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Добірка наукової літератури з теми "Calogero-Moser-Sutherland systems"

Автор: Grafiati
Опубліковано: 7 липня 2024
Оновлено: 7 липня 2024

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Зміст

  1. Статті в журналах
  2. Дисертації
  3. Книги
  4. Частини книг

Статті в журналах з теми "Calogero-Moser-Sutherland systems":

1

Feigin, Misha. "Bispectrality for deformed Calogero–Moser–Sutherland systems." Journal of Nonlinear Mathematical Physics 12, sup2 (January 2005): 95–136. http://dx.doi.org/10.2991/jnmp.2005.12.s2.8.

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2

Sergeev, A. N. "Lie Superalgebras and Calogero–Moser–Sutherland Systems." Journal of Mathematical Sciences 235, no. 6 (October 24, 2018): 756–87. http://dx.doi.org/10.1007/s10958-018-4092-6.

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3

Fring, Andreas. "PT -symmetric deformations of integrable models." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371, no. 1989 (April 28, 2013): 20120046. http://dx.doi.org/10.1098/rsta.2012.0046.

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Анотація:
We review recent results on new physical models constructed as -symmetrical deformations or extensions of different types of integrable models. We present non-Hermitian versions of quantum spin chains, multi-particle systems of Calogero–Moser–Sutherland type and nonlinear integrable field equations of Korteweg–de Vries type. The quantum spin chain discussed is related to the first example in the series of the non-unitary models of minimal conformal field theories. For the Calogero–Moser–Sutherland models, we provide three alternative deformations: a complex extension for models related to all types of Coxeter/Weyl groups; models describing the evolution of poles in constrained real-valued field equations of nonlinear integrable systems; and genuine deformations based on antilinearly invariant deformed root systems. Deformations of complex nonlinear integrable field equations of Korteweg–de Vries type are studied with regard to different kinds of -symmetrical scenarios. A reduction to simple complex quantum mechanical models currently under discussion is presented.
4

Odake, S., and R. Sasaki. "Calogero-Sutherland-Moser Systems, Ruijsenaars-Schneider-van Diejen Systems and Orthogonal Polynomials." Progress of Theoretical Physics 114, no. 6 (December 1, 2005): 1245–60. http://dx.doi.org/10.1143/ptp.114.1245.

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5

Ghosh, Pijush K. "Super-Calogero–Moser–Sutherland systems and free super-oscillators: a mapping." Nuclear Physics B 595, no. 1-2 (February 2001): 519–35. http://dx.doi.org/10.1016/s0550-3213(00)00691-x.

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6

Hikami, Kazuhiro, and Yasushi Komori. "Integrability, Fusion, and Duality in the Elliptic Ruijsenaars Model." Modern Physics Letters A 12, no. 11 (April 10, 1997): 751–61. http://dx.doi.org/10.1142/s0217732397000789.

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Анотація:
The generalized elliptic Ruijsenaars models, which are regarded as a difference analog of the Calogero–Sutherland–Moser models associated with the classical root systems are studied. The integrability and the duality using the fusion procedure of operator-valued solutions of the Yang–Baxter equation and the reflection equation are shown. In particular a new integrable difference operator of type-D is proposed. The trigonometric models are also considered in terms of the representation of the affine Hecke algebra.
7

Matsuno, Yoshimasa. "Calogero–Moser–Sutherland Dynamical Systems Associated with Nonlocal Nonlinear Schrödinger Equation for Envelope Waves." Journal of the Physical Society of Japan 71, no. 6 (June 15, 2002): 1415–18. http://dx.doi.org/10.1143/jpsj.71.1415.

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8

van Diejen, J. F. "On the eigenfunctions of hyperbolic quantum Calogero–Moser–Sutherland systems in a Morse potential." Letters in Mathematical Physics 110, no. 6 (January 31, 2020): 1215–35. http://dx.doi.org/10.1007/s11005-020-01260-6.

