Skip to main content

Statistical Treatment of Open Systems by Generalized Master Equations

  • Chapter
Springer Tracts in Modern Physics

Abstract

This paper deals with the dynamics of open systems (S) moving irreversibly under the influence of their surroundings (B). As a basis for the discussion of an open system S we use a complete microscopic description of the composite system S⊕B. By eliminating the coordinates of B we infer the behavior of S. The motivation for this investigation is that nature frequently confronts us with coupled systems S and B only one of which, say S, is of experimental relevance. It is then a dictate of economy to look for a “closed” description of the dynamics of S alone. Let us mention just three out of the countless examples.

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

Access this chapter

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).

    MathSciNet  ADS  MATH  Google Scholar 

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

    MathSciNet  ADS  MATH  Google Scholar 

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

    MathSciNet  ADS  Google Scholar 

  5. Zwanzig, R.: Lect. Theoret. Phys. (Boulder) 3, 106 (1960).

    Google Scholar 

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

    Google Scholar 

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

    MathSciNet  ADS  Google Scholar 

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

    MathSciNet  ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  11. Moyal, J.E.: Proc. Cambridge Phil. Soc. 45, 99 (1948).

    MathSciNet  ADS  Google Scholar 

  12. Moyal, J.E.: Proc. Cambridge Phil. Soc. 45, 545 (1949).

    MathSciNet  ADS  MATH  Google Scholar 

  13. Glauber, R.J.: Phys. Rev. 130, 2529 (1963).

    MathSciNet  ADS  Google Scholar 

  14. Glauber, R.J.: Phys. Rev. 131, 2766 (1963).

    MathSciNet  ADS  Google Scholar 

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

    MathSciNet  ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  MATH  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    Google Scholar 

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

    ADS  MATH  Google Scholar 

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

    ADS  MATH  Google Scholar 

  28. Senitzky, J.R.: Phys. Rev. 119, 670 (1960).

    MathSciNet  ADS  MATH  Google Scholar 

  29. Senitzky, J.R.: Phys. Rev. 124, 642 (1961).

    MathSciNet  ADS  MATH  Google Scholar 

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

    ADS  MATH  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    MathSciNet  ADS  MATH  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    Google Scholar 

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

    ADS  MATH  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  MATH  Google Scholar 

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

    MathSciNet  ADS  MATH  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  45. Eliashberg, G.M.: Zh. Eksperim. i. Teor. Fiz. 38, 966 (1960).

    Google Scholar 

  46. Eliashberg, G.M.: Zh. Eksperim. i. Teor. Fiz. Sov. Phys. JETP 11, 696 (1960).

    Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    MathSciNet  ADS  MATH  Google Scholar 

  50. Migdal, A.B.: Zh. Eksperim. Teor. Fiz. 34, 139 (1958).

    MathSciNet  Google Scholar 

  51. Migdal, A.B.: Sov. Phys. JETP 7, 996 (1958).

    MathSciNet  Google Scholar 

  52. Hohenberg, P. C.: Proceedings of the Conference on Fluctuations in Superconductors, Asilomar 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, CaliforniaLow Temp. Phys. Dept. Stanford Res. Inst. Menlo Park, California 94025.

    Google Scholar 

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

    ADS  Google Scholar 

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

    Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  58. Agarwal, G.S.: Phys. Rev. A2, 2038 (1970).

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    Google Scholar 

  67. Schwendimann, P.: to be published.

    Google Scholar 

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

    Google Scholar 

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

    ADS  Google Scholar 

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

    MathSciNet  ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    Google Scholar 

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

    ADS  Google Scholar 

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

    Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  77. Risken, H.: Z. Physik 186, 85 (1965).

    ADS  Google Scholar 

  78. Risken, H.: Fortschr. Physik 16, 261 (1968).

    ADS  Google Scholar 

  79. Risken, H., Vollmer, H.: Z. Physik 201, 323 (1967).

    ADS  Google Scholar 

  80. Risken, H., Vollmer, H.: Z. Physik 204, 240 (1967).

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    Google Scholar 

  83. Arecchi, T. et al: Phys. Rev. Letters 16, 32 (1966).

    ADS  Google Scholar 

  84. Arecchi, T. et al: Phys. Letters 25A, 59 (1967).

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  88. Haken, H.: Z. Physik 181, 96 (1964).

    ADS  Google Scholar 

  89. Haken, H.: Z. Physik 182, 346 (1965).

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  MATH  Google Scholar 

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

    Google Scholar 

  95. Halperin, B.L, Hohenberg, P.C.: Phys. Rev. 177, 952 (1969).

    ADS  Google Scholar 

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

    Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    MathSciNet  ADS  MATH  Google Scholar 

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

    ADS  MATH  Google Scholar 

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

    ADS  Google Scholar 

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

    MathSciNet  ADS  Google Scholar 

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

    Google Scholar 

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

    MathSciNet  ADS  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1973 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Haake, F. (1973). Statistical Treatment of Open Systems by Generalized Master Equations. In: Höhler, G. (eds) Springer Tracts in Modern Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-40468-3_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-40468-3_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-39407-6

  • Online ISBN: 978-3-662-40468-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics