Український математичний конгрес - 2009

Анна Игнатенко (Одесский государственный экологический университет, Одесса, Украина)

New quantum approach to treating chaotic and statistical phenomena in a multi-wave atomic ionization

In last years a phenomenon of multi-wave atomic ionization in low-frequency electromagnetic fields attracts a great interest due to the possibility of realizing quantum chaos phenomenon in quantum system. The important features of process are a diffusion on atomic states, which are strongly perturbed by a field, and stochastic character of electron vibrations. In series of papers by Casati et al [1] a dynamical chaos effect for hydrogen atom in a field was at first correctly described by the non-linear classic mechanics methods. Here we present new quantum approach to treating the chaotic phenomena in the multi-wave atomic ionization. It is based on the operator perturbation theory, complex coordinates method, non-relativistic one-channel quantum defect theory and chaos theory algorithms [2,3].

[1] M. W. Noel, M. W. Griffith, T. F. Gallagher, Phys. Rev. A 62:063401, 2000; F.Benvenuto, G.Casati, D.L.Shepelyansky, Z.Phys.B. 94:481-486, 1996; G.Casati, I.Guarneri, G.Mantica, Phys.Rev.A. 50:5018-5024, 1994.
[2] A.V.Glushkov, Atom in electromagnetic field: Numerical models, Kiev, KNT (2005) 450P; A.V.Glushkov, L.N.Ivanov, J.Phys.B:At.Mol.Opt.Phys. 26:L379-388, 1993.
[3] A. Glushkov, S.Ambrosov, A.Ignatenko, Int.J.Quant.Chem. 99:889-896 (2004).