Time-evolution stability of order parameters and phase diagrams of bosons on optical lattice

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Stemming from the Heisenberg equations of motion, we study the time-evolution stability of the order parameters for the cold atoms on optical lattices. The requirement of this stability of the order parameters endows the phase diagram with a fruitful structure in the superfluid phase. For the one-component Bose-Hubbard model, we see that this stability of order parameter leads to a physically receivable phase diagram. For two-component bosons, we show that the molecules are preformed in the atomic superfluid and then condenses into a molecular superfluid phase at a critical repulsive inter-species interaction, which resembles the pre-pairing mechanism in high Tc superconductor of Cu-O cuprates.