miramos el número de puntos de una recta que pasa por el origen que se encuentran en el mismo nivel de energía. Puesto que los polinomios Hamiltonianos de las doce familias de sistemas son de cuarto grado, no puede haber más que cuatro de tales puntos. Si encontramos que sólo un retrato de fase global es posible para una familia, entonces este es el retrato de fase de la familia. Si hay más de un retrato de fase global posible, entonces mostramos que podemos elegir los parámetros de forma que los retratos de fase se realicen. Por último, después de haber determinado los retratos de fase global para cada familia, describimos sus diagramas de bifurcación utilizando las dos diferencias principales entre estos retratos de fase: el número de puntos singulares finitos y el número de sillas en el mismo nivel de energía. [1] A. Cima and J. Llibre, “Algebraic and topological classification of the homogeneous cubic vector fields in the plane”, J. Math. Anal. and Appl. 147 (1990), 420–448.
In this work we provide twelve normal forms for all the Hamiltonian planar polynomial vector fields having linear plus cubic homogeneous terms which possess a linear type center or a nilpotent center at the origin, and find their global phase portraits on the Poincaré disk. Moreover we provide the bifurcation diagrams of these differential systems. We obtain the normal forms of these systems using the normal forms of cubic homogeneous systems given in [1], and by adding to them the linear terms such that the origin is a linear type center or a nilpotent center. Then we describe the global phase portraits on the Poincaré disk of these twelve families of systems. To do this we first find the phase portraits at infinity of those systems, and then we find the local phase portraits at the finite singular points. Using these two results we determine the possible global phase portraits of each family. For some families the finite singular points are too complicated to study their local phase portraits, in some other cases we even cannot calculate the finite singular points. In these situations we first determine the maximum number of finite singular points that the systems can have, then using the fact that the total index of all the singular points of a vector field on the Poincaré sphere with a finite number of singular points is 2 (this result is known as the Poincaré–Hopf theorem) we determine the possible number of finite singular points and their possible local phase portraits. To determine the possible global phase portraits we look at the number of points of a straight line passing through the origin that are at the same energy level. Since the Hamiltonian polynomials of the twelve families of systems are quartic, there can be at most four such points. If we find only one possible global phase portrait for a family then we are done. If there are more than one possible global phase portrait then we show that for some specific choice of parameters those phase portraits are indeed realizable. Finally, after having determined the global phase portraits for each fam- ily, we describe their bifurcation diagrams using the two main differences between these phase portraits: the number of finite singular points and the number of saddles at the same energy level. [1] A. Cima and J. Llibre, “Algebraic and topological classification of the homogeneous cubic vector fields in the plane”, J. Math. Anal. and Appl. 147 (1990), 420–448.
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SCHUMAN, BERTRAND. "Sur le probleme du centre isochrone des systemes hamiltoniens polynomiaux." Paris 6, 1998. http://www.theses.fr/1998PA066617.

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On presente une approche du probleme du centre qui utilise la theorie des formes normales de germes de champs de vecteurs polynomiaux a l'origine dans r 2 n. Un de nos points de vue est l'effectivite, au sens ou on utilise le calcul formel pour obtenir et calculer les coefficients de la forme normale de birkhoff. On calcule explicitement les premiers coefficients de la forme normale d'un champ de vecteurs hamiltonien polynomial homogene, et un debut d'etude des champs hamiltoniens non homogenes est entreprise, au sens ou, la aussi, on calcule completement les premiers coefficients des formes normales mises en jeu. Notre travail permet d'attacher des invariants algebriques aux champs de vecteurs, et donc d'ebaucher une classification de ces champs. De plus, les equations algebriques provenant des ces invariants completement explicites dans certains cas, en particulier pour le cas hamiltonien, permettent de generer des conditions pour la linearisation des champs polynomiaux au voisinage de l'origine, qui est un point critique de type elliptique. Le probleme de la linearisation, ou encore du probleme du centre, est ainsi aborde par le biais des varietes algebriques definies par les equations associees aux champs de vecteurs etudies.
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Ghazo, Hanna Zeina. "Cycles combinatoires et géométriques." Thesis, Brest, 2020. http://www.theses.fr/2020BRES0006.

