Skip to main content
SpringerLink
Log in

Statistical treatment of open systems by generalized master equations

  • Chapter
  • First Online:
Quantum Statistics in Optics and Solid-State Physics

Part of the book series: Springer Tracts in Modern Physics ((STMP,volume 66))

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

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 16.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Pauli,W.: Festschrift zum 60. Geburtstage A. Sommerfeld, S. 30. Leipzig: Hirzel 1928.

    Google Scholar 

  2. van Hove,L.: Physica 23, 441 (1957).

    Article  MathSciNet  ADS  Google Scholar 

  3. Nakajima,S.: Progr. Theor. Phys. 20, 948 (1958).

    Article  ADS  Google Scholar 

  4. Zwanzig,R.: J. Chem. Phys. 33, 1338 (1960) and Lect. Theoret. Phys. (Boulder) 3, 106 (1960).

    Article  MathSciNet  ADS  Google Scholar 

  5. Montroll,E.W.: Fundamental problems in statistical mechanics, compiled by Cohen, E.G.D. Amsterdam: North Holland Publ. Co. 1962.

    Google Scholar 

  6. Prigogine,I., Resibois,P.: Physica 27, 629 (1961).

    Article  MathSciNet  ADS  Google Scholar 

  7. Zwanzig,R.: Physica 30, 1109 (1964).

    Article  MathSciNet  ADS  Google Scholar 

  8. Argyres,P.N., Kelley,P.L.: Phys. Rev. 134, A98 (1964).

    Article  ADS  Google Scholar 

  9. Wigner,E.P.: Phys. Rev. 40, 749 (1932).

    Article  ADS  Google Scholar 

  10. Moyal,J.E.: Proc. Cambridge Phil. Soc. 45, 99 (1948); 45, 545 (1949).

    Article  ADS  Google Scholar 

  11. Glauber,R.J.: Phys. Rev. 130, 2529 (1963); 131, 2766 (1963).

    Article  MathSciNet  ADS  Google Scholar 

  12. Mehta,C.L., Sudarshan,E.C.G.: Phys. Rev. 138, B274 (1965).

    Article  ADS  Google Scholar 

  13. Cahill,K.E., Glauber,R.J.: Phys. Rev. 177, 1857 (1969); 177, 1882 (1969).

    Article  ADS  Google Scholar 

  14. Agarwal,G.S., Wolf,E.: Phys. Rev. Letters 21, 180 (1968).

    Article  ADS  Google Scholar 

  15. Haken,H.: Z. Physik 219, 411 (1969).

    Article  ADS  Google Scholar 

  16. Haken,H., Weidlich,W.: Z. Physik 205, 96 (1967).

    Article  ADS  Google Scholar 

  17. Haake,F.: Phys. Rev. A3, 1723 (1971).

    Article  ADS  Google Scholar 

  18. Bonifacio,R., Haake,F.: Z. Physik 200, 526 (1967).

    Article  ADS  Google Scholar 

  19. Lax,M.: Phys. Rev. 172, 350 (1968).

    Article  ADS  Google Scholar 

  20. Graham,R., Haake,F., Haken,H., Weidlich,W.: Z. Physik 213, 21 (1968).

    Article  ADS  Google Scholar 

  21. Gnutzmann,U.: Z. Physik 225, 364 (1969).

    Article  Google Scholar 

  22. Wangsness,R.K., Bloch,F.: Phys. Rev. 89, 728 (1953).

    Article  ADS  Google Scholar 

  23. Weidlich,W., Haake,F.: Z. Physik 185, 30 (1965).

    Article  ADS  Google Scholar 

  24. Senitzky,J.R.: Phys. Rev. 119, 670 (1960); 124, 642 (1961).

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  26. Bonch Bruevich Tyablikov: The Green's function method in statistical mechanics. Amsterdam: North-Holland 1962.

