Skip to main content
SpringerLink
Log in

“Global” and “Local” Approaches to the Theory of Open Quantum Optical Systems

  • REVIEW
  • Published:
Journal of Experimental and Theoretical Physics Aims and scope Submit manuscript

Abstract

The application of “exact/complete” initial Hamiltonian of an open optical system and its surroundings and “approximate” effective Hamiltonian for the derivation of the kinetic equation of the open optical system is analyzed in the conditions of the Markovian approximation and the representation of the open system surroundings (thermostat) as a delta-correlated noise. It is shown that the characteristic time hierarchy of the open system naturally necessitates a transition from the aforementioned exact Hamiltonian to the approximate effective Hamiltonian for the subsequent use of the Markovian approximation and the model of delta-correlated surroundings of the open system in the local approach. The Schrödinger equation for the wavevector of the open system and its surroundings is a quantum stochastic differential equation, from which the kinetic equation describing both familiar and new results can be derived easily in the standard manner.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.

Similar content being viewed by others

REFERENCES

  1. H. Carmichael, An Open Systems Approach to Quantum Optics (Springer, Berlin, 1993).

    Book  MATH  Google Scholar 

  2. H. J. Carmichael, Statistical Methods in Quantum Optics. 2. Non-Classical Fields (Springer, Berlin, 2008).

    Book  MATH  Google Scholar 

  3. G. Compagno, R. Passante, and F. Persico, Atom-Field Interactions and Dressed Atoms (Cambridge Univ. Press, Cambridge, 1995).

    Book  Google Scholar 

  4. Y. Yamamoto and A. Imamoglu, Mesoscopic Quantum Optics (Wiley, New York, 1999).

    MATH  Google Scholar 

  5. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge Univ., Cambridge, 1995).

    Book  Google Scholar 

  6. W. P. Schleich, Quantum Optics in Phase Space (Wiley-VCH, Berlin, 2001).

    Book  MATH  Google Scholar 

  7. P. Lambropoulos and D. Petrosyan, Fundamentals of Quantum Optics and Quantum Information (Springer, Berlin, 2007).

    Google Scholar 

  8. A. B. Klimov and S. M. Chumakov, A Group-Theoretical Approach to Quantum Optics. Models of Atom-Field Interactions (Wiley, Chichester, 2009).

    Book  Google Scholar 

  9. O. Keller, Quantum Theory of Near-Field Electrodynamics (Springer, Berlin, 2011).

    Book  MATH  Google Scholar 

  10. R. Chiao and J. Garrison, Quantum Optics (Oxford Univ. Press, New York, 2008).

    Google Scholar 

  11. C. W. Gardiner and P. Zoller, Quantum Noise (Springer, Berlin, 2000; 2004).

  12. R. R. Puri, Mathematical Methods of Quantum Optics (Springer, Berlin, 2001).

    Book  MATH  Google Scholar 

  13. D. Dubbers and H.-J. Stöckmann, Quantum Physics: The Bottom-Up Approach. From the Simple Two-Level System to Irreducible Representations (Springer, Berlin, 2013).

    MATH  Google Scholar 

  14. A. M. Basharov, J. Exp. Theor. Phys. 110, 951 (2010).

    Article  ADS  Google Scholar 

  15. V. P. Karasev, Theor. Math. Phys. 95, 367 (1993).

    Article  Google Scholar 

  16. V. P. Karassiov, J. Phys. A 27, 153 (1994).

    Article  ADS  MathSciNet  Google Scholar 

  17. C. W. Gardiner, Opt. Commun. 243, 57 (2004).

    Article  ADS  Google Scholar 

  18. A. A. Dzhioev and D. S. Kosov, J. Chem. Phys. 134, 044121 (2011).

    Article  ADS  Google Scholar 

  19. Y. J. Yan, J. Chem. Phys. 140, 054105 (2014).

    Article  ADS  Google Scholar 

  20. R. Kh. Gainutdinov, D. G. Blum, A. Shirdelhavar, and A. A. Mutygullina, J. Phys.: Conf. Ser. 1283, 012005 (2019).

    Google Scholar 

  21. A. Ghosh, S. S. Sinha, and D. S. Ray, Phys. Rev. E 86, 011138 (2012).

    Article  ADS  Google Scholar 

  22. C. W. Gardiner, Handbook of Stochastic Methods for Physics, Chemistry and Natural Sciences (Springer, Berlin, New York, Tokyo, 1985).

