Dynamical symmetries of nonlinear dynamical processes

Dynamical symmetry is an underlying order, hidden in a group-theoretical structure of the respective evolution equation, which manifests itself in the course of the system's evolution. A group-theoretical approach and Lie-algebraic methods for solving quantum and classical operator evolution equations (Schroedinger, Heisenberg, Bloch, Liouville, Dirac, Fokker-Plank, etc.) have been used to study dynamics of nonstationary processes, in particular, the processes of the matter-radiation interaction. This approach enables to derive exact solutions in nontrivial cases and find approximate analytic solutions for the evolution equations when the perturbation theory fails. The theory of dynamical symmetries provides a formal basis in searching for and establishing analogies between seemingly different systems and phenomena. The method developed is used for solving problems of quantum control of the field and atomic states, the topic of great importance in quantum computers and processing quantum information.

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12. S.V. Prants. Nonadiabatic population transfer in driven four-level systems. Optics and Spectroscopy (USSR). V. 77 (1994) 155-159. [Optika i Spektroskopiya. V. 76 (1994) 173-177].

13. S. V. Prants. Dynamics of a multilevel atom in a polychomatic modulated laser field. Izvestiya of the Russian Academy of Sciences. Ser. Fiz. V. 58 (1994) 30-35.

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21. S.V. Prants. Coherent transient effects of population locking and population transfer in three-level media. Optics and Spectroscopy. V. 83 (1997) 23-27 [Optika i Spektroskopiya. V. 83 (1997) 23-27].

22. S.V. Prants.  Symmetry and chaos in dynamical phenomena. Vestnik DVO RAN N 4 (1997) P.51-61.

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24. M.Yu.Uleysky and S. V. Prants. A nonlinear oscillator with two degrees of freedom in a laser field. Journal of Russian Laser Research. V.22 N1 (2001) 69-81.  DOI   10.1023/A:1009503712423

25. S.V Prants. Group-theoretical approach to study atomic motion in a laser field. Journal of Physics A. V. 44 (2011) art.no. 265101.

26.  S.V. Prants. Dynamical symmetries, control and chaos with moving atoms in high-quality cavities. Journal of Russian Laser Research. V. 36 N3, p.211-227 (2015). DOI  10.1007/s10946-015-9494-z C.2015.09.004