Computational Investigation of the Interaction Between Hydrogen Atoms and an Intense Circularly Polarized Laser Field

The study of interactions between a high-power laser and atoms has been one of the fundamental and interesting topics in strong field physics for decades. Based on a nonperturbative model, ten years ago, we developed a set of programs to facilitate the study of interactions between a circularly polarized laser and atomic hydrogen. These programs included only contribution from the bound states of the hydrogen atom. However, as the laser intensity increases, contribution from continuum states to the excitation and ionization processes becomes larger and can no longer be neglected. Furthermore, because the original code is not able to add this contribution directly due to its many disadvantages, a major upgrade of the code is required before including the contribution from continuum states in future. In this paper, first we deduce some important formulas for contribution of continuum states and present modifications and tests for the upgraded code in detail. Second we show some comparisons among new results, old results from the original codes and the available experimental data. Overall the new result agrees with experimental data well. Last we present our calculation of above-threshold ionization (ATI) rate and compare it with a pertuba-tive calculation. The comparison shows that our nonperturbative calculation can also produce ATI peak suppression.

BUILDING COSMOLOGICAL MODELS VIA NONCOMMUTATIVE GEOMETRY

This is an overview of new and ongoing research developments aimed at constructing cosmological models based on noncommutative geometry, via the spectral action functional, thought of as a modified gravity action, which includes the coupling with matter when computed on an almost commutative geometry. This survey is mostly based on recent results obtained in collaboration with Elena Pierpaoli and Kevin Teh. We describe various aspects of cosmological models of the very early universe, developed by the author and Pierpaoli, based on the asymptotic expansion of the spectral action functional and on renormalization group analysis of the associated particle physics model (an extension of the standard model with right-handed neutrinos and Majorana mass terms previously developed in collaboration with Chamseddine and Connes). We also describe nonperturbative results, more recently obtained by Pierpaoli, Teh, and the author, which extend to the more modern universe, which show that, for different candidate cosmic topologies, the form of the slow-roll inflation potentials obtained from the nonperturbative calculation of the spectral action are strongly coupled to the underlying geometry and topology. We discuss some ongoing directions of research and open questions in this new field of "noncommutative cosmology". The paper is based on the talk given by the author at the conference "Geometry and Quantum Field Theory" at the MPI, in honor of Alan Carey.