Relevant bibliographies by topics / Monodromy operator

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Monodromy operator'

Author: Grafiati
Published: 4 June 2021
Last updated: 16 February 2022

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Journal articles on the topic "Monodromy operator"

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Dimca, Alexandru. "Tate properties, polynomial-count varieties, and monodromy of hyperplane arrangements." Nagoya Mathematical Journal 206 (June 2012): 75–97. http://dx.doi.org/10.1017/s0027763000010540.

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AbstractThe order of the Milnor fiber monodromy operator of a central hyperplane arrangement is shown to be combinatorially determined. In particular, a necessary and sufficient condition for the triviality of this monodromy operator is given.It is known that the complement of a complex hyperplane arrangement is cohomologically Tate and, if the arrangement is defined over ℚ, has polynomial count. We show that these properties hold for the corresponding Milnor fibers if the monodromy is trivial.We construct a hyperplane arrangement defined over ℚ, whose Milnor fiber has a nontrivial monodromy operator, is cohomologically Tate, and has no polynomial count. Such examples are shown not to exist in low dimensions.
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Dimca, Alexandru. "Tate properties, polynomial-count varieties, and monodromy of hyperplane arrangements." Nagoya Mathematical Journal 206 (June 2012): 75–97. http://dx.doi.org/10.1215/00277630-1548502.

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AbstractThe order of the Milnor fiber monodromy operator of a central hyperplane arrangement is shown to be combinatorially determined. In particular, a necessary and sufficient condition for the triviality of this monodromy operator is given.It is known that the complement of a complex hyperplane arrangement is cohomologically Tate and, if the arrangement is defined over ℚ, has polynomial count. We show that these properties hold for the corresponding Milnor fibers if the monodromy is trivial.We construct a hyperplane arrangement defined over ℚ, whose Milnor fiber has a nontrivial monodromy operator, is cohomologically Tate, and has no polynomial count. Such examples are shown not to exist in low dimensions.
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Wang, Na, and Ke Wu. "Vertex operators, t-boson model and weighted plane partitions in finite boxes." Modern Physics Letters B 32, no. 05 (February 20, 2018): 1850061. http://dx.doi.org/10.1142/s0217984918500616.

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We consider two different subjects: the algebra of Hall–Littlewood functions and t-boson model. Tsilevich and Sułkowski, respectively, give that the creation operator [Formula: see text] in the monodromy matrix of t-boson model can be represented by [Formula: see text], where [Formula: see text] and [Formula: see text] are vertex operators closely related to the Hall–Littlewood functions. In this paper, we obtain that the annihilation operator [Formula: see text] in the monodromy matrix and other relations of t-boson model can also be realized in the algebra of Hall–Littlewood functions. Meanwhile, we get that the generating functions of weighted plane partitions in finite boxes can be obtained from the operators [Formula: see text].
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BHATTACHARYA, GAUTAM, and SASANKA GHOSH. "ALGEBRAIC BETHE ANSATZ SCHEME FOR RELATIVISTIC INTEGRABLE FIELD THEORIES IN CONTINUUM-: SINE-GORDON MODEL." International Journal of Modern Physics A 04, no. 03 (February 1989): 627–47. http://dx.doi.org/10.1142/s0217751x89000303.

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The linear problem associated with the Lax operator of the classical sine-Gordon theory can be recast into the monodromy matrix form that can be extended to quantum theory as well. Product of the quantum monodromy matrices will have contributions from the singularities arising out of the operator product expansions of sine-Gordon field. This enables one to find the star-triangle relations. This is a generalization of the method used by Thacker for the non-relativistic nonlinear Schrödinger field theory. In the infinite volume limit, it leads to an unambiguous description of the algebra involving the scattering data operators. Starting from a vacuum the module of physical states are constructed by the application of chains of the scattering operators and they turn out to have definite eigenvalues of energy and momentum. The mass-spectra and two-particle S matrix elements can be calculated straightforwardly and they coincide with the well-known results of Zamolodchikov and Zamolodchikov. It is also shown that the particle states can be created by a generalized Jordon-Wigner transformation of the free fermionic creation operators — thus establishing a link between the S matrix element and certain co-cycles.
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BRODA, B. "A THREE-DIMENSIONAL COVARIANT APPROACH TO MONODROMY (SKEIN RELATIONS) IN CHERN-SIMONS THEORY." Modern Physics Letters A 05, no. 32 (December 30, 1990): 2747–51. http://dx.doi.org/10.1142/s0217732390003206.