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Le travail de cette thèse se situe dans les domaines de la théorie combinatoire des graphes, la combinatoire algébrique et la géométrie discrète. D'un part, il concerne l'énumération des chemins et cycles Hamiltoniens de type donné dans un tournoi ; de l'autre part, il étudie des suites numériques vérifiant une équation à différence quadratique. Parmi les résultats obtenus dans la première partie, on trouve : une égalité entre le nombre des chemins (resp. cycles) Hamiltoniens d’un type donné dans un tournoi et dans son complément; une expression du nombre de chemins Hamiltoniens d’un type donné pour un tournoi transitif en termes d'une fonction récursive F appelée « path-function »; la construction d'un algorithme pour le calcul de F. L'objet fondamental dans la deuxième partie est un graphe cyclique muni d'une solution d'une équation à différence quadratique. Un paramètre de cette équation distingue les solutions réelles et les solutions complexes. Une correspondance entre les solutions réelles et une classe de polynômes à coefficients entiers positifs est établie. Pour compléter la correspondance, les digraphes Eulériens à un pas interviennent. Une solution complexe détermine une marche fermée dans le plan pour laquelle à chaque pas on tourne à gauche ou à droite par un angle constant (l'angle tournant). Cette fois-ci les polynômes cyclotomiques jouent un rôle important. La caractérisation des polynômes qui déterminent de telles suites est un problème qu’on surmonte afin d'élucider des propriétés géométriques de tels cycles polygonaux. Notamment, lorsque la marche exploite les côtés d'un polygone régulier avec angle extérieur 2π/n, on trouve des phénomènes non anticipés lorsque n≥12
The work in this thesis concerns the combinatorial theory of graphs, algebraic combinatorics and discrete geometry. On one side, it is about enumerating Hamiltonian paths and cycles of a given type in a tournament; On the other side, it studies numerical sequences verifying a quadratic difference equation.Concerning the results of the first part, we find: an equality between the number of Hamiltonians paths (resp. cycles) of a given type, in a tournament and its complement; an expression of the number of Hamiltonian oriented paths of a given type in a transitive tournament in terms of a recursive function F called the « path-function »; and the construction of an algorithm to compute F.In the second part of the work, we study cyclic graphs altogether with a solution to a quadratic difference equation.A parameter of this equation distinguishes real and complex sequences. A correspondence between real solutions and a class of polynomials with positive integer coefficients is established. To complete the correspondence, 1-step Eulerian digraphs interfere. A complex solution determines a closed planar walk in the plane, for which at each step we turn either left or right by a constant angle (the turning angle). This time, cyclotomic polynomials play a major role. Characterizing polynomials that determine such a solution is a problem that we study to the end of finding geometric properties of such polygonal cycles.When the walk exploits the sides of a regular polygon with exterior angle 2 π/n, we find unexpected phenomena when n≥ 12
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Abouelaoualim, Abdelfattah. "Exploration des graphes arêtes-colorées : topologie, algorithmes, complexité et (non)-approximabilité." Paris 11, 2007. https://tel.archives-ouvertes.fr/tel-00281533.

