Simple models of quantum chaos: Spectrum and eigenfunctions

Quantum mechanics of classically non-integrable systems

/pdf/principles-of-quantum-computation-and-information-3dhqj8q4yl.pdf

Principles of quantum computation and information

https://www.quantware.ups-tlse.fr/chirikov/refs/chi1987a.pdf

Relevance of classical chaos in quantum mechanics: The hydrogen atom in a monochromatic field

We review the status of the theory of ionization of atoms and ions by intense laser radiation (Keldysh's theory). We discuss the applicability of the theory, its relation to the Landau–Dykhne method, and its application to the ionization of atoms by ultrashort nonmonochromatic laser pulses of an arbitrary shape. The semiclassical imaginary time method is applied to describe electron sub-barrier motion using classical equations of motion with an imaginary time i for an electron in the field of an electromagnetic wave. We also discuss tunneling interference of transition amplitudes, a phenomenon occurring due to the existence of several saddle points in the complex time plane and leading to fast oscillations in the momentum distribution of photoelectrons. Nonperturbatively taking the Coulomb interaction between an outgoing electron and the atomic residual into account causes significant changes in the photoelectron momentum distribution and in the level ionization rates, the latter usually increasing by orders of magnitude for both tunneling and multiquantum ionization. The effect of a static magnetic field on the ionization rate and the magnetic cumulation process is examined. The theory of relativistic tunneling is discussed, relativistic and spin corrections to the ionization rate are calculated, and the applicability limits of the nonrelativistic Keldysh theory are determined. Finally, the application of the Fock method to the covariant description of nonlinear ionization in the relativistic regime is discussed.

Current progress in developing the nonlinear ionization theory of atoms and ions

A review is given of the properties of highly excited atoms placed in an electromagnetic field. The probabilities of bound-bound and bound-free transitions between quasiclassical atomic states, and also approximate selection rules for such transitions, are examined. The properties of the dynamic polarizability of highly excited states of atoms are investigated. Quantum-mechanical ionization mechanisms (multiphoton and tunneling) are discussed for highly excited states. Much space is devoted to the stochastic dynamics of classical atomic electrons in a varying monochromatic electromagnetic field. The threshold electric field for the stochastic motion of an electron and the ionization of an atom is given as a function of the field frequency, its polarization, and the principal quantum number of the atomic state under consideration. The influence of orbital angular momentum of the state from which ionization takes place on the stochastization process is discussed. Classical diffusion ionization of a highly excited atom in an electromagnetic field is considered within the framework of classical mechanics and the quasiclassical quantum-mechanical approximation. The validity of classical mechanics in relation to the properties of highly excited atoms in an electromagnetic field is examined. The realization of quantum and quasiclassical ionization of highly excited atoms is considered. The final part of the review analyzes experimental data on the behavior of highly excited atoms in a radiofrequency field. Comparison of experimental data with the theory given in this review has demonstrated good agreement between them.

https://iopscience.iop.org/article/10.1070/PU1983v026n07ABEH004445/pdf

D L Shepelyanskiĭ

Papers

Highly-excited atoms in the electromagnetic field