    Book  MATH  Google Scholar 

  23. D. F. Walls, Z. Phys. 234, 231 (1970).

    Article  ADS  Google Scholar 

  24. R. P. Feynman, F. L. Vernon, Jr., and R. W. Hellwarth, J. Appl Phys. 28, 49 (1957).

    Article  ADS  Google Scholar 

  25. L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover, New York, 1987).

    Google Scholar 

  26. J. H. van Vleck, Phys. Rev. 33, 467 (1929).

    Article  ADS  Google Scholar 

  27. G. Wentzel, Quantum Theory of Fields (Dover, New York, 2003).

    MATH  Google Scholar 

  28. W. Heitler, The Quantum Theory of Radiation (Dover, New York, 2010).

    MATH  Google Scholar 

  29. J. D. Bjorken and S. D. Drell, Relativistic Quantum Mechanics (McGraw Hill, New York, 1964), Vol. 1, Chap. 4.

    MATH  Google Scholar 

  30. J. da Providencia and C. M. Shakin, Ann. Phys. 30, 95 (1964).

    Article  ADS  Google Scholar 

  31. M. Yamamura and A. Kuriyama, Prog. Theor. Phys. Suppl. 93, 1 (1987).

    Article  ADS  Google Scholar 

  32. M. Wagner, Unitary Transformations in Solid State Physics (Elsevier, Amsterdam, 1986).

    Google Scholar 

  33. G. L. Bir and G. E. Pikus, Symmetry and Stain-Induced Effects in Semiconductors (Nauka, Moscow, 1972; Wiley, New York, 1975).

  34. M. Takatsuji, Phys. Rev. 155, 980 (1967).

    Article  ADS  Google Scholar 

  35. M. Takatsuji, Phys. Rev. B 2, 340 (1970).

    Article  ADS  Google Scholar 

  36. M. Takatsuji, Phys. Rev. A 4, 808 (1974).

    Article  ADS  Google Scholar 

  37. M. Takatsuji, Phys. Rev. 11, 619 (1975).

    Article  ADS  Google Scholar 

  38. F. Jørgensen, Mol. Phys. 29, 1137 (1975).

    Article  ADS  Google Scholar 

  39. G. Compagno and F. Persico, Phys. Rev. A 25, 3138 (1982).

    Article  ADS  Google Scholar 

  40. G. Compagno, J. S. Peng, and F. Persico, Opt. Commun. 57, 415 (1986).

    Article  ADS  Google Scholar 

  41. V. Denner and M. Wagner, J. Phys. C 17, 153 (1984).

    Article  ADS  Google Scholar 

  42. V. Denner and M. Wagner, Z. Phys. B 58, 255 (1985).

    Article  ADS  MathSciNet  Google Scholar 

  43. C. A. Coulter, Phys. Rev. A 10, 1946 (1974).

    Article  ADS  Google Scholar 

  44. M. Wagner and J. Vazquez-Marquez, J. Phys.: Condens. Matter 2, 5943 (1990).

    ADS  Google Scholar 

  45. D. Grischkowsky, M. M. T. Loy, and P. F. Liao, Phys. Rev. A 12, 2514 (1975).

    Article  ADS  Google Scholar 

  46. V. A. Kovarskii and E. Yu. Perlin, Sov. Phys. Solid State 13, 1013 (1970).

    Google Scholar 

  47. S. D. Ganichev, S. A. Emel’yanov, E. L. Ivchenko, E. Yu. Perlin, and I. D. Yaroshetskii, JETP Lett. 37, 568 (1983).

    ADS  Google Scholar 

  48. S. D. Ganichev, S. A. Emel’yanov, E. L. Ivchenko, E. Yu. Perlin, Ya. V. Terent’ev, A. V. Fedorov, and I. D. Yaroshetskii, Sov. Phys. JETP 64, 729 (1986).

    Google Scholar 

  49. E. Yu. Perlin, A. B. Fedorov, and M. B. Kashevnik, Sov. Phys. JETP 58, 787 (1983).

    Google Scholar 

  50. N. M. Krylov and N. N. Bogoliubov, Introduction to Non-Linear Mechanics (RKhD, Moscow, 2004; Princeton Univ. Press, Princeton, 1950).

  51. N. N. Bogolyubov and Yu. A. Mitropol’skii, Asymptotic Methods in the Theory of Nonlinear Oscillations (Fizmatgiz, Moscow, 1958) [in Russian].