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A genuinely three-dimensional covariant approach to the monodromy operator (skein relations) in the context of Chern-Simons theory is proposed. A holomorphic path-integral representation for the holonomy operator (Wilson loop) and for the non-abelian Stokes theorem is used.
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Helm, David, and Eric Katz. "Monodromy Filtrations and the Topology of Tropical Varieties." Canadian Journal of Mathematics 64, no. 4 (August 1, 2012): 845–68. http://dx.doi.org/10.4153/cjm-2011-067-9.

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AbstractWe study the topology of tropical varieties that arise from a certain natural class of varieties. We use the theory of tropical degenerations to construct a natural, “multiplicity-free” parameterization of Trop(X) by a topological space ГXand give a geometric interpretation of the cohomology of ГXin terms of the action of a monodromy operator on the cohomology ofX. This gives bounds on the Betti numbers of ГXin terms of the Betti numbers ofXwhich constrain the topology of Trop(X). We also obtain a description of the top power of the monodromy operator acting on middle cohomology ofXin terms of the volume pairing on ГX.
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Yudovich, V. I. "Periodic differential equations with self-adjoint monodromy operator." Sbornik: Mathematics 192, no. 3 (April 30, 2001): 455–78. http://dx.doi.org/10.1070/sm2001v192n03abeh000554.

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Dat, Jean-François. "Opérateur de Lefschetz sur les tours de Drinfeld et Lubin–Tate." Compositio Mathematica 148, no. 2 (January 25, 2012): 507–30. http://dx.doi.org/10.1112/s0010437x11007214.

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AbstractWe define and study a Lefschetz operator on the equivariant cohomology complex of the Drinfeld and Lubin–Tate towers. For ℓ-adic coefficients we show how this operator induces a geometric realization of the Langlands correspondence composed with the Zelevinski involution for elliptic representations. Combined with our previous study of the monodromy operator, this suggests a possible extension of Arthur’s philosophy for unitary representations occurring in the intersection cohomology of Shimura varieties to the possibly non-unitary representations occurring in the cohomology of Rapoport–Zink spaces. However, our motivation for studying the Lefschetz operator comes from the hope that its geometric nature will enable us to realize the mod-ℓ Langlands correspondence due to Vignéras. We discuss this problem and propose a conjecture.
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OVCHINNIKOV, A. A. "CONSTRUCTION OF MONODROMY MATRIX IN THE F-BASIS AND SCALAR PRODUCTS IN SPIN CHAINS." International Journal of Modern Physics A 16, no. 12 (May 10, 2001): 2175–93. http://dx.doi.org/10.1142/s0217751x01003743.

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We present in a simple terms the theory of the factorizing operator introduced recently by Maillet and Sanches de Santos for the spin-1/2 chains. We obtain the explicit expressions for the matrix elements of the factorizing operator in terms of the elements of the monodromy matrix. We use this results to derive the expression for the general scalar product for the quantum spin chain. We comment on the previous determination of the scalar product of Bethe eigenstate with an arbitrary dual state. We also establish the direct correspondence between the calculations of scalar products in the F-basis and the usual basis.
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Korotyaev, E. L. "ON THE EIGENFUNCTIONS OF THE MONODROMY OPERATOR OF THE SCHRÖDINGER OPERATOR WITH A TIME-PERIODIC POTENTIAL." Mathematics of the USSR-Sbornik 52, no. 2 (February 28, 1985): 423–38. http://dx.doi.org/10.1070/sm1985v052n02abeh002898.

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Dissertations / Theses on the topic "Monodromy operator"

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Louati, Hanen. "Règles de quantification semi-classique pour une orbite périodique de type hyberbolique." Thesis, Toulon, 2017. http://www.theses.fr/2017TOUL0004/document.

