Geodesic
Incoherent control of open quantum systems
Contemporary Mathematics. Fundamental Directions, Proceedings of the International Conference on Mathematical Control Theory and Mechanics (Suzdal, July 3–7, 2009), Tome 42 (2011), pp. 179-185.

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This work reviews various topics in the control of open quantum systems interacting with the environment. The topics include the formulation of coherent and incoherent quantum control, analysis of control landscapes and their critical points for typical objective functionals, controllability properties, and the relation to the optimization over complex Stiefel manifolds. 
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A. Pechen; H. Rabitz. Incoherent control of open quantum systems. Contemporary Mathematics. Fundamental Directions, Proceedings of the International Conference on Mathematical Control Theory and Mechanics (Suzdal, July 3–7, 2009), Tome 42 (2011), pp. 179-185. http://geodesic.mathdoc.fr/item/CMFD_2011_42_a16/

[1] Butkovskii A. G., Samoilenko Yu. I., Upravlenie kvantovomekhanicheskimi protsessami, Nauka, M., 1984 | MR

[2] Accardi L., Lu Y. G., Volovich I. V., Quantum theory and its stochastic limit, Springer-Verlag, Berlin, 2002 | MR

[3] Altafini C., “Coherent control of open quantum dynamical systems”, Phys. Rev. A, 70 (2004), 062321 | DOI

[4] Brif C., Chakrabarti R., Rabitz H., “Control of quantum phenomena: past, present, and future”, New J. Phys., 12 (2010), 075008 | DOI | MR

[5] Dantus M., Lozovoy V. V., “Experimental coherent laser control of physicochemical processes”, Chem. Rev., 104 (2004), 1813–1860 | DOI

[6] Davis E. B., Quantum theory of open systems, Academic Press Inc., London–New York, 1976 | MR

[7] Ding Y. et al., “Thermal beam of metastable krypton atoms produced by optical excitation”, Rev. Sci. Instruments, 78 (2007), 023103 | DOI

[8] Dümcke R., “The low density limit for an $N$-level system interacting with a free Bose or Fermi gas”, Comm. Math. Phys., 97 (1985), 331–359 | DOI | MR

[9] Fonseca Romero K. M., Talkner P., Hänggi P., “Is the dynamics of open quantum systems always linear?”, Phys. Rev. A, 69 (2004), 052109 | DOI

[10] Gordon R. J., Zhu L., Seideman T., “Coherent control of chemical reactions”, Acc. Chem. Research, 32 (1999), 1007 | DOI

[11] Gorini V., Kossakowski A., Sudarshan E. C. G., “Completely positive dynamical semigroups of $N$-level systems”, J. Math. Phys., 17 (1976), 821–825 | DOI | MR

[12] Huang G. M., Tarn T. J., Clark J. W., “On the controllability of quantum mechanical systems”, J. Math. Phys., 24 (1983), 2608–2618 | DOI | MR | Zbl

[13] Jirari H., Pötz W., “Optimal coherent control of dissipative $N$-level systems”, Phys. Rev. A, 72 (2005), 013409 | DOI

[14] Judson R. S., Rabitz H., “Teaching lasers to control molecules”, Phys. Rev. Lett., 68 (1992), 1500–1503 | DOI

[15] Kraus K., States, effects, and operations, Springer, Berlin, 1983 | MR

[16] Lindblad G., “On the generators of quantum dynamical semigroups”, Comm. Math. Phys., 48 (1976), 119–130 | DOI | MR | Zbl

[17] Lloyd S., Viola L., “Engineering quantum dynamics”, Phys. Rev. A, 65 (2001), 010101(R) | DOI | MR

[18] Meier C., Tannor D. J., “Non-Markovian evolution of the density operator in the presence of strong laser field”, J. Chem. Phys., 111 (1999), 3365–3376 | DOI

[19] Oza A., Pechen A., Dominy J., Beltrani V., Moore K., Rabitz H., “Optimization search effort over the control landscapes for open quantum systems with Kraus-map evolution”, J. Phys. A: Math. Theor., 42 (2009), 205305 | DOI | MR | Zbl

[20] Pechen A. N., “White noise approach to the low density limit”, QP-PQ: Quantum Probability and White Noise Analysis, 18 (2005), 428–447 | DOI | MR

[21] Pechen A., Prokhorenko D., Wu R., Rabitz H., “Control landscapes for two-level open quantum systems”, J. Phys. A: Math. Theor., 41 (2008), 045205 | DOI | MR | Zbl

[22] Pechen A., Rabitz H., “Teaching the environment to control quantum systems”, Phys. Rev. A, 73 (2006), 062102 | DOI

[23] Pechukas P., “Reduced dynamics need not be completely positive”, Phys. Rev. Lett., 73 (1994), 1060–1062 | DOI | MR | Zbl

[24] Preskill J., Lecture notes on quantum information and computation, Preprint, 2004 http://www.theory.caltech.edu/people/preskill/ph229

[25] Shaji A., Sudarshan E. C. G., “Who's afraid of not completely positive maps?”, Phys. Lett. A, 341 (2005), 48–54 | DOI | MR | Zbl

[26] Shapiro M., Brumer P., “Coherent chemistry: controlling chemical reactions with lasers”, Acc. Chem. Soc., 22 (1989), 407–413 | DOI

[27] Shapiro M., Brumer P., Principles of the quantum control of molecular processes, Wiley-Interscience, Hoboken, 2003 | Zbl

[28] Sukharev M., Seideman T., “Coherent control approaches to light guidance in the nanoscale”, J. Chem. Phys., 124 (2006), 144707 | DOI

[29] Tannor D., Rice S., “Control of selectivity of chemical reaction via control of wave packet evolution”, J. Chem. Phys., 83 (1985), 5013–5018 | DOI

[30] Wu R., Pechen A., Brif. C, Rabitz H., “Controllability of open quantum systems with Kraus-map dynamics”, J. Phys. A: Math. Theor., 40 (2007), 5681–5693 | DOI | MR | Zbl

[31] Wu R., Pechen A., Rabitz H., Hsieh M, Tsou B., “Control landscapes for observable preparation with open quantum systems”, J. Math. Phys., 49 (2008), 022108 | DOI | MR | Zbl