    MATH  Google Scholar 

  52. V. S. Butylkin, A. E. Kaplan, Yu. G. Khronopulo, and E. I. Yakubovich, Resonant Interactions of Light with Matter (Nauka, Moscow, 1977) [in Russian].

    Google Scholar 

  53. A. M. Basharov, A. I. Maimistov, and E. A. Manykin, Sov. Phys. JETP 57, 282 (1983).

    Google Scholar 

  54. A. M. Basharov, Photonics. The Method of Unitary Transformation in Nonlinear Optics (MIFI, Moscow, 1990) [in Russian].

    Google Scholar 

  55. A. V. Ivanova and G. G. Melikyan, Khim. Fiz. 3, 297 (1983).

    Google Scholar 

  56. A. V. Ivanova and G. G. Melikyan, J. Phys. B 18, 557 (1985).

    Article  ADS  Google Scholar 

  57. A. M. Basharov, Sov. Phys. JETP 75, 611 (1992).

    Google Scholar 

  58. K. Blum, Density Matrix Theory and Applications (Plenum, New York, 1996).

    Book  MATH  Google Scholar 

  59. H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford Univ. Press, Oxford, 2007).

    Book  MATH  Google Scholar 

  60. L. Accardi, Y. G. Lu, and I. Volovich, Quantum Theory and its Stochastic Limit (Springer, Berlin, 2002).

    Book  MATH  Google Scholar 

  61. V. N. Bogaevski and A. Povzner, Algebraic Methods in Nonlinear Perturbation Theory (Springer, 1991).

    Book  Google Scholar 

  62. J. Schwinger, Quantum Kinematics and Dynamics (Basic Books, 1991).

    MATH  Google Scholar 

  63. J. Schwinger, Quantum Mechanics. Symbolism of Atomic Measurement (Springer, Berlin, Heidelberg, 2001).

    MATH  Google Scholar 

  64. G. Lindblad, Commun. Math. Phys. 40, 147 (1975);

    Article  ADS  Google Scholar 

  65. Commun. Math. Phys. 48, 119 (1976).

  66. V. Gorini, A. Kossakowski, and E. C. G. Sundarsham, J. Math. Phys. 17, 821 (1976).

    Article  ADS  Google Scholar 

  67. A. S. Holevo, J. Math. Phys. 37, 1812 (1996).

    Article  ADS  MathSciNet  Google Scholar 

  68. A. S. Holevo, Irreversibility and Causality, Vol. 504 of Lecture Notes in Physics (Springer, Berlin, 1998), p. 67.

  69. A. Barchielli and V. P. Belavkin, J. Phys. A 24, 1495 (1991).

    Article  ADS  MathSciNet  Google Scholar 

  70. D. Keys and J. Wehr, J. Math. Phys. 61, 032101 (2020).

    Article  ADS  MathSciNet  Google Scholar 

  71. A. E. Teretenkov, Infin. Dim. Anal. Quantum Prob. Relat. Top. 22, 1930001 (2019).

    Article  ADS  MathSciNet  Google Scholar 

  72. F. Wegner, Ann. Phys. 3, 77 (1994).

    Article  Google Scholar 

  73. S. D. Glazek and K. G. Wilson, Phys. Rev. D 48, 5863 (1993).

    Article  ADS  Google Scholar 

  74. S. D. Glazek and K. G. Wilson, Phys. Rev. D 49, 4214 (1994).

    Article  ADS  Google Scholar 

  75. N. Bogolubov, J. Phys. 9, 23 (1947).

    MathSciNet  Google Scholar 

  76. N. N. Bogolyubov, V. V. Tolmachev, and D. V. Shirkov, A New Method in the Theory of Superconductivity (Akad. Nauk SSSR, Moscow 1958; Consultants Bureau, New York, 1959).

  77. M. Takatsuji, Phys. A (Amsterdam, Neth.) 84, 68 (1976).

  78. H. Umezawa, H. Matsumoto, and M. Tachiki, Thermo Field Dynamics and Condensed States (North-Holland, Amsterdam, 1982).