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9

Prykarpatski, Anatolij K. "Quantum Current Algebra in Action: Linearization, Integrability of Classical and Factorization of Quantum Nonlinear Dynamical Systems." Universe 8, no. 5 (May 20, 2022): 288. http://dx.doi.org/10.3390/universe8050288.

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Анотація:
This review is devoted to the universal algebraic and geometric properties of the non-relativistic quantum current algebra symmetry and to their representations subject to applications in describing geometrical and analytical properties of quantum and classical integrable Hamiltonian systems of theoretical and mathematical physics. The Fock space, the non-relativistic quantum current algebra symmetry and its cyclic representations on separable Hilbert spaces are reviewed and described in detail. The unitary current algebra family of operators and generating functional equations are described. A generating functional method to constructing irreducible current algebra representations is reviewed, and the ergodicity of the corresponding representation Hilbert space measure is mentioned. The algebraic properties of the so called coherent states are also reviewed, generated by cyclic representations of the Heisenberg algebra on Hilbert spaces. Unbelievable and impressive applications of coherent states to the theory of nonlinear dynamical systems on Hilbert spaces are described, along with their linearization and integrability. Moreover, we present a further development of these results within the modern Lie-algebraic approach to nonlinear dynamical systems on Poissonian functional manifolds, which proved to be both unexpected and important for the classification of integrable Hamiltonian flows on Hilbert spaces. The quantum current Lie algebra symmetry properties and their functional representations, interpreted as a universal algebraic structure of symmetries of completely integrable nonlinear dynamical systems of theoretical and mathematical physics on functional manifolds, are analyzed in detail. Based on the current algebra symmetry structure and their functional representations, an effective integrability criterion is formulated for a wide class of completely integrable Hamiltonian systems on functional manifolds. The related algebraic structure of the Poissonian operators and an effective algorithm of their analytical construction are described. The current algebra representations in separable Hilbert spaces and the factorized structure of quantum integrable many-particle Hamiltonian systems are reviewed. The related current algebra-based Hamiltonian reconstruction of the many-particle oscillatory and Calogero–Moser–Sutherland quantum models are reviewed and discussed in detail. The related quasi-classical quantum current algebra density representations and the collective variable approach in equilibrium statistical physics are reviewed. In addition, the classical Wigner type current algebra representation and its application to non-equilibrium classical statistical mechanics are described, and the construction of the Lie–Poisson structure on the phase space of the infinite hierarchy of distribution functions is presented. The related Boltzmann–Bogolubov type kinetic equation for the generating functional of many-particle distribution functions is constructed, and the invariant reduction scheme, compatible with imposed correlation functions constraints, is suggested and analyzed in detail. We also review current algebra functional representations and their geometric structure subject to the analytical description of quasi-stationary hydrodynamic flows and their magneto-hydrodynamic generalizations. A unified geometric description of the ideal idiabatic liquid dynamics is presented, and its Hamiltonian structure is analyzed. A special chapter of the review is devoted to recent results on the description of modified current Lie algebra symmetries on torus and their Lie-algebraic structures, related to integrable so-called heavenly type spatially many-dimensional dynamical systems on functional manifolds.
10

Hallnäs, Martin. "New Orthogonality Relations for Super-Jack Polynomials and an Associated Lassalle–Nekrasov Correspondence." Constructive Approximation, March 17, 2023. http://dx.doi.org/10.1007/s00365-023-09636-2.

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AbstractThe super-Jack polynomials, introduced by Kerov, Okounkov and Olshanski, are polynomials in $$n+m$$ n + m variables, which reduce to the Jack polynomials when $$n=0$$ n = 0 or $$m=0$$ m = 0 and provide joint eigenfunctions of the quantum integrals of the deformed trigonometric Calogero–Moser–Sutherland system. We prove that the super-Jack polynomials are orthogonal with respect to a bilinear form of the form $$(p,q)\mapsto (L_pq)(0)$$ ( p , q ) ↦ ( L p q ) ( 0 ) , with $$L_p$$ L p quantum integrals of the deformed rational Calogero–Moser–Sutherland system. In addition, we provide a new proof of the Lassalle–Nekrasov correspondence between deformed trigonometric and rational harmonic Calogero–Moser–Sutherland systems and infer orthogonality of super-Hermite polynomials, which provide joint eigenfunctions of the latter system.
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Статті в журналах

Дисертації з теми "Calogero-Moser-Sutherland systems":

1

Badreddine, Rana. "On a DNLS equation related to the Calogero-Sutherland-Moser Hamiltonian system." Electronic Thesis or Diss., université Paris-Saclay, 2024. http://www.theses.fr/2024UPASM008.

