The Structure-preserving Computation For The Model Atoms In The Intense Laser Field

With the rapid development of the laser technique, the theoreticalresearch on the interaction between the intense laser and matter, theexplanation for the new experimental phenomena, the prediction for thebehavior and the law of the matter in the stronger laser field, which isnot realized in the lab, are attractive. Especially in these recent years,the laser pulse with the maximum intensity about 1020W /cm2 can beobtained in the experiment, which prompt the research on theinteraction between the intense laser and matter. The theoreticalfoundation about the interaction with the intense laser and matter is theinteraction with the intense laser and atom, where many newphenomena have been generated by nonlinear interaction. Thesephenomena include the electron emission under the laser, i.e.,multiphoton ionization, above-threshold ionization, tunneling ionizationand over-barrier ionization, and the photon emission under the laser, i.e.,the high-order harmonics generation, etc. The high-order harmonicgeneration not only provides a new source of XUV and the soft X-rayradiations, but also shows a new possible way for extremely shortpulses. In the traditional quantum mechanics, the interaction with the laserand matter is regarded as the perturbation of the coulomb field and isdealt with perturbation theory. When the electron locates at the groundstate of the hydrogen atom, its coulomb electronic field isE0 = e =1a.u.=5.14×109V /cm(e is the charge of the electron, a0 is the a0 2Bohr radius), corresponding to the light intensity 5吉林大学博士学位论文I0 = 3.51×1016W / cm2 =1a.u., which cannot reach up in the previous lasermachine, so the previous result from the perturbation theory is accordto the one from the experiment. But when intensity of the laser fieldreaches up to 1013Wcm?2 , some experimental phenomena cannot beexplained by the perturbation theory, that is to say, the traditionalperturbation theory in the quantum mechanics will be invalidated forthe interaction with the laser and atom. In the past decade, variousnonperturbative methods have been developed and adopted, i.e.,Floquet theory method, R-matrix method, etc, but these methods cannotbe applied to the super-short and super-intense laser field. The methodssolving numerically time-dependent Schr?dinger equation (TDSE) havebeen applied to describe the interaction between the super-short andsuper-intense laser and atom, that is, TDSE is directly dicretized usingfinite differece, discrete variable representation, finite elements, Bsplines or a basis set expansion approach. In the basis set expansionapproach, the basis function set may be chosen as the eigenstate offree-field, Volkov state and so on. TDSE implies all the physical messages about the atom, the laserfield and the interaction with the laser and atom, so solving numericallyTDSE is one of the popular and the reasonable methods for the researchabout the interaction with the laser and atom in the present theoreticalresearch. In the interaction with the laser and atom, the electronicinfluence in the direction along the polarization of the laser field isgreater than by other directions, so the one-dimensional model atom ischosen in the research about the interaction between the laser and atomand makes the problem simpler. There is symplectic structure in the Hamilton system. Hamiltoncanonical equation maintains symplectic structure after symplectictransformation. The solutions of the Hamilton canonical equation canbe generated from symplectic group. Based on this, in the early 1980's,Ruth and Feng Kang presented the symplectic algorithm of theHamilton system, which maintains the symplectic structure of thesystem. After that, many people have investigated on the symplecticstructure. Feng Kang and his research group presented the methodsgenerating the symplectic schemes, i.e., generating function metho...