Quantum Chaos and Statistical Properties of Energy Levels: Numerical Study of the Hydrogen Atom in a Magnetic Field
- 20 October 1986
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 57 (16) , 2006-2009
- https://doi.org/10.1103/physrevlett.57.2006
Abstract
The transition to chaos in "the hydrogen atom in a magnetic field" is numerically studied and shown to lead to well-defined signature on the energy-level fluctuations. Upon an increase in the energy, the calculated statistics evolve from Poisson to Gaussian orthogonal ensemble according to the regular or chaotic character of the classical motion. Several methods are employed to test the generic nature of these distributions.Keywords
This publication has 13 references indexed in Scilit:
- Matching the low-field region and the high-field region for the hydrogen atom in a uniform magnetic fieldJournal of Physics B: Atomic and Molecular Physics, 1986
- The hydrogen atom in a magnetic field. Spectrum from the Coulomb dynamical group approachJournal of Physics B: Atomic and Molecular Physics, 1986
- Hydrogen atom in a strong magnetic field: calculation of the energy levels by quantising the normal form of the regularised Kepler HamiltonianJournal of Physics A: General Physics, 1985
- Spectral fluctuation properties of Hamiltonian systems: the transition region between order and chaosJournal of Physics A: General Physics, 1985
- Fluctuations of quantum spectra and their semiclassical limit in the transition between order and chaosJournal of Physics A: General Physics, 1985
- Trajectories of an atomic electron in a magnetic fieldPhysical Review A, 1984
- Quantum Spectra and Transition from Regular to Chaotic Classical MotionPhysical Review Letters, 1984
- Group theory applied to the hydrogen atom in a strong magnetic field. Derivation of the effective diamagnetic HamiltonianJournal of Physics B: Atomic and Molecular Physics, 1984
- Characterization of Chaotic Quantum Spectra and Universality of Level Fluctuation LawsPhysical Review Letters, 1984
- Hydrogen atom in a strong magnetic field: on the existence of the third integral of motionJournal of Physics A: General Physics, 1981