Main interests Dynamical symmetries of nonlinear dynamical processes
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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.
1. U. Kopvillem, S. V. Prants. Polarisation Echo. Nauka: Moscow, 1985, 192 p. (in Russian)
2. U. Kopvillem, S. V. Prants, V. V. Samartsev et al. Polarisation Echo and its Applications. Nauka: Moscow, 1992, 220 p. (in Russian)
3. Nonlinear Dynamical Processes (edited by S.V. Prants). Dalnauka: Vladivostok, 2004, 260 p. (in Russian)
4. S.V. Prants. An algebraic approach to quadratic parametric processes. Journal of Physics A. V. 19 (1986) 3457-3462. doi: 10.1088/0305-4470/19/17/012
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6. S.V. Prants, L.S. Yacoupova. Analytic solutions to the Bloch equations for amplitude-and frequency-modulated fields. Soviet Physics JETP V. 70 (1990) 639-644 [ZhETP. V. 97 (1990) 1140-1150]. DOI 0038-5646/90/040639-06
7. S.V. Prants. Parametric amplification and frequency conversion with time-dependent pump amplitude and phase. Optics Communications. V. 78 (1990) 271-273. (Correction, ibid. V. 83 (1991) 390). doi:10.1016/0030-4018(90)90359-2
8. S.V. Prants. Quantum dynamics of atoms in modulated laser fields. Journal of Russian Laser Research. V. 12 (1991) 165-195. DOI 10.1007/BF01126636
9. S.V. Prants, L.S. Yacoupova. The Jaynes-Cummings model with modulated field-atom coupling in resonator quantum electrodynamics. Journal of Modern Optics. V. 39 (1992) 961-971. DOI: 10.1080/09500349214550991
10. S.V. Prants. Nonadiabatic neutrino oscillations in inhomogeneous media. Soviet Physics JETP. V. 77 (1993) 176-180 [ZhETP. V. 104 (1993) 2590-2598]. DOI 1063-7761/93/080176-06
11. S.V. Prants. Lie-group treatment for two- and three-neutrino oscillations in matter with arbitrary density variations. Modern Physics Letters A. V. 8 (1993) 2671-2678. DOI: 10.1142/S0217732393003056
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.
14. S. V. Prants, L. E. Kon'kov. Quantum ergodicity of an excited two-level atom. Bulletin of the Russian Academy of Sciences. Physics. Supplement Physics of Vibrations. V. 58 (1994) 57-62.
15. S.V. Prants. Controlling atom-field dynamics. Journal of Russian Laser Research. V. 16 (1995) 83-97. DOI 10.1007/BF02581077
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17. S.V. Prants. Population locking in nonstationary two- and tri-photon resonances. Optics communications. V. 125 (1996) 222-225. doi:10.1016/0030-4018(96)00029-6
18. S.V. Prants. Dynamical complexity of driven two-level systems. I. External driving by a prescribed laser field. Journal of Russian Laser Research. V. 17 (1996) 539-550. DOI 10.1007/BF02090635
19. S. V. Prants. Finite control of the populations of quantum systems on their dynamic groups. Automation and Remote Control. V. 57 (1996) 204-211. [Automatica i Telemekhanika. No 2. (1996) 66-75].
20. S.V. Prants. Dynamical complexity of driven two-level systems. II. Dynamical driving by a self-consistent radiation field. Journal of Russian Laser Research. V.18 (1997) 69-86. DOI 10.1007/BF02558669
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.
23. I. L. Kiriluyk, L. E. Kon'kov, S. V. Prants. Dynamical complexity in a quantum-optical model with a simple Lie-algebraic structure. Reports on Mathematical Physics. V. 43 (1999) 195-205.
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
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