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Related papers: Geometric scattering monodromy

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In this paper, Hamiltonian monodromy is studied from the point of view of geometric quantization abd theta functions, and various differential geometric aspects thereof are dealt with, all related to holonomies of suitable flat connections.

Symplectic Geometry · Mathematics 2022-07-06 Nicola Sansonetto , Mauro Spera

In a plane-wave matrix model we discuss a two-body scattering of gravitons in the SO(3) symmetric space. In this case the graviton solutions are point-like in contrast to the scattering in the SO(6) symmetric space where spherical membranes…

High Energy Physics - Theory · Physics 2009-11-11 Hyeonjoon Shin , Kentaroh Yoshida

We study scattering rigidity for Hamiltonian systems on $T^*M\setminus 0$, where $M$ is a manifold with boundary equipped with a positively homogeneous Hamiltonian function $H(x,\xi)$. We show that $H$ can be uniquely determined by the…

Differential Geometry · Mathematics 2026-03-10 Nikolas Eptaminitakis , Plamen Stefanov

We propose a novel scheme to normalize scattering modes of the electromagnetic field. By relying on analytical solutions for Maxwell's equations in the homogenous medium outside the scatterer, we derive normalization conditions that only…

Optics · Physics 2018-06-06 J. Oppermann , J. Straubel , I. Fernandez-Corbaton , C. Rockstuhl

We apply scattering theory on asymptotically hyperbolic manifolds to singular Yamabe metrics, applying the results to the study of the conformal geometry of compact manifolds with boundary. In particular, we define extrinsic versions of the…

Differential Geometry · Mathematics 2021-09-07 Sun-Yung Alice Chang , Stephen E. McKeown , Paul Yang

We develop a scattering theory for perturbations of powers of the Laplacian on asymptotically Euclidean manifolds. The (absolute) scattering matrix is shown to be a Fourier integral operator associated to the geodesic flow at time \pi on…

Analysis of PDEs · Mathematics 2007-05-23 T. J. Christiansen , M. S. Joshi

We study the monodromy of vanishing cycles for map-germs $f:(C^{2n},0) \to (\CM^k,0)$ whose components are in involution. Although the singular fibres of such maps have non-isolated singularities, it is shown that the regular fibres are…

Algebraic Geometry · Mathematics 2007-05-23 Mauricio D. Garay

The only one example has been known of magnetic geodesic flow on the 2-torus which has a polynomial in momenta integral independent of the Hamiltonian. In this example the integral is linear in momenta and corresponds to a one parametric…

Dynamical Systems · Mathematics 2017-02-01 Sergey V. Agapov , Michael , Bialy , Andrey E. Mironov

We show a natural relation between the monodromy formula for focus-focus singularities of integrable Hamiltonian systems and a formula of Duistermaat-Heckman, and extend the main results of our previous note on focus-focus singularities…

Dynamical Systems · Mathematics 2007-05-23 Nguyen Tien Zung

Within a formulation of $\pi\pi$ scattering, we investigate the use of the finite-volume Hamiltonian approach to resolving scattering observables from lattice QCD spectra. We consider spectra in the centre-of-mass and moving frames for both…

High Energy Physics - Lattice · Physics 2016-06-22 Jia-Jun Wu , T. -S. Harry Lee , Derek B. Leinweber , A. W. Thomas , Ross D. Young

Effective Hamiltonians can explain in a much simpler way the physics behind a scattering process. Chaotic scattering is directly related to Lorentzian Hamiltonians which, because of their properties, can be reduced to a $2\times 2$ matrix…

Disordered Systems and Neural Networks · Physics 2013-04-03 Adel Abbout , Peng Mei

In this paper we explore the general conditions in order that a 2-dimensional natural Hamiltonian system possess a second invariant which is a polynomial in the momenta and is therefore Liouville integrable. We examine the possibility that…

Exactly Solvable and Integrable Systems · Physics 2009-11-13 Giuseppe Pucacco , Kjell Rosquist

The main purpose of this paper is to introduce a new class of Hamiltonian scattering systems of the cone potential type that can be integrated via the asymptotic velocity. For a large subclass, the asymptotic data of the trajectories define…

Exactly Solvable and Integrable Systems · Physics 2012-07-13 Gianluca Gorni , Gaetano Zampieri

The S-matrices for the scattering of two excitations in the XYZ model and in all of its SU(n)-type generalizations are obtained from the asymptotic behavior of Kerov's generalized Hall-Littlewood polynomials. These physical scattering…

High Energy Physics - Theory · Physics 2009-10-22 Peter G. O. Freund , Anton V. Zabrodin

The Champagne bottle is one of the simplest and typical examples of Liouville integrable systems that exhibit a non-trivial classical monodromy. This geometrical invariant perturbs globally the existence of action-angle coordinates on the…

Mathematical Physics · Physics 2020-09-23 Quang Sang Phan

We describe a unitary scattering process, as observed from spatial infinity, of massless scalar particles on an asymptotically flat Schwarzschild black hole background. In order to do so, we split the problem in two different regimes…

High Energy Physics - Theory · Physics 2021-07-21 Panos Betzios , Nava Gaddam , Olga Papadoulaki

This article studies the rational solutions of the Half-Wave Maps equation (HWM) in the non-singular spectrum case. We first provide characterizations to what we call \emph{scattering behavior}, and show that they imply scattering in…

Analysis of PDEs · Mathematics 2025-03-03 Gaspard Ohlmann

We study projective structures on a surface having poles of prescribed orders. We obtain a monodromy map from a complex manifold parameterising such structures to the stack of framed $\mathrm{PGL}_2(\mathbb{C})$ local systems on the…

Geometric Topology · Mathematics 2020-07-14 Dylan G. L. Allegretti , Tom Bridgeland

A non-relativistic scalar particle moving on a curved surface undergoes a geometric scattering whose behavior is sensitive to the theoretically ambiguous values of the intrinsic and extrinsic curvature coefficients entering the expression…

Quantum Physics · Physics 2021-02-12 Hai Viet Bui , Ali Mostafazadeh , Sema Seymen

The scattering phase-shifts are invariant under unitary transformations of the Hamiltonian. However, the numerical solution of the scattering problem that requires to discretize the continuum violates this phase-shift invariance among…

Nuclear Theory · Physics 2020-02-12 María Gómez-Rocha , Enrique Ruiz Arriola