    MATH  Google Scholar 

  27. Stratonivich,R.L.: Topics in the theory of random noise. New York: Gordon and Breach 1963.

    Google Scholar 

  28. Wang,N.Ch., Uhlenbeck,G.E.: Rev. Mod. Phys. 17, 323 (1945).

    Article  ADS  Google Scholar 

  29. Haake,F.: Z. Physik 223, 364 (1969).

    Article  ADS  Google Scholar 

  30. Weidlich,W., Haake,F.: Z. Physik 186, 203 (1965).

    Article  ADS  Google Scholar 

  31. Agarwal,G.S.: to be published.

    Google Scholar 

  32. Fröhlich,H.: Phys. Rev. 79, 845 (1950).

    Article  ADS  Google Scholar 

  33. Maxwell,E.: Phys. Rev. 78, 477 (1950).

    Article  ADS  Google Scholar 

  34. Reynolds,C.A. et al.: Phys. Rev. 78, 487 (1950).

    Article  ADS  Google Scholar 

  35. Cooper,L.N.: Phys. Rev. 104, 1189 (1956).

    Article  ADS  Google Scholar 

  36. Bardeen,J., Cooper,L.N., Schrieffer,J.R.: Phys. Rev. 108, 1175 (1957).

    Article  MathSciNet  ADS  Google Scholar 

  37. Meservey,R., Schwartz,B.B.: In: Superconductivity, Kap. 4, edited by Parks,R.D. New York: Marcel Dekker, Inc. 1969.

    Google Scholar 

  38. Ginsberg,D.M., Hebel,L.C.: In: Superconductivity, Kap. 4, edited by Parks,R.D. New York: Marcel Dekker, Inc. 1969.

    Google Scholar 

  39. Scalapino,D.L.: In: Superconductivity, Kap. 10, edited by Parks,R.D. New York: Marcel Dekker, Inc. 1969.

    Google Scholar 

  40. Eliashberg,G.M.: Zh. Eksperim. i. Teor. Fiz. 38, 966 (1960); Sov. Phys. JETP 11, 696 (1960).

    Google Scholar 

  41. Scalapino,D.J., Schrieffer,I.R., Wilkins,J.W.: Phys. Rev. 148, 263 (1966).

    Article  ADS  Google Scholar 

  42. Yang,C.N.: Rev. Mod. Phys. 34, 694 (1962).

    Article  ADS  Google Scholar 

  43. Schwinger,J., Martin,P.C.: Phys. Rev. 115, 1342 (1959).

    Article  MathSciNet  ADS  Google Scholar 

  44. Migdal,A.B.: Zh. Eksperim. Teor. Fiz. 34, 139 (1958); Sov. Phys. JETP 7, 996 (1958).

    Google Scholar 

  45. Hohenberg,P.C.: Proceedings of the Conference on Fluctuations in Superconductors, Asilomar, 1968, ed. by W. S. Goree and F. Chilton, Low Temp. Phys. Dept. Stanford Res. Inst. Menlo Park, California 94025.