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On étudie les résonances semi-excitées pour un Opérateur h-Pseudo-différentiel (h-PDO)H(x, hDx) sur L2(M) induites par une orbite périodique de type hyperbolique à l’énergie E = 0. Par exemple M = Rn et H(x, hDx; h) est l’opérateur de Schrödinger avec effet Stark, ouH(x, hDx; h) est le flot géodesique sur une variété axi-symétrique M, généralisant l’exemplede Poincaré de systèmes Lagrangiens à 2 degrés de liberté. On étend le formalisme de Gérard and Sjöstrand, au sens où on autorise des valeurs propres hyperboliques et elliptiques del’application de Poincaré, et où l’on considère des résonances dont la partie imaginaire est del’ordre de hs, pour 0 < s < 1.On établit une règle de quantification de type Bohr-Sommerfeld au premier ordre en fonction des nombres quantiques longitudinaux (réels) et transverses (complexes), incluantl’intégrale d’action le long de l’orbite, la 1-forme sous-principale, et l’indice de Conley-Zehnder
In this Thesis we consider semi-excited resonances for a h-Pseudo-Differential Operator (h-PDO for short) H(x, hDx; h) on L2(M) induced by a periodic orbit of hyperbolic type at energy E = 0, as arises when M = Rn and H(x, hDx; h) is Schrödinger operator withAC Stark effect, or H(x, hDx; h) is the geodesic flow on an axially symmetric manifold M,extending Poincaré example of Lagrangian systems with 2 degree of freedom. We generalizethe framework of Gérard and Sjöstrand, in the sense that we allow for hyperbolic and ellipticeigenvalues of Poincaré map, and look for (excited) resonances with imaginary part of magnitude hs, with 0 < s < 1,It is known that these resonances are given by the zeroes of a determinant associatedwith Poincaré map. We make here this result more precise, in providing a first order asymptoticsof Bohr-Sommerfeld quantization rule in terms of the (real) longitudinal and (complex)transverse quantum numbers, including the action integral, the sub-principal 1-form and Gelfand-Lidskii index
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Onorati, Claudio. "Irreducible holomorphic symplectic manifolds and monodromy operators." Thesis, University of Bath, 2018. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.767583.

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One of the most important tools to study the geometry of irreducible holomorphic symplectic manifolds is the monodromy group. The first part of this dissertation concerns the construction and studyof monodromy operators on irreducible holomorphic symplectic manifolds which are deformation equivalent to the 10-dimensional example constructed by O'Grady. The second part uses the knowledge of the monodromy group to compute the number of connected components of moduli spaces of bothmarked and polarised irreducible holomorphic symplectic manifolds which are deformationequivalent to generalised Kummer varieties.
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Hemery, Adrian D. "The spectral properties and singularities of monodromy-free Schrödinger operators." Thesis, Loughborough University, 2012. https://dspace.lboro.ac.uk/2134/10200.

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The main object of study is the theory of Schrödinger operators with meromorphic potentials, having trivial monodromy in the complex domain. In the first part we study the spectral properties of a class of such operators related to the classical Whittaker-Hill equation (-d^2/dx^2+Acos2x+Bcos4x)Ψ=λΨ. The equation, for special choices of A and B, is known to have the remarkable property that half of the gaps eventually become closed (semifinite-gap operator). Using the Darboux transformation we construct new trigonometric examples of semifinite-gap operators with real, smooth potentials. A similar technique applied to the Lamé operator gives smooth, real, finite-gap potentials in terms of classical Jacobi elliptic functions. In the second part we study the singular locus of monodromy-free potentials in the complex domain. A particular case is given by the zeros of Wronskians of Hermite polynomials, which are studied in detail. We introduce a class of partitions (doubled partitions) for which we observe a direct qualitative relationship between the pattern of zeros and the shape of the corresponding Young diagram. For the Wronskians W(H_n,H_{n+k}) we give an asymptotic formula for the curve on which zeros lie as n → ∞. We also give some empirical formulas for asymptotic behaviour of zeros of Wronskians of 3 and 4 Hermite polynomials. In the last chapter we apply the theory of monodromy-free operators to produce new vortex equilibria in the periodic case and in the presence of background flow.
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Haese-Hill, William. "Spectral properties of integrable Schrodinger operators with singular potentials." Thesis, Loughborough University, 2015. https://dspace.lboro.ac.uk/2134/19929.

