Universality and Diversity in Science

The following sections are included:

• Foreword

• Contents

I revisit the first publication on ATI by shining on it the light of the knowledge accumulated over the last 25 years. What we missed is thus revealed but N K Rahman's contribution to the paper may now be seen as an ancestor of Simpleman's Theory.

The following sections are included:

• Introduction

• Molecular Time-Dependent Coupled Equations

• Diabatic TDSUSY

• Conclusion

• Acknowledgments

• References

Atom Ionization by intense ultra-short intense laser pulse, whose electric field performs less than ten oscillations during the pulse is investigated by direct integration of time dependent Schrodinger's equation. The target wave functions are expanded in terms of an accurate and discrete L² basis which is optimized for convergence making the approach more realistic. Further results showing ionization stabilization at high intensities and high frequencies is supported strongly by the results. The effect of chirped pulse on the atomic system is analysed by varying the chirping parameter.

We created a model of a several dimensional physical universe. The extra dimensions associated with the four dimensional physical universe is assumed to have a modified Gidding-Strominger wormhole core. This core is separated by a flexible wall, but it allows the adiabatic pressure generated in the wormhole to penetrate in the extra dimensions. We assume that the extra dimensions are a contracting Robinson-Walker space. We show that the associated physical universe accelerates under a certain restriction of the parameters introduced. The extra dimensional space is very large at the begining, however at present time this space will be very reduced. As a result the physical universe will appear to us four dimensional the way we observe it now.

The application of the Maximum Entropy principle in Liquid Crystal NMR spectroscopy is reviewed. The general theoretical background is recalled together with the description of the major mean field theories used to interpret experimental dipolar couplings and obtain information on the orientationalconformational state of molecules dissolved in fluid phases. The Maximum Entropy principle is then presented, and merits and flaws of its application to the study of flexible molecules discussed with the help of significant examples. The paper terminates with a discussion of the advantageous inclusion in the same framework of other pieces of information, of theoretical, simulational and experimental nature, and with considerations about the outlook to apply the method in the conformational analysis of molecules of biological interest.

In this paper, the cause-effect relationships concerning the occurrence of the period-doubling bifurcation are analysed. Such analysis is carried out by investigating the dynamic of the simplest ODE systems. The governing equations of the system, in fact, contain only one non-linear term. Furthermore, the three state equations can be interpreted in ecological terms.

The state equations were integrated using a purposely developed algorithm, based on a fourth order Taylor series expansion. This method allows one to follow the trajectories in a step-by-step detail and to compare the pre- and post-bifurcation ones. The results showed that the bifurcation is due to a very small change in the logarithmic derivative of the state variable which is directly affected by the non-linear term. This change cumulates over time and, in turn, affects the first two main variables, which can be taken as representative of the prey and predator density. The mechanism causes both, the detachment of the two limit cycles and their re-conjunction, after the next period. This finding is also interpreted in thermodynamic terms, by analysing the evolution of an entropy-like function.

The above analysis showed that it is possible to detect early signs of bifurcation also for more complex systems and, in these cases, to identify the sub-set of state variables which is more affected by structural changes of the bifurcation dynamic of such systems.

We analyze a simple three level atom that has two upper degenerate level. The matrix elements of the dipole moment between the upper states and the ground state are equal. In this situation, with the help of the Floquet theory, we can find the analytical solution of the Schroedinger equation of the atom interacting with a classic electromagnetic field and so we are able to evaluate the spectrum of the radiation emitted by the atom.

My contribution is dedicated to the 60th birthday of Naseem Rahman, whom I have met a number of times at the ICTP in Trieste as well as at other places. It was a great pleasure for me to join him and to have stimulating discussions about his own elegant work, in particular on laser physics, but also about other problems of common interest. I have always enjoyed and appreciated the lively and active role he played at the ICTP and the kind support he gave me. I also want to mention his important initiative to create an international and interdisciplinary center dedicated to the study of complex systems.

A previously developed method for designing optimal pulses for the control of molecular processes by weak laser pulses is briefly reviewed and discussed. Two new applications are presented. The first concerns the two-pulse charge transfer in a simple model of a nearly-symmetric mixed-valence system and the second the absorption of light from the B850 light-harvesting complex present in photosyntetic bacteria, described by a Frenkel exciton Hamiltonian with the inclusion of exciton decoherence through a Redfield master equation approach.

The Feynman propagator, and its parallel in statistical mechanics, namely the canonical density matrix, are first used to treat both homogeneous and confined electron assemblies in the presence of a static electric field of arbitrary strength. The models are relevant to plasmas having variable electron density and degeneracy. The second topic concerns atomic ions in intense magnetic fields. Semiclassical theory is here applied, non-relativistic and relativistic approximations being invoked. Both treatments are shown to be embraced by a generalization of Emden's equation.

We discuss and proceed the cross-disciplinary view that a recent geometrical frame of scaling in polymer solutions gives rise both for chain molecule statistics and statistical physics in general. The complexity of the present picture, however, may be focused on and therefore simplified by the notion of scaling law for geometry, generalizing the current scaling concept in macromolecules. We also believe that some open questions at the cutting edge of other theoretical disciplines may effectively take advantage of this novel conceptual background.

The structure and dynamics of the Enhanced Green Fluorescent Protein (EGFP), with the chromophore in the zwitterionic protonation state is analysed. To date there is no direct evidence of its presence within the protein; however, the zwitterionic state of the chromophore may play an important role in the complex photophysics of GFP. In fact it could be linked to the fluorescence fluctuations observed in solution and single molecule experiments whose microscopic origin is still unaccounted for. A force-field molecular dynamics simulation of the whole solvated protein is reported in order to investigate how the amino acid residues around the chromophore adjust themselves upon change in chromophore protonation, from anionic to zwitterionic. We then use ab initio molecular dynamics to test the stability of this conformation and suggest possible paths of transition between the two forms.

In this paper I review the main features of the collective atomic recoil lasing (CARL) when the atomic medium is a Bose-Einstein condensate instead of the usual thermal gas. In a complete absence of thermal Doppler broadening the discreteness of the photon exchanged in the elementary scattering process becomes highly visible in CARL. Starting from the semi-classical CARL model in which the atomic motion is described classically, I discuss a simple quantum model for the self-consistent evolution of the matter-wave and the single mode radiation fields. A full quantum treatment of the linear evolution of the system shows that is possible to produce atom-atom or atom-photon entanglement in CARL. Ignoring the quantum statistics aspects of the problem, the temporal evolution of the condensate and scattered field in CARL is described, showing the main differences between the semi-classical and the quantum regimes.

The advent of extremely intense, short-pulse lasers has made possible a physical environment altogether distinct from the type of quantum physics for which most physicists were prepared as students. In consequence, an alternative intuition has to be developed by the individual researcher in order to guide his understanding of this very active field of research. We discuss some concepts useful specifically for strong-field physics, while pointing out misconceptions that were (or are still) widely held.