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Les graphes dont les arêtes sont coloriées par c>1 couleurs, avec c un entier donné, autrement dit les graphes c-arêtes-colorées, connaissent un nombre grandissant de champs d’applications notamment en biologie moléculaire et en technologie intégrée à très grande échelle sans oublier leur intérêt théorique puisqu’ils sont une généralisation des graphes orientés. Dans cette thèse nous explorons ces graphes pour extraire et étudier les structures (i. E. , les sous-graphes) dites proprement-arêtes-coloriées c'est-à-dire dans lesquelles chaque paire d’arêtes adjacentes sont de couleurs distinctes. Tout d’abord, nous avons jugé nécessaire de réserver la première partie de la thèse à un état de l’art qui présente les travaux les plus importants et couvre la majorité des questions traitées dans ce domaine depuis les années soixante. En suite, dans une deuxième partie, nous avons commencé par donner des caractérisations de certaines structures proprement-arêtes-coloriées telles que les chaînes et les cycles, et puis nous nous sommes orientés vers la construction des algorithmes, l’étude de l’aspect de la complexité et l’approximabilité d’une variété de structures
The graphs which edges are colored with c>1 colors, with c is a given integer, in other words c-edge-colored graphs, have a growing number of fields of applications particularly in molecular biology and VLSI. Their theoretical motivation is obvious sine they are a generalization of digraphs. In the present work, we explore these graphs to extract and study structures (i. E. Subgraphs) called properly-edge-colored which every pair of adjacent edges differ in color. We start this work by a part introducing the most notable results in the literature and cover the majority of questions treated in this topic since the sixties. In the second part, first we give characterizations of certain properly-edge-colored structures such as paths and cycles. After that, we were interested by the construction of polynomial algorithms, the study of complexity and approximability aspect of a variety of structures
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Oltean, Elvis. "Modelling income, wealth, and expenditure data by use of Econophysics." Thesis, Loughborough University, 2016. https://dspace.lboro.ac.uk/2134/20203.

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In the present paper, we identify several distributions from Physics and study their applicability to phenomena such as distribution of income, wealth, and expenditure. Firstly, we apply logistic distribution to these data and we find that it fits very well the annual data for the entire income interval including for upper income segment of population. Secondly, we apply Fermi-Dirac distribution to these data. We seek to explain possible correlations and analogies between economic systems and statistical thermodynamics systems. We try to explain their behaviour and properties when we correlate physical variables with macroeconomic aggregates and indicators. Then we draw some analogies between parameters of the Fermi-Dirac distribution and macroeconomic variables. Thirdly, as complex systems are modelled using polynomial distributions, we apply polynomials to the annual sets of data and we find that it fits very well also the entire income interval. Fourthly, we develop a new methodology to approach dynamically the income, wealth, and expenditure distribution similarly with dynamical complex systems. This methodology was applied to different time intervals consisting of consecutive years up to 35 years. Finally, we develop a mathematical model based on a Hamiltonian that maximises utility function applied to Ramsey model using Fermi-Dirac and polynomial utility functions. We find some theoretical connections with time preference theory. We apply these distributions to a large pool of data from countries with different levels of development, using different methods for calculation of income, wealth, and expenditure.
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Books on the topic "Polynomial Hamiltonians"

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Zabrodin, Anton. Quantum spin chains and classical integrable systems. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797319.003.0013.

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This chapter is a review of the recently established quantum-classical correspondence for integrable systems based on the construction of the master T-operator. For integrable inhomogeneous quantum spin chains with gl(N)-invariant R-matrices in finite-dimensional representations, the master T-operator is a sort of generating function for the family of commuting quantum transfer matrices depending on an infinite number of parameters. Any eigenvalue of the master T-operator is the tau-function of the classical modified KP hierarchy. It is a polynomial in the spectral parameter which is identified with the 0th time of the hierarchy. This implies a remarkable relation between the quantum spin chains and classical many-body integrable systems of particles of the Ruijsenaars-Schneider type. As an outcome, a system of algebraic equations can be obtained for the spectrum of the spin chain Hamiltonians.
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Premios de investicación [i.e. investigación] concedidos por la Academia en las secciones de exactas y físicas durante el periodo (1999-2000). [Zaragoza, Spain: Academia de Ciencias Exactas, Físicas, Químicas y Naturales de Zaragoza], 2000.

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Book chapters on the topic "Polynomial Hamiltonians"

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Abenda, Simonetta. "Time Singularities for Polynomial Hamiltonians with Analytic Time Dependence." In Hamiltonian Systems with Three or More Degrees of Freedom, 285–89. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-011-4673-9_24.

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Uwano, Yoshio, Nikolai Chekanov, Vitaly Rostovtsev, and Sergue Vinitsky. "On Normalization of a Class of Polynomial Hamiltonians: From Ordinary and Inverse Points of View." In Computer Algebra in Scientific Computing CASC’99, 441–61. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/978-3-642-60218-4_34.