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The integrable Schrödinger operators often have a singularity on the real line, which creates problems for their spectral analysis. In several particular cases we show that all closed gaps lie on the infinite spectral arc. In the second part we develop a theory of complex exceptional orthogonal polynomials corresponding to integrable rational and trigonometric Schrödinger operators, which may have a singularity on the real line. In particular, we study the properties of the corresponding complex exceptional Hermite polynomials related to Darboux transformations of the harmonic oscillator, and exceptional Laurent orthogonal polynomials related to trigonometric monodromy-free operators.
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Fedosov, Boris, Bert-Wolfgang Schulze, and Nikolai N. Tarkhanov. "The index of higher order operators on singular surfaces." Universität Potsdam, 1998. http://opus.kobv.de/ubp/volltexte/2008/2512/.

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The index formula for elliptic pseudodifferential operators on a two-dimensional manifold with conical points contains the Atiyah-Singer integral as well as two additional terms. One of the two is the 'eta' invariant defined by the conormal symbol, and the other term is explicitly expressed via the principal and subprincipal symbols of the operator at conical points. In the preceding paper we clarified the meaning of the additional terms for first-order differential operators. The aim of this paper is an explicit description of the contribution of a conical point for higher-order differential operators. We show that changing the origin in the complex plane reduces the entire contribution of the conical point to the shifted 'eta' invariant. In turn this latter is expressed in terms of the monodromy matrix for an ordinary differential equation defined by the conormal symbol.
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Fedosov, Boris, Bert-Wolfgang Schulze, and Nikolai Tarkhanov. "On the index formula for singular surfaces." Universität Potsdam, 1997. http://opus.kobv.de/ubp/volltexte/2008/2511/.

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In the preceding paper we proved an explicit index formula for elliptic pseudodifferential operators on a two-dimensional manifold with conical points. Apart from the Atiyah-Singer integral, it contains two additional terms, one of the two being the 'eta' invariant defined by the conormal symbol. In this paper we clarify the meaning of the additional terms for differential operators.
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Lynch, Geoffrey D. "The local monodromy operator as an algebraic cycle." 2008. http://link.library.utoronto.ca/eir/EIRdetail.cfm?Resources__ID=742555&T=F.

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Gehre, Nico. "Lösungsoperatoren für Delaysysteme und Nutzung zur Stabilitätsanalyse." 2017. https://monarch.qucosa.de/id/qucosa%3A21053.