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Il s'agit d'étudier une EDP obtenue par A. Abanov et al (J. Phys. A, 2009) à partir de la limite hydrodynamique du système hamiltonien de Calogero-Sutherland-Moser. On obtient ainsi une équation intégrable de type Schrödinger non linéaire sur l'espace de Hardy qui se trouve posséder une paire de Lax sur la droite et sur le cercle. Le but de cette thèse est d'utiliser la structure d'intégrabilité afin d'établir que l'équation est globalement bien-posée sur le cercle en allant jusqu'à l'espace de régularité critique. En second lieu, on s'intéresse à l'existence de solutions particulières sur le tore. Ainsi, on caractérise les ondes progressives de cette équation, ainsi qu'une classe de solutions s'écrivant sous la forme de fractions rationnelles et qui sont définies spectralement à partir de l'opérateur de Lax. En troisième lieu, on étudie la limite à faible-dispersion (semi-classique) de cette équation sur la droite et on caractérise ses solutions grâce à une formule explicite
This thesis is devoted to a PDE obtained by A. Abanov et al (J. Phys. A, 2009) from the hydrodynamic limit of the Calogero-Sutherland Hamiltonian system. A nonlinear integrable Schrödinger-type equation on the Hardy space is obtained and has a Lax pair structure on the line and on the circle. The goal of this thesis is to establish, by using the integrability structure of this PDE, some global well-posedness results on the circle, extending down to the critical regularity space. Secondly, we investigate the existence of particular solutions. Thus, we characterize the traveling waves and finite gap potentials of this equation on the circle. Thirdly, we study the zero-dispersion (or semiclassical) limit of this equation on the line and characterize its solutions using an explicit formula
2

Möller, Gunnar. "Dynamically reduced spaces in condensed matter physics : quantum Hall bilayers, dimensional reduction and magnetic spin systems." Paris 11, 2006. http://www.theses.fr/2006PA112131.

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Pour la description des propriétés de basse température des systèmes en physique de la matière condensée, il est souvent utile de travailler avec un espace dynamique réduit. Cette philosophie s'applique aux systèmes bicouches à effet Hall quantique comme aux systèmes d'anyons et aux systèmes magnétiques frustrés qui représentent les exemples discutés dans cette thèse. On introduit une classe générale d'états appariés de fermions composites. Ces fonctions d'onde sont exploitées pour analyser l'état fondamental des systèmes bicouches à effet Hall au facteur de remplissage total un. A partir d'une étude de Monte Carlo variationnel nous concluons que la transition de phase compressible à incompressible observée dans ce système est du deuxième ordre. Nous étudions également la question de l'existence d'un état apparié à demi-remplissage dans les simples couches. Ensuite nous considérons des schémas de réduction dimensionnelle de systèmes bidimensionnels sur la sphère vers des systèmes unidimensionnels sur le cercle. Un tel mapping est établi pour des systèmes libres et un candidat pour un système d'anyons généralisé est proposé. Finalement, nous analysons les systèmes de spins magnétiques sur réseaux bidimensionnels et discutons si un état de glace de spins peut exister en présence d'interactions dipolaires à longue portée
For a description of the low-temperature physics of condensed-matter systems, it is often useful to work within dynamically reduced spaces. This philosophy equally applies to quantum Hall bilayer systems, anyon systems, and frustrated magnetic spin systems - three examples studied in this thesis. First, we developed a new class of wave functions based upon paired composite fermions. These were applied to analyze the physics of the quantum Hall bilayer system at total filling one. Studying these via variational Monte Carlo methods, we concluded that the compressible to incompressible transition in the bilayer system is of second order. Furthermore, we pursued the longstanding question of whether pairing in the single layer might cause an incompressible quantum state at half filling. We then considered schemes of dimensional reduction for quantum mechanical models on the sphere. We achieved a mapping from non-interacting particles on the sphere to free particles on the circle. We proposed that an analogous mapping might exist for interacting anyons, and an appropriate anyon-like model on the sphere was introduced. Lastly, we performed an analysis of magnetic spin systems on two-dimensional lattices addressing the question of whether spin-ice can be realized in the presence of long-range dipolar interactions