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Delgado, J., E. A. Lacomba, J. Llibre, and E. Pérez. "Poincaré Compactification of Hamiltonian Polynomial Vector Fields." In Hamiltonian Dynamical Systems, 99–114. New York, NY: Springer New York, 1995. http://dx.doi.org/10.1007/978-1-4613-8448-9_6.

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Kozlov, Valerij V. "Polynomial Integrals of Hamiltonian Systems." In Symmetries, Topology and Resonances in Hamiltonian Mechanics, 337–66. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/978-3-642-78393-7_9.

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Krall, Allan M. "Regular Linear Hamiltonian Systems." In Hilbert Space, Boundary Value Problems and Orthogonal Polynomials, 51–72. Basel: Birkhäuser Basel, 2002. http://dx.doi.org/10.1007/978-3-0348-8155-5_4.

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Reyes-Bustos, Cid. "Extended Divisibility Relations for Constraint Polynomials of the Asymmetric Quantum Rabi Model." In International Symposium on Mathematics, Quantum Theory, and Cryptography, 149–68. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-5191-8_13.

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Abstract The quantum Rabi model (QRM) is widely regarded as one of the fundamental models of quantum optics. One of its generalizations is the asymmetric quantum Rabi model (AQRM), obtained by introducing a symmetry-breaking term depending on a parameter $$\varepsilon \in \mathbb {R}$$ to the Hamiltonian of the QRM. The AQRM was shown to possess degeneracies in the spectrum for values $$\epsilon \in 1/2\mathbb {Z}$$ via the study of the divisibility of the so-called constraint polynomials. In this article, we aim to provide further insight into the structure of Juddian solutions of the AQRM by extending the divisibility properties and the relations between the constraint polynomials with the solution of the AQRM in the Bargmann space. In particular we discuss a conjecture proposed by Masato Wakayama.
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Krall, Allan M. "The Niessen Approach to Singular Hamiltonian Systems." In Hilbert Space, Boundary Value Problems and Orthogonal Polynomials, 87–106. Basel: Birkhäuser Basel, 2002. http://dx.doi.org/10.1007/978-3-0348-8155-5_6.

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Froeschlé, Claude, and Elena Lega. "Polynomial Approximation of Poincaré Maps for Hamiltonian Systems." In Worlds in Interaction: Small Bodies and Planets of the Solar System, 51–56. Dordrecht: Springer Netherlands, 1996. http://dx.doi.org/10.1007/978-94-009-0209-1_10.

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Krall, Allan M. "Atkinson’s Theory for Singular Hamiltonian Systems of Even Dimension." In Hilbert Space, Boundary Value Problems and Orthogonal Polynomials, 73–85. Basel: Birkhäuser Basel, 2002. http://dx.doi.org/10.1007/978-3-0348-8155-5_5.

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Mir, Arnau, and Amadeu Delshams. "Psi-Series, Singularities of Solutions and Integrability of Polynomial Systems." In Hamiltonian Systems with Three or More Degrees of Freedom, 504–8. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-011-4673-9_66.

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Conference papers on the topic "Polynomial Hamiltonians"

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Brugnano, Luigi, Felice Iavernaro, Donato Trigiante, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Hamiltonian BVMs (HBVMs): A Family of “Drift Free” Methods for Integrating polynomial Hamiltonian problems." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2009: Volume 1 and Volume 2. AIP, 2009. http://dx.doi.org/10.1063/1.3241566.

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Regniers, G., J. Van der Jeugt, and Vladimir Dobrev. "Analytically Solvable Quantum Hamiltonians and Relations to Orthogonal Polynomials." In LIE THEORY AND ITS APPLICATIONS IN PHYSICS: VIII International Workshop. AIP, 2010. http://dx.doi.org/10.1063/1.3460184.

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Pasini, Jose Miguel, and Tuhin Sahai. "Polynomial chaos based uncertainty quantification in Hamiltonian and chaotic systems." In 2013 IEEE 52nd Annual Conference on Decision and Control (CDC). IEEE, 2013. http://dx.doi.org/10.1109/cdc.2013.6760031.