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In diese Dissertation werden lineare retardierte Differentialgleichungen (DDEs) und deren Lösungsoperatoren untersucht. Wir stellen eine neue Methode vor, mit der die Lösungsoperatoren für autonome und nicht-autonome DDEs bestimmt werden. Die neue Methode basiert auf dem Pfadintegralformalismus, der aus der Quantenmechanik und von der Analyse stochastischer Differentialgleichungen bekannt ist. Es zeigt sich, dass die Lösung eines Delaysystems zum Zeitpunkt t durch die Integration aller möglicher Pfade von der Anfangsbedingung bis zur Zeit t gebildet werden kann. Die Pfade bestehen dabei aus verschiedenen Schritten unterschiedlicher Längen und Gewichte. Für skalare autonome DDEs können analytische Ausdrücke des Lösungsoperators in der Literatur gefunden werden, allerdings existieren keine für nicht-autonome oder höherdimensionale DDEs. Mithilfe der neuen Methode werden wir die Lösungsoperatoren der genannten DDEs aufstellen und zusätzlich auf Delaysysteme mit mehreren Delaytermen erweitern. Dabei bestätigen wir unsere Ergebnisse sowohl analytisch wie auch numerisch. Die gewonnenen Lösungsoperatoren verwenden wir anschließend zur Stabilitätsanalyse periodischer Delaysysteme. Es werden zwei neue Verfahren präsentiert, die mithilfe des Lösungsoperators den transformierten Monodromieoperator des Delaysystems nähern und daraus die Stabilität bestimmen können. Beide neue Verfahren sind spektrale Methoden für autonome sowie nicht-autonome Delaysysteme und haben keine Einschränkungen wie bei der bekannten Chebyshev-Kollokationsmethode oder der Chebyshev-Polynomentwicklung. Die beiden bisherigen Verfahren beschränken sich auf Delaysysteme mit rationalem Verhältnis zwischen Periode und Delay. Außerdem werden wir eine bereits bekannte Methode erweitern und zu einer spektralen Methode für periodische nicht-autonome Delaysysteme entwickeln. Wir bestätigen alle drei neue Verfahren numerisch. Damit werden in dieser Dissertation drei neue spektrale Verfahren zur Stabilitätsanalyse periodischer Delaysysteme vorgestellt.
In this thesis linear delay differential equations (DDEs) and its solutions operators are studied. We present a new method to calculate the solution operators for autonomous and non-autonomous DDEs. The new method is related to the path integral formalism, which is known from quantum mechanics and the analysis of stochastic differential equations. It will be shown that the solution of a time delay system at time t can be constructed by integrating over all paths from the initial condition to time t. The paths consist of several steps with different lengths and weights. Analytic expressions for the solution operator for scalar autonomous DDEs can be found in the literature but no results exist for non-autonomous or high dimensional DDEs. With the help of the new method we can calculate the solution operators for such DDEs and for time delay systems with several delay terms. We verify our results analytically and numerically. We use the obtained solution operators for the stability analysis of periodic time delay systems. Two new methods will be presented to approximate the transformed monodromy operator with the help of the solution operator and to get the stability. Both new methods are spectral methods for autonomous and non-autonomous delay systems and have no limitations like the known Chebyshev collocation method or Chebyshev polynomial expansion. Both previously known methods are limited to time delay systems with a rational relation between period and delay. Furthermore we will extend a known method to a spectral method for non-autonomous time delay systems. We verify all three new methods numerically. Hence, in this thesis three new spectral methods for the stability analysis of periodic time delay systems are presented.
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Books on the topic "Monodromy operator"

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Vercoe, Elizabeth. Herstory III: Jehanne de Lorraine : a monodrama for mezzo soprano and piano. Washington, D.C. (1719 Bay St. S.E., Washington D.C. 20003): Arsis Press, 1991.

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Book chapters on the topic "Monodromy operator"

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Arov, Damir Z., and Harry Dym. "Some Remarks on the Inverse Monodromy Problem for 2 x 2 Canonical Differential Systems." In Operator Theory and Analysis, 53–87. Basel: Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8283-5_3.

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Unterberger, Jérémie, and Claude Roger. "Monodromy of Schrödinger Operators." In Theoretical and Mathematical Physics, 161–205. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-22717-2_9.

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Dong, Chongying, and James Lepowsky. "Monodromy representations of braid groups." In Generalized Vertex Algebras and Relative Vertex Operators, 77–81. Boston, MA: Birkhäuser Boston, 1993. http://dx.doi.org/10.1007/978-1-4612-0353-7_8.

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Tsuchiya, Akihiro, and Yukihiro Kanie. "Vertex Operators in Conformal Field Theory on P1 and Monodromy Representations of Braid Group." In Conformal Field Theory and Solvable Lattice Models, 297–372. Elsevier, 1988. http://dx.doi.org/10.1016/b978-0-12-385340-0.50013-9.

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Tsuchiya, Akihiro, and Yukihiro Kanie. "Vertex Operators in Conformal Field Theory on P1 and Monodromy Representations of Braid Group." In New Developments in the Theory of Knots, 643–718. WORLD SCIENTIFIC, 1990. http://dx.doi.org/10.1142/9789812798329_0034.

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Tsuchiya, A., and Y. Kanie. "Errata to Vertex Operators in Conformal Field Theory on P1 and Monodromy Representations of Braid Group in Advanced Studies in Pure Mathematics 16,1988." In Integrable Sys Quantum Field Theory, 675–82. Elsevier, 1989. http://dx.doi.org/10.1016/b978-0-12-385342-4.50023-8.