    Google Scholar 

  79. A. M. Basharov and S. A. Dubovis, Opt. Spektrosk. 99, 607 (2005).

    Google Scholar 

  80. A. M. Basharov and S. A. Dubovis, Quantum Electron. 35, 683 (2005).

    Article  ADS  Google Scholar 

  81. S. A. Dubovis and A. M. Basharov, Phys. Lett. A 359, 308 (2006).

    Article  ADS  Google Scholar 

  82. A. M. Basharov, Opt. Spectrosc. 128, 182 (2020).

    Article  ADS  Google Scholar 

  83. C. M. Bender, Rep. Prog. Phys. 70, 947 (2007).

    Article  ADS  Google Scholar 

  84. I. Rotter, J. Phys. A 42, 153001 (2009).

    Article  ADS  MathSciNet  Google Scholar 

  85. M. M. Alperin, Ya. D. Klubis, and A. I. Khizhnyak, Introduction to the Physics of Two-Level Systems (Naukova Dumka, Kiev, 1982) [in Russian].

    Google Scholar 

  86. J. Ziman, Elements of Advanced Quantum Theory (Cambridge Univ. Press, Cambridge, 1975).

    MATH  Google Scholar 

  87. L. Lang, K. Sivalingam, and F. Neesea, J. Chem. Phys. 152, 014109 (2020).

    Article  Google Scholar 

  88. A. V. Andreev, V. I. Emel’yanov, and Yu. A. Il’insky, Cooperative Phenomena in Optics (Nauka, Moscow, 1988) [in. Russian].

    Google Scholar 

  89. M. G. Benedict, A. M. Ermolaev, V. A. Malyshev, I. V. Sokolov, and E. D. Trifonov, Super-Radiance: Multiatomic Coherent Emission (IOP, Bristol, Philadelphia, 1996).

    Google Scholar 

  90. A. I. Maimistov and A. M. Basharov, Nonlinear Optical Waves (Kluwer Academic, Dordrecht, 1999).

    Book  MATH  Google Scholar 

  91. P. Langevin, C. R. Acad. Sci. (Paris) 146, 530 (1908).

    Google Scholar 

  92. A. Levy and R. Kozloff, Europhys. Lett. 107, 20004 (2014).

    Article  ADS  Google Scholar 

  93. L. A. Khalfin, Sov. Phys. Dokl. 2, 340 (1957).

    ADS  Google Scholar 

  94. L. A. Khalfin, Sov. Phys. JETP 6, 1053 (1958).

    ADS  Google Scholar 

  95. H. Haas, D. Puzzuoli, F. Zhang, and D. G. Cory, New J. Phys. 21, 103011 (2019).

    Article  ADS  MathSciNet  Google Scholar 

  96. C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Photons and Atoms. Introduction to Quantum Electrodynamics (Wiley, New York, 1997).

    Book  Google Scholar 

  97. P. P. Hofer, M. Perarnau-Llobet, L. D. M. Miranda, G. Haack, R. Silva, J. B. Brask, and N. Brunner, New J. Phys. 19, 123037 (2017).