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Kyrola, Erkki, and Markus Lindberg. "Spectra of ladder systems." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1988. http://dx.doi.org/10.1364/oam.1988.my5.

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A strong laser field interacting with an atom or a molecule can induce a coherent process which includes a large number of energy levels. If we can find a transformation which eliminates the explicit time dependence of the interaction Hamiltonian (for example, the rotating-wave approximation), we can reduce the dynamic problem to the consideration of eigenvalues and eigenvectors of the Hamiltonian. However, the complexity of an arbitrary multilevel Hamiltonian usually forces us to use numerical methods, and, therefore, not much general understanding about multilevel systems can be achieved. We consider the multilevel problems in a more general setting. Our approach is based on the observation that an arbitrary Hamiltonian matrix can be transformed into a tridiagonal form by unitary transformation.1 A tridiagonal form represents a ladder-type multilevel system. From all W-level systems the ladder configuration is the simplest in the sense that the number of level connections is the smallest possible. This means that the most effective analysis of a given multilevel system can be achieved using the transformation to ladder configuration. The spectral analysis of ladders is facilitated by the connections to orthogonal polynomials and continued fractions. The investigations about the spectral properties of ladders are reported.
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Iavernaro, Felice, and Brigida Pace. "Conservative Block‐Boundary Value Methods for the Solution of Polynomial Hamiltonian Systems." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2008. American Institute of Physics, 2008. http://dx.doi.org/10.1063/1.2991075.

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FALCONI, MANUEL, ERNESTO A. LACOMBA, and JAUME LLIBRE. "INFINITY MANIFOLDS OF CUBIC POLYNOMIAL HAMILTONIAN VECTOR FIELDS WITH 2 DEGREES OF FREEDOM." In Proceedings of the III International Symposium. WORLD SCIENTIFIC, 2000. http://dx.doi.org/10.1142/9789812792099_0008.

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Iavernaro, Felice, Brigida Pace, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "s-stage Trapezoidal Methods for the Conservation of Hamiltonian Functions of Polynomial Type." In Numerical Analysis and Applied Mathematics. AIP, 2007. http://dx.doi.org/10.1063/1.2790219.

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Hong, Xiao-Chun, Jian Huang, and Zhonghuan Cai. "Global bifurcation of limit cycles in an integrable non-Hamiltonian system under polynomial perturbations." In 2011 Seventh International Conference on Natural Computation (ICNC). IEEE, 2011. http://dx.doi.org/10.1109/icnc.2011.6022497.

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Bauchau, Olivier A., and Shilei Han. "Advanced Plate Theory for Multibody Dynamics." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-12415.

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In flexible multibody systems, many components are often approximated as plates. More often that not, classical plate theories, such as Kirchhoff or Reissner-Mindlin plate theory, form the basis of the analytical development for plate dynamics. The advantage of this approach is that it leads to a very simple kinematic representation of the problem: the plate’s normal material line is assumed to remain straight and its displacement field is fully defined by three displacement and two rotation components. While such approach is capable of capturing the kinetic energy of the system accurately, it cannot represent the strain energy adequately. For instance, it is well known from three-dimensional elasticity theory that the normal material line will warp under load for laminated composite plates, leading to a three-dimensional deformation state that generates a complex stress state. To overcome this problem, several high-order and refined plate theory were proposed. While these approaches work well for some cases, they typically lead to inefficient formulation because they introduce numerous additional variables. This paper presents a different approach to the problem, which is based on a finite element discretization of the normal material line, and relies of the Hamiltonian formalism of obtain solutions of the governing equations. Polynomial solutions, also known as central solutions, are obtained that propagate over the entire span of the plate.
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Reports on the topic "Polynomial Hamiltonians"

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Degroote, M., T. M. Henderson, J. Zhao, J. Dukelsky, and G. E. Scuseria. Polynomial Similarity Transformation Theory: A smooth interpolation between coupled cluster doubles and projected BCS applied to the reduced BCS Hamiltonian. Office of Scientific and Technical Information (OSTI), January 2018. http://dx.doi.org/10.2172/1416504.

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