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Tsuchiya, A., and Y. Kanie. "Errata to Vertex Operators in Conformal Field Theory on P1 and Monodromy Representations of Braid Group in Advanced Studies in Pure Mathematics 16,1988." In New Developments in the Theory of Knots, 719–26. WORLD SCIENTIFIC, 1990. http://dx.doi.org/10.1142/9789812798329_0035.

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Conference papers on the topic "Monodromy operator"

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Dabiri, Arman, Eric A. Butcher, and Mohammad Poursina. "Fractional Delayed Control Design for Linear Periodic Systems." In ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/detc2016-60322.

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In this paper, the fractional Chebyshev collocation (FCC) method is proposed to design fractional delay controllers for linear systems with periodic coefficients. In our previous study, it was shown that this method can be successfully used to stabilize fractional periodic time-delay systems with the delay terms being of integer orders. In the current paper, it is shown that this method can be extended successfully to design fractional delay controllers for fractional periodic systems. For this propose, the solution of linear periodic systems with fractional delay terms is expressed in a Banach space. The short memory principle is used to show that the actual response of the system can be approximated by an approximated monodromy operator. The approximated monodromy operator yields the solution of a fixed length interval by mapping the solution of the previous interval with the same length. Usually obtaining the approximated monodromy operator is complicated or even impossible. The spectral radius of the approximated monodromy matrix indicates the asymptotic stability of the system. The efficiency of the proposed fractional delayed control is illustrated in the case of a second order system with periodic coefficients.
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Vazquez, Eli Abraham, and Joaquin Collado. "Monodromy operator approximation of periodic delay differential equations by Walsh functions." In 2016 13th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE). IEEE, 2016. http://dx.doi.org/10.1109/iceee.2016.7751222.

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Deshmukh, Venkatesh. "Stability Analysis and Computation of Solutions of Nonlinear Delay Differential Algebraic Equations With Time Periodic Coefficients." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35263.

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Stability theory of Nonlinear Delay Differential Algebraic Equations (DDAE) with periodic coefficients is proposed with a geometric interpretation of the evolution of the linearized system. First, a numerical algorithm based on direct integration by expansion in terms of Chebyshev polynomials is derived for linear analysis. The proposed algorithm is shown to have deeper connections with and computationally less cumbersome than the solution of the underlying semi-explicit system via a similarity transformation. The stability of time periodic DDAE systems is characterized by the spectral radius of a finite dimensional approximation or a “monodromy matrix” of a compact infinite dimensional operator. The monodromy operator is essentially a map of the Chebyshev coefficients of the state form the delay interval to the next adjacent interval of time. The monodromy matrix is obtained by a similarity transformation of the momodromy matrix of the associated semi-explicit system. The computations are entirely performed in the original system form to avoid cumbersome transformations associated with the semi-explicit system. Next, two computational algorithms are detailed for obtaining solutions of nonlinear DDAEs with periodic coefficients for consistent initial functions.
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Kim, Jung Hoon, Tomomichi Hagiwara, and Kentaro Hirata. "A study on the spectrum of monodromy operator for a time-delay system." In 2013 9th Asian Control Conference (ASCC). IEEE, 2013. http://dx.doi.org/10.1109/ascc.2013.6606024.

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Saito, Yuki, and Tomomichi Hagiwara. "Stability analysis of time-delay systems based on a power of the monodromy operator." In 2013 European Control Conference (ECC). IEEE, 2013. http://dx.doi.org/10.23919/ecc.2013.6669151.

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Kiss, Adam K., Daniel Bachrathy, and Gabor Stepan. "Experimental Determination of Dominant Multipliers in Milling Process by Means of Homogeneous Coordinate Transformation." In ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/detc2017-67827.

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In this contribution, a chatter detection method is investigated for milling operations. The proposed approach can give not only qualitative condition (stable or unstable), but a quantitative measure of stability. For this purpose, it requires an external excitation of stable machining condition. Transient vibration of the perturbation is captured by means of stroboscopic section, and the corresponding monodromy operator is approximated by its projection to the subspace of the dominant modes. The monodromy matrix is determined with the application of homogeneous coordinate representation. Then, the periodic solution and the dominant characteristic multipliers are calculated and their modulus determines the quantitative measure of stability condition.
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