Monodromy in the hydrogen atom in crossed fields

DOI10.1016/S0167-2789(00)00053-1zbMath0985.37104MaRDI QIDQ1570809

Richard H. Cushman, Dmitrií A. Sadovskií

Publication date: 11 July 2000

Published in: Physica D (Search for Journal in Brave)

zbMATH Keywords

monodromymagnetic and electric fieldssemi-classial quantization

Mathematics Subject Classification ID

Atomic physics (81V45) Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) (37N20) Electro- and magnetostatics (78A30)

Related Items (34)

Nekhoroshev's approach to Hamiltonian monodromy ⋮ The problem of two fixed centers: bifurcations, actions, monodromy ⋮ The Keplerian regime of charged particles in planetary magnetospheres ⋮ Hamiltonian Hopf bifurcation of the hydrogen atom in crossed fields ⋮ Rearrangement of energy bands: topological aspects ⋮ Dynamics of a satellite orbiting a planet with an inhomogeneous gravitational field ⋮ Hamiltonian systems with detuned 1:1:2 resonance: manifestation of bidromy ⋮ Hamiltonian monodromy and Morse theory ⋮ Uncovering fractional monodromy ⋮ Parallel transport along Seifert manifolds and fractional monodromy ⋮ Symplectic coordinates on \(S^2\times S^2\) for perturbed Keplerian problems: application to the dynamics of a generalised Størmer problem ⋮ Hamiltonian Monodromy via spectral Lax pairs ⋮ Bifurcations of the Hamiltonian fourfold 1:1 resonance with toroidal symmetry ⋮ Poisson and symplectic reductions of 4–DOF isotropic oscillators. The van der Waals system as benchmark ⋮ Rotation forms and local Hamiltonian monodromy ⋮ Influence of planetary oblateness on Keplerian dynamics in magnetospheres and existence of invariant tori ⋮ A Lagrangian fibration of the isotropic 3-dimensional harmonic oscillator with monodromy ⋮ Global properties of integrable Hamiltonian systems ⋮ Recent advances in the monodromy theory of integrable Hamiltonian systems ⋮ Asymptotic invariant tori of perturbed two-body problems ⋮ Normalization through invariants in \(n\)-dimensional Kepler problems ⋮ Algebraic approach to two-dimensional systems: Shape phase transitions, monodromy, and thermodynamic quantities ⋮ Geodesics on the ellipsoid and monodromy ⋮ Interpretation of quantum Hamiltonian monodromy in terms of lattice defects ⋮ Classification of perturbations of the hydrogen atom by small static electric and magnetic fields ⋮ Monodromy in non-integrable systems on certain compact classical phase spaces ⋮ Frequency modulation indicator, Arnold's web and diffusion in the Stark-quadratic-Zeeman problem ⋮ Fractional monodromy of resonant classical and quantum oscillators ⋮ Fractional Hamiltonian monodromy from a Gauss–Manin monodromy ⋮ Normal forms for perturbed Keplerian systems. ⋮ Perturbations of superintegrable systems ⋮ Quantum monodromy in prolate ellipsoidal billiards ⋮ Reduction of some perturbed Keplerian problems ⋮ An application of Nekhoroshev theory to the study of the perturbed hydrogen atom

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