Monodromy of the LiNC/NCLi molecule

Using the potential surface of Essers, Tennyson, and Wormer in [Chem. Phys. Lett. 89 (1982) 223], we show that the system of bending vibrational states of the isomerizing molecule LiNC/NCLi has monodromy. On the basis of a deformed spherical pendulum model, we explain dynamical and geometric reasons of this phenomenon and of its absence in the similar system HCN/CNH

Semitoric integrable systems on symplectic 4-manifolds

Let M be a symplectic 4-manifold. A semitoric integrable system on M is a pair of real-valued smooth functions J, H on M for which J generates a Hamiltonian S^1-action and the Poisson brackets {J,H} vanish. We shall introduce new global symplectic invariants for these systems; some of these invariants encode topological or geometric aspects, while others encode analytical information about the singularities and how they stand with respect to the system. Our goal is to prove that a semitoric system is completely determined by the invariants we introduce

Monodromy in the Hydrogen Atom in Crossed Fields

We show that the hydrogen atom in orthogonal electric and magnetic fields has a special property of certain integrable classical Hamiltonian systems known as monodromy. The strength of the fields is assumed to be small enough to validate the use of a normal form H snf which is obtained from a two step normalization of the original system. We consider the level sets of H snf on the second reduced phase space. For an open set of field parameters we show that there is a special dynamically invariant set which is a "doubly pinched 2-torus". This implies that the integrable Hamiltonian H snf has monodromy. Manifestation of monodromy in quantum mechanics is also discussed. PACS : 03.20.+i; 32.60+i Keywords : Singular reduction; Monodromy; Energy-momentum map 1 Introduction This paper studies the hydrogen atom in crossed fields. We consider an integrable approximation. We give a detailed analysis of the geometry of this integrable approximation and show that it has a geometric property cal..

Monodromy in the hydrogen atom in crossed fields

We show that the hydrogen atom in orthogonal electric and magnetic elds has a special property of certain integrable classical Hamiltonian systems known as monodromy The strength of the elds is assumed to be small enough to validate the use of a normal form Hsnf which is obtained from a two step normalization of the original system We consider the level sets of Hsnf on the second reduced phase space For an open set of eld parameters we show that there is a special dynamically invariant set which is a doubly pinched torus This implies that the integrable Hamiltonian Hsnf has monodromy Manifestation of monodromy in quantum mechanics is also discusse

Infinitesimally Stable and Unstable Singularities of 2-Degrees of Freedom Completely Integrable Systems

In this article we give a list of 10 rank zero and 6 rank one singularities of 2-degrees of freedom completely integrable systems. Among such singularities, 14 are the singularities that satisfy a non-vanishing condition on the quadratic part, the remaining 2 are rank 1 singularities that play a role in the geometry of completely integrable systems with fractional monodromy. We describe which of them are stable and which are unstable under infinitesimal completely integrable deformations of the system