Книги з теми "Calogero-Moser-Sutherland systems":

1

Vinet, Luc, and Jan F. van Diejen. Calogero-Moser- Sutherland Models. Springer, 2011.

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2

Vinet, Luc, and Jan F. van Diejen. Calogero-Moser- Sutherland Models. Springer, 2012.

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3

Vinet, Luc, and Jan F. van Diejen. Calogero--Moser-- Sutherland Models. Springer, 2012.

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4

Jan F. van Diejen (Editor) and Luc Vinet (Editor), eds. Calogero-Moser-Sutherland Models (CRM Series in Mathematical Physics). Springer, 2000.

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Частини книг з теми "Calogero-Moser-Sutherland systems":

1

Polychronakos, Alexios P. "Generalizations of Calogero Systems." In Calogero—Moser— Sutherland Models, 399–410. New York, NY: Springer New York, 2000. http://dx.doi.org/10.1007/978-1-4612-1206-5_24.

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2

Wilson, George. "The Complex Calogero—Moser and KP Systems." In Calogero—Moser— Sutherland Models, 539–48. New York, NY: Springer New York, 2000. http://dx.doi.org/10.1007/978-1-4612-1206-5_35.

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3

Berest, Yuri Yu. "The Theory of Lacunas and Quantum Integrable Systems." In Calogero—Moser— Sutherland Models, 53–64. New York, NY: Springer New York, 2000. http://dx.doi.org/10.1007/978-1-4612-1206-5_4.

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4

Avan, J. "Classical Dynamical r-Matrices for Calogero—Moser Systems and Their Generalizations." In Calogero—Moser— Sutherland Models, 1–21. New York, NY: Springer New York, 2000. http://dx.doi.org/10.1007/978-1-4612-1206-5_1.

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5

Calogero, Francesco. "Tricks of the Trade: Relating and Deriving Solvable and Integrable Dynamical Systems." In Calogero—Moser— Sutherland Models, 93–116. New York, NY: Springer New York, 2000. http://dx.doi.org/10.1007/978-1-4612-1206-5_7.

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6

Veselov, A. P. "New Integrable Generalizations of the CMS Quantum Problem and Deformations of Root Systems." In Calogero—Moser— Sutherland Models, 507–19. New York, NY: Springer New York, 2000. http://dx.doi.org/10.1007/978-1-4612-1206-5_33.

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7

Desrosiers, Patrick, Luc Lapointe, and Pierre Mathieu. "Supersymmetric Calogero-Moser-Sutherland models: Superintegrability structure and eigenfunctions." In Superintegrability in Classical and Quantum Systems, 109–24. Providence, Rhode Island: American Mathematical Society, 2004. http://dx.doi.org/10.1090/crmp/037/10.

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8

Hasegawa, Koji. "Ruijsenaars’s Commuting Difference System from Belavin’s Elliptic R-Matrix." In Calogero—Moser— Sutherland Models, 193–202. New York, NY: Springer New York, 2000. http://dx.doi.org/10.1007/978-1-4612-1206-5_13.

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9

Ruijsenaars, S. N. M. "Calogero–Moser–Sutherland Systems of Nonrelativistic and Relativistic Type." In Encyclopedia of Mathematical Physics, 403–11. Elsevier, 2006. http://dx.doi.org/10.1016/b0-12-512666-2/00185-1.

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