    Google Scholar 

  46. Bogolyubov,N.N.: Physica 26, 1 (1960).

    Article  ADS  Google Scholar 

  47. Dicke,R.M.: Phys. Rev. 93, 493 (1954).

    Article  Google Scholar 

  48. Ernst,V., Stehle,P.: Phys. Rev. 176, 1456 (1968).

    Article  ADS  Google Scholar 

  49. Dialetis,D.: Phys. Rev. A2, 599 (1970).

    Article  ADS  Google Scholar 

  50. Lehmberg,R.H.: Phys. Rev. A2, 833 (1970).

    ADS  Google Scholar 

  51. Agarwal,O.S.: Phys. Rev. A2, 2038 (1970).

    Article  ADS  Google Scholar 

  52. Rehler,N.W., Eberly,J.H.: Phys. Rev. A3, 1735 (1971).

    Article  ADS  Google Scholar 

  53. Bonifacio,R., Schwendimann,P., Haake,F.: Phys. Rev. A4, 302 (1971).

    Article  ADS  Google Scholar 

  54. Bonifacio,R., Schwendimann,P., Haake,F.: Phys. Rev. A4, 854 (1971).

    Article  ADS  Google Scholar 

  55. Degiorgio,V.: Optics Com. 2, 362 (1971).

    Article  Google Scholar 

  56. Bonifacio,R., Gronchi,M.: Nuovo Cim. Letters I, 1105 (1971).

    Article  Google Scholar 

  57. Degiorgio,V., Ghielmetti: Phys. Rev. A4, 2415 (1971).

    Article  ADS  Google Scholar 

  58. Haake,F., Glauber,R.: Phys. Rev. A5, 1457 (1972).

    Article  ADS  Google Scholar 

  59. Bonifacio,R., Banfi,G.: to be published.

    Google Scholar 

  60. Schwendimann,P.: to be published.

    Google Scholar 

  61. Haken,H.: Handbuch der Physik, Bd. XXV/2c. Berlin: Springer 1970.

    Google Scholar 

  62. Kryukov,P.G., Letokhov,V.S.: Sov. Phys. 12, 641 (1970).

    Article  ADS  Google Scholar 

  63. Lamb,G.L., Jr.: Rev. Mod. Phys. 43, 99 (1971).

    Article  ADS  Google Scholar 

  64. Arecchi,T., Courtens,E.: Phys. Rev. A2, 1730 (1970).

    Article  ADS  Google Scholar 

  65. Scharf,G.: Helv. Phys. Acta 43, 806 (1970).

    Google Scholar 

  66. Bonifacio,R., Preparate,G.: Phys. Rev. A2, 336 (1970).

    Article  ADS  Google Scholar 

  67. Glauber,R.I.: In: Quantum optics and electronics. New York: Gordon and Breach 1965.

    Google Scholar 

  68. Arecchi,T., Degiorgio,V.: Phys. Rev. A3, 1108 (1970).

    ADS  Google Scholar 

  69. Lax,M., Louisell,W.H.: IEEE J. Quant. Electr. QE 3, 47 (1967).

    Article  ADS  Google Scholar 

  70. Risken,H.: Z. Physik 186, 85 (1965); Fortschr. Physik 16, 261 (1968).

    Article  ADS  Google Scholar 

  71. Risken,H., Vollmer,H.: Z. Physik 201, 323 (1967); 204, 240 (1967).

    Article  ADS  Google Scholar 

  72. Hempstead,R.D., Lax,M.: Phys. Rev. 161, 350 (1967).

    Article  ADS  Google Scholar 

  73. van der Pol,B.: Phil. Mag. 3, 65 (1927).

    Article  Google Scholar 

  74. Arecchi,T. et al.: Phys. Rev. Letters 16, 32 (1966); Phys. Letters 25A, 59 (1967).

    Article  ADS  Google Scholar 

  75. Meltzer,D., Mandel,L.: Phys. Rev. A3, 1763 (1971).

    Article  ADS  Google Scholar 

  76. Gerhardt,H., Welling,H., Güttner,A.: Z. Physik 253, 113 (1972).

    Article  ADS  Google Scholar 

  77. Gnutzmann,U.: Z. Physik 222, 283 (1969).

    Article  ADS  Google Scholar 

  78. Haken,H.: Z. Physik 181, 96 (1964); 182, 346 (1965).

    Article  ADS  Google Scholar 

  79. Resibois,P., de Leener,M.: Phys. Rev. 178, 806 (1969); 178, 819 (1969).

    Article  ADS  Google Scholar 

  80. Resibois,P., Dewel,G.: Ann. Phys. (N. Y.) 69, 299 (1972).

    Article  ADS  Google Scholar 

  81. Kawasaki,K.: Ann. Phys. (N. Y.) 61, 1 (1970); hier sind weitere einschlägige Arbeiten von Kawasaki zitiert.

    Article  ADS  Google Scholar 

  82. van Hove,L.: Phys. Rev. 95, 1374 (1954).

    Article  ADS  Google Scholar 

  83. Landau,L.D., Khalatnikov,I.M.: Dokl. Akad. Nauk SSSR 90, 469 (1954).

    Google Scholar 

  84. Halperin,B.I., Hohenberg,P.C.: Phys. Rev. 177, 952 (1969).

    Article  ADS  Google Scholar 

  85. Kadanoff,L.P.: Physics 2, 263 (1966).

    Google Scholar 

  86. Kadanoff,L.P. et al.: Rev. Mod. Phys. 39, 395 (1967).

    Article  ADS  Google Scholar 

  87. Kadanoff,L.P., Swift,J.: Phys. Rev. 166, 89 (1968).

    Article  ADS  Google Scholar 

  88. Wyld,H.W., Jr.: Ann. Phys. (N. Y.) 14, 143 (1961).

    Article  MathSciNet  ADS  Google Scholar 

  89. Lee,L.L.: Ann. Phys. (N. Y.) 32, 292 (1965).

    Article  ADS  Google Scholar 

  90. Haake,F.: Z. Physik 252, 118 (1972).

    Article  ADS  Google Scholar 

  91. Bennett,H.S., Martin,P.C.: Phys. Rev. 138, A 608 (1965).

    Article  MathSciNet  ADS  Google Scholar 

  92. Kittel,C.: Introduction to Solid State Physics, Kap. 15. New York: Wiley 1968.

    Google Scholar 

  93. Graham,R., Haken,H.: Z. Physik 243, 289 (1971).

    Article  MathSciNet  ADS  Google Scholar 

  94. Graham,R.: Springer Tracts in Modern Physics 66, 1 (1973).

    Article  Google Scholar 

  95. Martin,P.C.: private communication.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für theoretische Physik der Universität Stuttgart, Herdweg 77, D-7000, Stuttgart, Federal Republic of Germany

    Dr. Fritz Haake

Authors
  1. Dr. Fritz Haake
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1973 Springer-Verlag

About this chapter

Cite this chapter

Haake, F. (1973). Statistical treatment of open systems by generalized master equations. In: Quantum Statistics in Optics and Solid-State Physics. Springer Tracts in Modern Physics, vol 66. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0044957

Download citation

  • DOI: https://doi.org/10.1007/BFb0044957

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06189-2

  • Online ISBN: 978-3-540-38458-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation