Quantum correlation effects and Bose-Einstein condensation in molecular formations in the ultra-cold atomic gases

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a) In ultra-cold atomic gases with molecular formations, the phase-structure changes and their temperature dependences have been calculated for all kinds of quantum-statistical correlations (Bose-Bose, Fermi-Fermi, Bose-Fermi systems of atomic-gas mixtures). The atom-atom and atom-molecule interactions have been introduced using the mean-field approximations; their effect on the molecular formations and Bose-Einstein condensation of the Bosonic atom/molecule has been clarified. Especially, in the case of strongly attractive interactions, the new phases that do not exist in the system of the ideal gases have been found to appear. In Bose-Bose mixtures, we have shown that the atom/molecule Bose-Einstein condensation appears in exclusive manner by the singularity effect coming from the phase transitions into the Bose-Einstein condensation. We also have formulated the law of quantum mass action for molecular formations in the ultra-cold atomic gas, which is the extension of the classical l … More aw of mass action in chemical reaction theory, and evaluated the quantum-statistical effects in the ultra-cold molecular formations. We have summarized these results and published them in Physical Review journals.b) The phase structures and their temperature dependences with molecular formations have been obtained also in the case of ultra-cold atomic gases trapped in the harmonic-oscillator potentials. The finite-size effects for molecular formations in the trapped atomic gasses are now under analysis, and should be published.c) We have applied the method to obtain the time-development of Bose-Fermi atomic-gas mixtures on the basis of the time-dependent Gross-Pitaevski and Vlasov equations, for the Yb-Yb atomic-gas system ; the oscillational excitation modes have been evaluated. The ultra-cold atomic-gas experiments is planned for the Yb-Yb system by several experimentalist groups, and, then, our results should be checked in near future. The papers where we have summarized our results are now in preparation. Less