    Article  ADS  Google Scholar 

  98. A. S. Trushechkin and I. V. Volovich, Eur. Phys. Lett. 113, 30005 (2016).

    Article  Google Scholar 

  99. A. M. Basharov, J. Exp. Theor. Phys. 115, 371 (2012).

    Article  ADS  Google Scholar 

  100. N. N. Rozanov, Dissipative Optical Solitons. From Micro to Nano to Atto (Fizmatlit, Moscow, 2011) [in Russian].

    Google Scholar 

  101. A. I. Maimistov and S. O. Elyutin, J. Mod. Opt. 39, 2201 (1992).

    Article  ADS  Google Scholar 

  102. A. V. Andreev, Phys. Lett. A 179, 23 (1993).

    Article  ADS  Google Scholar 

  103. A. Yu. Parkhomenko and S. V. Sazonov, J. Exp. Theor. Phys. 87, 864 (1998).

    Article  ADS  Google Scholar 

  104. A. V. Andreev, S. Yu. Stremoukhov, and O. A. Shutova, JETP Lett. 93, 476 (2011).

    Article  ADS  Google Scholar 

  105. E. T. Jaynes and F. W. Cummings, Proc. IEEE 51, 89 (1963).

    Article  Google Scholar 

  106. M. Tavis and F. W. Cummings, Phys. Rev. 170, 379 (1968).

    Article  ADS  Google Scholar 

  107. B. W. Shore and P. L. Knight, J. Mod. Opt. 40, 1195 (1993).

    Article  ADS  Google Scholar 

  108. M. Chaichian, D. Ellinas, and P. Kulish, Phys. Rev. Lett. 65, 980 (1990).

    Article  ADS  MathSciNet  Google Scholar 

  109. M. Schiirmann, Commun. Math. Phys. 140, 589 (1991).

    Article  ADS  Google Scholar 

  110. I. P. Vadeiko, G. P. Miroshnichenko, A. V. Rybin, and J. Timonen, Phys. Rev. A 67, 053808 (2003).

    Article  ADS  Google Scholar 

  111. A. Messinger, A. Ritboon, F. Crimin, S. Croke, and S. M. Barnett, New J. Phys. 22, 043008 (2020).

    Article  ADS  MathSciNet  Google Scholar 

  112. A. M. Basharov, Phys. Rev. A 84, 013801 (2011).

    Article  ADS  Google Scholar 

  113. A. M. Basharov, V. N. Gorbachev, and A. A. Rodichkina, Phys. Rev. A 74, 042313 (2006).

    Article  ADS  Google Scholar 

  114. A. M. Basharov, V. N. Gorbachev, and N. V. Znamenskii, Quantum Electron. 36, 785 (2006).

    Article  ADS  Google Scholar 

  115. A. M. Basharov, Phys. Lett. A 376, 1881 (2012).

    Article  ADS  Google Scholar 

  116. A. I. Trubilko and A. M. Basharov, J. Exp. Theor. Phys. 130, 62 (2020).

    Article  ADS  Google Scholar 

  117. A. I. Trubilko and A. M. Basharov, JETP Lett. 110, 517 (2019).

    Article  ADS  Google Scholar 

  118. A. I. Trubilko and A. M. Basharov, Phys. Scr. 95, 045106 (2020).

    Article  ADS  Google Scholar 

  119. V. N. Gorbachev and A. I. Trubilko, J. Exp. Theor. Phys. 108, 203 (2009).

    Article  ADS  Google Scholar 

  120. A. I. Trubilko, J. Exp. Theor. Phys. 114, 575 (2012).

    Article  ADS  Google Scholar 

  121. A. M. Basharov, J. Exp. Theor. Phys. 94, 1070 (2002).

    Article  ADS  Google Scholar 

  122. A. M. Basharov, A. A. Bashkeev, and E. A. Manykin, J. Exp. Theor. Phys. 100, 475 (2005).

    Article  ADS  Google Scholar 

  123. A. M. Basharov, J. Exp. Theor. Phys. 113, 376 (2011).

    Article  ADS  Google Scholar 

  124. A. M. Basharov, JETP Lett. 107, 143 (2018).

    Article  ADS  Google Scholar 

  125. A. M. Basharov and A. I. Trubilko, J. Exp. Theor. Phys. 128, 366 (2019).

    Article  ADS  Google Scholar 

  126. A. M. Basharov and A. I. Trubilko, J. Exp. Theor. Phys. 128, 560 (2019).

    Article  ADS  Google Scholar 

  127. A. I. Trubilko and A. M. Basharov, JETP Lett. 111, 532 (2020).

    Article  ADS  Google Scholar 

  128. A. M. Basharov and A. I. Trubilko, J. Exp. Theor. Phys. 130, 833 (2020).

    Article  ADS  Google Scholar 

  129. P. W. Milonni, The Quantum Vacuum (Academic, Boston, 1994).

    Book  Google Scholar 

  130. A. M. Basharov, J. Exp. Theor. Phys. 89, 249 (1999).

    Article  ADS  Google Scholar 

  131. A. I. Trubilko and A. M. Basharov, J. Exp. Theor. Phys. 129, 339 (2019).

    Article  ADS  Google Scholar 

  132. M. Lax, Phys. Rev. 145, 110 (1966).

    Article  ADS  Google Scholar 

  133. A. M. Chebotarev, Lectures on Quantum Probability (Soc. Math. Mex., 2000).

  134. V. P. Belavkin, Usp. Mat. Nauk 47, 47 (1992).

