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

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

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

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

Statistical Theory of Asteroid Escape Rates

Transition states in phase space are identified and shown to regulate the rate of escape of asteroids temporarily captured in circumplanetary orbits. The transition states, similar to those occurring in chemical reaction dynamics, are then used to develop a statistical semianalytical theory for the rate of escape of asteroids temporarily captured by Mars. Theory and numerical simulations are found to agree to better than 1%. These calculations suggest that further development of transition state theory in celestial mechanics, as an alternative to large-scale numerical simulations, will be a fruitful approach to mass transport calculations

The Transition State in a Noisy Environment

Transition State Theory overestimates reaction rates in solution because conventional dividing surfaces between reagents and products are crossed many times by the same reactive trajectory. We describe a recipe for constructing a time-dependent dividing surface free of such recrossings in the presence of noise. The no-recrossing limit of Transition State Theory thus becomes generally available for the description of reactions in a fluctuating environment