Quantization with operators appropriate to shapes of trajectories and classical perturbation theory

Quantization is discussed for molecular systems having a zeroth order pair of doubly degenerate normal modes. Algebraic quantization is employed using quantum operators appropriate to the shape of the classical trajectories or wave functions, together with Birkhoff-Gustavson perturbation theory and the W eyl correspondence for operators. The results are compared with a previous algebraic quantization made with operators not appropriate to the trajectory shape. Analogous results are given for a uniform semiclassical quantization based on Mathieu functions of fractional order. The relative sensitivities of these two methods (AQ and US) to the use of operators and coordinates related to and not related to the trajectory shape is discussed. The arguments are illustrated using principally a Hamiltonian for which many previous results are available

Time-frequency analysis of chaotic systems

We describe a method for analyzing the phase space structures of Hamiltonian systems. This method is based on a time-frequency decomposition of a trajectory using wavelets. The ridges of the time-frequency landscape of a trajectory, also called instantaneous frequencies, enable us to analyze the phase space structures. In particular, this method detects resonance trappings and transitions and allows a characterization of the notion of weak and strong chaos. We illustrate the method with the trajectories of the standard map and the hydrogen atom in crossed magnetic and elliptically polarized microwave fields.Comment: 36 pages, 18 figure

Envelope-driven recollisions triggered by an elliptically polarized laser pulse

Increasing ellipticity usually suppresses the recollision probability drastically. In contrast, we report on a recollision channel with large return energy and a substantial probability, regardless of the ellipticity. The laser envelope plays a dominant role in the energy gained by the electron, and in the conditions under which the electron comes back to the core. We show that this recollision channel eciently triggers multiple ionization with an elliptically polarized pulse

Circularly Polarized Molecular High Harmonic Generation Using a Bicircular Laser

We investigate the process of circularly polarized high harmonic generation in molecules using a bicircular laser field. In this context, we show that molecules offer a very robust framework for the production of circularly polarized harmonics, provided their symmetry is compatible with that of the laser field. Using a discrete time-dependent symmetry analysis, we show how all the features (harmonic order and polarization) of spectra can be explained and predicted. The symmetry analysis is generic and can easily be applied to other target and/or field configurations

Electron stripping and re-attachment at atomic centers using attosecond half-cycle pulses

We investigate the response of two three-body Coulomb systems when driven by attosecond half-cycle pulses: The hydrogen molecular ion and the helium atom. Using very short half-cycle pulses (HCPs) which effectively deliver ``kicks'' to the electrons, we first study how a carefully chosen sequence of HCPs can be used to control to which of one of the two fixed atomic centers the electron gets re-attached. Moving from one electron in two atomic centers to two electrons in one atomic center we then study the double ionization from the ground state of He by a sequence of attosecond time-scale HCPs, with each electron receiving effectively a ``kick'' from each HCP. We investigate how the net electric field of the sequence of HCPs affects the total and differential ionization probabilities

Uniform semiclassical theory of avoided crossings

A voided crossings influence spectra and intramolecular redistribution of energy. A semiclassical theory of these avoided crossings shows that when primitive semiclassical eigenvalues are plotted vs a parameter in the Hamiltonian they cross instead of avoiding each other. The trajectories for each are connected by a classically forbidden path. To obtain the avoided crossing behavior, a uniform semiclassical theory of avoided crossings is presented in this article for the case where that behavior is generated by a classical resonance. A low order perturbation theory expression is used as the basis for a functional form for the treatment. The parameters in the expression are evaluated from canonical invariants (phase integrals) obtained from classical trajectory data. The results are compared with quantum mechanical results for the splitting, and reasonable agreement is obtained. Other advantages of the uniform method are described

Transition state in atomic physics

The transition state is fundamental to modern theories of reaction dynamics: essentially, the transition state is a structure in phase space that all reactive trajectories must cross. While transition-state theory (TST) has been used mainly in chemical physics, it is possible to apply the theory to considerable advantage in any collision problem that involves some form of reaction. Of special interest are systems in which chaotic scattering or half-scattering occurs such as the ionization of Rydberg atoms in external fields. In this paper the ionization dynamics of a hydrogen atom in crossed electric and magnetic fields are shown to possess a transition state: We compute the periodic orbit dividing surface (PODS) which is found not to be a dividing surface when projected into configuration space. Although the possibility of a PODS occurring in phase space rather than configuration space has been recognized before, to our knowledge this is the first actual example: its origin is traced directly to the presence of velocity-dependent terms in the Hamiltonian. Our findings establish TST as the method of choice for understanding ionization of Rydberg atoms in the presence of velocity-dependent forces. To demonstrate this TST is used to (i) uncover a multiple-scattering mechanism for ionization and (ii) compute ionization rates. In the process we also develop a method of computing surfaces of section that uses periodic orbits to define the surface, and examine the fractal nature of the dynamics