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Relevant bibliographies by topics / Polynomial Hamiltonians

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Academic literature on the topic 'Polynomial Hamiltonians'

Author: Grafiati

Published: 14 March 2023

Last updated: 31 July 2025

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Journal articles on the topic "Polynomial Hamiltonians"

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Marti, Lucas, Refik Mansuroglu, and Michael J. Hartmann. "Efficient Quantum Cooling Algorithm for Fermionic Systems." Quantum 9 (February 18, 2025): 1635. https://doi.org/10.22331/q-2025-02-18-1635.

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We present a cooling algorithm for ground state preparation of fermionic Hamiltonians. Our algorithm makes use of the Hamiltonian simulation of the considered system coupled to an ancillary fridge, which is regularly reset to its known ground state. We derive suitable interaction Hamiltonians that originate from ladder operators of the free theory and initiate resonant gaps between system and fridge. We further propose a spectroscopic scan to find the relevant eigenenergies of the system using energy measurements on the fridge. With these insights, we design a ground state cooling algorithm fo

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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 (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 p

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RÜHL, WERNER, and ALEXANDER TURBINER. "EXACT SOLVABILITY OF THE CALOGERO AND SUTHERLAND MODELS." Modern Physics Letters A 10, no. 29 (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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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 pr

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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 (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 eac

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Sokolov, A. V. "Polynomial supersymmetry for matrix Hamiltonians." Physics Letters A 377, no. 9 (2013): 655–62. http://dx.doi.org/10.1016/j.physleta.2013.01.012.

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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 po

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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 (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 communi

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UENO, YUICHI. "POLYNOMIAL HAMILTONIANS FOR QUANTUM PAINLEVÉ EQUATIONS." International Journal of Mathematics 20, no. 11 (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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Hussin, V., I. Marquette, and K. Zelaya. "Third-order ladder operators, generalized Okamoto and exceptional orthogonal polynomials." Journal of Physics A: Mathematical and Theoretical 55, no. 4 (2022): 045205. http://dx.doi.org/10.1088/1751-8121/ac43cc.

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Abstract We extend and generalize the construction of Sturm–Liouville problems for a family of Hamiltonians constrained to fulfill a third-order shape-invariance condition and focusing on the ‘−2x/3’ hierarchy of solutions to the fourth Painlevé transcendent. Such a construction has been previously addressed in the literature for some particular cases but we realize it here in the most general case. The corresponding potential in the Hamiltonian operator is a rationally extended oscillator defined in terms of the conventional Okamoto polynomials, from which we identify three different zero-mod

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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

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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 n

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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 donn

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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 distinct

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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

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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 identifie

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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). 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. 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. 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. 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. 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. Birkhäuser Basel, 2002. http://dx.doi.org/10.1007/978-3-0348-8155-5_4.

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Krall, Allan M. "The Niessen Approach to Singular Hamiltonian Systems." In Hilbert Space, Boundary Value Problems and Orthogonal Polynomials. 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. Springer Netherlands, 1996. http://dx.doi.org/10.1007/978-94-009-0209-1_10.

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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. 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

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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. 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. 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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Bakshi, Ainesh, Allen Liu, Ankur Moitra, and Ewin Tang. "Learning Quantum Hamiltonians at Any Temperature in Polynomial Time." In STOC '24: 56th Annual ACM Symposium on Theory of Computing. ACM, 2024. http://dx.doi.org/10.1145/3618260.3649619.

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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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Lamač, Jan, and Miloslav Vlasák. "Finding a Hamiltonian cycle using the Chebyshev polynomials." In Programs and Algorithms of Numerical Mathematics 22. Institute of Mathematics, Czech Academy of Sciences, 2025. https://doi.org/10.21136/panm.2024.09.

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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. 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

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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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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), 2018. http://dx.doi.org/10.2172/1416504.

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