How the Dimension of Space Affects the Products of Pre-Biotic Evolution: The Spatial Population Dynamics of Structural Complexity and The Emergence of Membranes

We show that autocatalytic networks of epsilon-machines and their population dynamics differ substantially between spatial (geographically distributed) and nonspatial (panmixia) populations. Generally, regions of spacetime-invariant autocatalytic networks---or domains---emerge in geographically distributed populations. These are separated by functional membranes of complementary epsilon-machines that actively translate between the domains and are responsible for their growth and stability. We analyze both spatial and nonspatial populations, determining the algebraic properties of the autocatalytic networks that allow for space to affect the dynamics and so generate autocatalytic domains and membranes. In addition, we analyze populations of intermediate spatial architecture, delineating the thresholds at which spatial memory (information storage) begins to determine the character of the emergent auto-catalytic organization.Comment: 9 pages, 7 figures, 2 tables; http://cse.ucdavis.edu/~cmg/compmech/pubs/ss.ht

Making Cold Molecules by Time-dependent Feshbach Resonances

Pairs of trapped atoms can be associated to make a diatomic molecule using a time dependent magnetic field to ramp the energy of a scattering resonance state from above to below the scattering threshold. A relatively simple model, parameterized in terms of the background scattering length and resonance width and magnetic moment, can be used to predict conversion probabilities from atoms to molecules. The model and its Landau-Zener interpretation are described and illustrated by specific calculations for $^{23}$Na, $^{87}$Rb, and $^{133}$Cs resonances. The model can be readily adapted to Bose-Einstein condensates. Comparison with full many-body calculations for the condensate case show that the model is very useful for making simple estimates of molecule conversion efficiencies.Comment: 11 pages, 11 figures; talk for Quantum Challenges Symposium, Warsaw, Poland, September 4-7, 2003. Published in Journal of Modern Optics 51, 1787-1806 (2004). Typographical errors in Journal article correcte

Resonant Auger decay of the core-excited C∗^\astO molecule in intense X-ray laser fields

The dynamics of the resonant Auger (RA) process of the core-excited C$^\ast$O(1s$^{-1}\pi^\ast,v_r=0$) molecule in an intense X-ray laser field is studied theoretically. The theoretical approach includes the analogue of the conical intersections of the complex potential energy surfaces of the ground and `dressed' resonant states due to intense X-ray pulses, taking into account the decay of the resonance and the direct photoionization of the ground state, both populating the same final ionic states coherently, as well as the direct photoionization of the resonance state itself. The light-induced non-adiabatic effect of the analogue of the conical intersections of the resulting complex potential energy surfaces gives rise to strong coupling between the electronic, vibrational and rotational degrees of freedom of the diatomic CO molecule. The interplay of the direct photoionization of the ground state and of the decay of the resonance increases dramatically with the field intensity. The coherent population of a final ionic state via both the direct photoionization and the resonant Auger decay channels induces strong interference effects with distinct patterns in the RA electron spectra. The individual impact of these physical processes on the total electron yield and on the CO$^+(A^2\Pi)$ electron spectrum are demonstrated.Comment: 13 figs, 1 tabe