    Google Scholar 

  135. R. L. Hudson and K. R. Parthasarathy, Comm. Math. Phys. 93, 301 (1984).

    Article  ADS  MathSciNet  Google Scholar 

  136. V. P. Belavkin, Theor. Math. Phys. 110, 35 (1997).

    Article  Google Scholar 

  137. A. S. Kholevo, Itogi Nauki Tekh., Ser.: Sovr. Probl. Mat. Fundam. Napravl. 83, 3 (1991).

    MathSciNet  Google Scholar 

  138. A. Barchielli, Phys. Rev. A 34, 1642 (1986).

    Article  ADS  MathSciNet  Google Scholar 

  139. A. N. Pechen, J. Math. Phys. 45, 400 (2004).

    Article  ADS  MathSciNet  Google Scholar 

  140. A. M. Basharov, J. Exp. Theor. Phys. 84, 13 (1997).

    Article  ADS  Google Scholar 

  141. A. M. Basharov, J. Exp. Theor. Phys. 126, 310 (2018).

    Article  ADS  Google Scholar 

  142. A. M. Basharov, JETP Lett. 75, 123 (2002).

    Article  ADS  Google Scholar 

  143. L. Aolita, F. de Melo, and L. Davidovich, Rep. Prog. Phys. 78, 042001 (2015).

    Article  ADS  Google Scholar 

  144. P. Lenz and F. Wegner, Nucl. Phys. B 482, 693 (1996).

    Article  ADS  Google Scholar 

  145. S. Kehrein, Nucl. Phys. B 592, 512 (2001).

    Article  ADS  MathSciNet  Google Scholar 

  146. S. Bravyi, D. P. DiVincenzo, and D. Loss, Ann. Phys. 326, 2793 (2011).

    Article  ADS  Google Scholar 

  147. R. Zwanzig, J. Chem. Phys. 33, 1338 (1960).

    Article  ADS  MathSciNet  Google Scholar 

  148. R. Zwanzig, Phys. Rev. 124, 985 (1961).

    Article  ADS  Google Scholar 

  149. H. Mori, Progr. Theor. Phys. 34, 765 (1965).

    Article  Google Scholar 

  150. H. Mori, Progr. Theor. Phys. 33, 423 (1965).

    Article  ADS  Google Scholar 

  151. R. Zwanzig, Ann. Rev. Phys. Chem. 16, 67 (1965).

    Article  ADS  Google Scholar 

  152. A. J. Lichtenberg and M. A. Lieberman, Regular and Stochastic Motion, Vol. 38 of Applied Mathematical Sciences (Springer, New York, 1983).

  153. S. Ferrazello, Canonical Perturbation Theories. Degenerate Systems and Resonance (Springer, New York, 2007).

    Book  Google Scholar 

  154. R. B. Gardner, The Method of Equivalence and its Applications (SIAM, Philadelphia, 1989).

    Book  MATH  Google Scholar 

  155. V. P. Maslov, Operator Methods (Nauka, Moscow, 1973) [in Russian].

    MATH  Google Scholar 

  156. A. S. Mishchenko, B. Yu. Sternin, and V. E. Shatalov, Lagrangian Varieties and the Canonical Operator Method (Nauka, Moscow, 1978) [in Russian].

    Google Scholar 

  157. W. Magnus, Comm. Pure Appl. Math. 7, 649 (1954).

    Article  MathSciNet  Google Scholar 

  158. S. Blanes, F. Casas, J. A. Oteo, and J. Ros, Phys. Rep. 470, 151 (2009).

    Article  ADS  MathSciNet  Google Scholar 

  159. R. Ernst, G. Bodenhausen, and A. Wokaun, Principles of NMR in One and Two Dimensions (Clarendon, Oxford, 1987).

    Google Scholar 

  160. S. Teufel, Adiabatic Perturbation Theory in Quantum Dynamics (Springer, Berlin, 2003).

    Book  MATH  Google Scholar 

  161. R. B. Laughlin, Rev. Mod. Phys. 71, 863 (1999).

    Article  ADS  MathSciNet  Google Scholar 

Download references

ACKNOWLEDGMENTS

The author is grateful to A.I. Maimistov and A.I. Trubilko for fruitful discussions, cooperation, and support.

Funding

This study was supported by the Russian Foundation for Basic Research (project no. 19-02-00234a).

Author information

Authors and Affiliations

  1. National Research Center “Kurchatov Institute”, 123182, Moscow, Russia

    A. M. Basharov

  2. Moscow Institute of Physics and Technology (Technical University), 141701, Dolgoprudnyi, Moscow oblast, Russia

    A. M. Basharov

Authors
  1. A. M. Basharov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. M. Basharov.

Additional information

Translated by N. Wadhwa

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Basharov, A.M. “Global” and “Local” Approaches to the Theory of Open Quantum Optical Systems. J. Exp. Theor. Phys. 131, 853–875 (2020). https://doi.org/10.1134/S1063776120110011

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063776120110011

Search

Navigation