Journal of Samara State Technical University, Ser. Physical and Mathematical SciencesJournal of Samara State Technical University, Ser. Physical and Mathematical Sciences1991-86152310-7081Samara State Technical University21025Some topics in dynamics and control of open quantum systemsPechenAlexander N(к.ф.-м.н.), научный сотрудник, отд. математической физики; Математический институт им. В. А. Стеклова РАН; Steklov Mathematical Institute, Russian Academy of Sciencesapechen@gmail.comSteklov Mathematical Institute, Russian Academy of Sciences1506201115215516118022020Copyright © 2011, Samara State Technical University2011This work reviews several topics in the non-equilibrium dynamics and control of open quantum systems, including the dynamics in the weak coupling and low density regimes, incoherent control and universal Kraus maps.open quantum systemsquantum controlincoherent controlоткрытые квантовые системыквантовое управлениенекогерентное управление[Breuer H.-P., Petruccione F. The theory of open quantum systems. Oxford: Oxford University Press, 2002. 648 pp.][Accardi L., Lu Y. G., Volovich I. V. Quantum theory and its stochastic limit. Berlin: Springer-Verlag, 2002. 473 pp.][Pechen A. N., Volovich I. V. Quantum multipole noise and generalized quantum stochastic equations // Infin. Dimens. Anal. Quantum Probab. Relat. Top., 2002. Vol. 5, no. 4. Pp. 441-464, arXiv: math-ph/0202046.][Печень А. Н. Об одном асимптотическом разложении в квантовой теории // Матем. заметки, 2004. Т. 75, № 3. С. 459-461.][Dümcke R. The low density limit for an N-level system interacting with a free Bose or Fermi gas // Comm. Math. Phys., 1985. Vol. 97, no. 3. Pp. 331-359.][Боголюбов Н. Н. Собрание научных трудов в двенадцати томах. Т. 5: Неравновесная статистическая механика, 1939-1980.][Accardi L., Pechen A. N., Volovich I. V. A stochastic golden rule and quantum Langevin equation for the low density limit // Infin. Dimens. Anal. Quantum Probab. Relat. Top., 2003. Vol. 6, no. 3. Pp. 431-453, arXiv: math-ph/0206032.][Pechen A. N. Quantum stochastic equation for a test particle interacting with a dilute Bose gas // J. Math. Phys., 2004. Vol. 45, no. 1. Pp. 400-417, arXiv: math-ph/0303020.][Бутковский А. Г., Самойленко Ю. И. Управление квантовомеханическими процессами. М.: Наука, 1984. 256 с.][Rice S. A., Zhao M. Optical control of molecular dynamics. New York: Wiley, 2000. 437 pp.][Brumer P. W., Shapiro M. Principles of the quantum control of molecular processes. Hoboken, NJ: Wiley-Interscience, 2003. 354 pp.][Letokhov V. S. Laser control of atoms and molecules. Oxford, New York: Oxford University Press, 2007. 310 pp.][Brif C., Chakrabarti R., Rabitz H. Control of quantum phenomena: past, present and future // New Journal of Physics, 2010. Vol. 12, no. 7, 075008. 69 pp., arXiv: 0912.5121 [quant-ph].][Tannor D J., Rice S. A. Control of selectivity of chemical reaction via control of wave packet evolution // J. Chem. Phys., 1985. Vol. 83, no. 10, 5013. 6 pp.][Dantus M., Lozovoy V. V. Experimental coherent laser control of physicochemical processes // Chem. Rev., 2004. Vol. 104, no. 4. Pp. 1813-1860.][Ruskov R., Korotkov A. N. Quantum feedback control of a solid-state qubit // Phys. Rev. B, 2002. Vol. 66, no. 4, 041401(R). 4 pp., arXiv: cond-mat/0204516 [cond-mat.mes-hall].][Zhdanov D. V., Zadkov V. N. Laser-assisted control of molecular orientation at high temperatures // Phys. Rev. A, 2008. Vol. 77, no. 1, 011401(R). 4 pp.][Tarasov V. E. Quantum computer with mixed states and four-valued logic // J. Phys. A, 2002. Vol. 35, no. 25. Pp. 5207-5235, arXiv: quant-ph/0312131.][Pechen A., Rabitz H. Teaching the environment to control quantum systems // Phys. Rev. A, 2006. Vol. 73, no. 6, 062102. 6 pp., arXiv: quant-ph/0609097.][Wu R., Pechen A., Brif C., Rabitz H. Controllability of open quantum systems with Krausmap dynamics // J. Phys. A, 2007. Vol. 40, no. Pp. 5681-5693, arXiv: quant-ph/0611215][Kraus K. States, effects, and operations / Lecture Notes in Physics. Vol. 190. Berlin: Springer-Verlag, 1983. 151 pp.]