Synergetics pp 225-261 | Cite as

Physical Systems

  • Hermann Haken


The laser is nowadays one of the best understood many-body problems. It is a system far from thermal equilibrium and it allows us to study cooperative effects in great detail. We take as an example the solid-state laser which consists of a set of laser-active atoms embedded in a solid state matrix (cf. Fig. 1.9). As usual, we assume that the laser end faces act as mirrors serving two purposes: They select modes in axial direction and with discrete cavity frequencies. In our model we shall treat atoms with two energy levels. In thermal equilibrium the levels are occupied according to the Boltzmann distribution function. By exciting the atoms, we create an inverted population which may be described by a negative temperature. The excited atoms now start to emit light which is eventually absorbed by the surroundings, whose temperature is much smaller than ħω/k B (where ω is the light frequency of the atomic transition and k B is Boltzmann’s constant) so that we may put this temperature ≈ 0. From a thermodynamic point of view the laser is a system (composed of the atoms and the field) which is coupled to reservoirs at different temperatures. Thus the laser is a system far from thermal equilibrium.


Rayleigh Number Electric Field Strength Saturable Absorber Elastic Stability Fluctuate Force 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. H. Haken: Rev. Mod. Phys. 47, 67 (1975)MathSciNetADSCrossRefGoogle Scholar
  2. H. Haken, ed.: Synergetics (Teubner, Stuttgart 1973)zbMATHGoogle Scholar
  3. H. Haken, M. Wagner, eds.: Cooperative Phenomena (Springer, Berlin-Heidelberg-New York 1973)zbMATHGoogle Scholar
  4. H. Haken, ed.: Cooperative Effects (North Holland, Amsterdam 1974)Google Scholar
  5. H. Haken: Z. Phys. 181, 96 (1964)ADSCrossRefGoogle Scholar
  6. H. Haken: In Encyclopedia of Physics, Vol. XXV/2c: Laser Theory (Springer, Berlin-Heidelberg-New York 1970)Google Scholar
  7. H. Haken: Rev. Mod. Phys. 47, 67 (1975)MathSciNetADSCrossRefGoogle Scholar
  8. H. Risken: Z. Phys. 186, 85 (1965) andADSCrossRefGoogle Scholar
  9. R. D. Hempstead, M. Lax: Phys. Rev. 161, 350 (1967)ADSCrossRefGoogle Scholar
  10. W. Weidlich, H. Risken, H. Haken: Z. Phys. 201, 396 (1967)ADSCrossRefGoogle Scholar
  11. M. Scully, W. E. Lamb: Phys. Rev. 159,208 (1967); 166, 246 (1968)ADSCrossRefGoogle Scholar
  12. H. Haken: Z. Phys. 219, 246 (1969)ADSCrossRefGoogle Scholar
  13. R. Graham, H. Haken: Z. Phys. 237, 31 (1970)MathSciNetADSCrossRefGoogle Scholar
  14. J. F. Scott, M. Sargent III, C. D. Cantrell: Opt. Commun. 15, 13 (1975)ADSCrossRefGoogle Scholar
  15. W. W. Chow, M. O. Scully, E. W. van Stryland: Opt. Commun. 15, 6 (1975)ADSCrossRefGoogle Scholar
  16. H. Haken, H. Ohno: Opt. Commun. 16,205 (1976)ADSCrossRefGoogle Scholar
  17. H. Risken, K. Nummedal: Phys. Lett. 26A, 275 (1968); J. appl. Phys. 39, 4662 (1968)ADSGoogle Scholar
  18. R. Graham, H. Haken: Z. Phys. 213, 420 (1968)ADSCrossRefGoogle Scholar
  19. K. Tomita, T. Todani, H. Kidachi: Phys. Lett. 51A, 483 (1975)ADSGoogle Scholar
  20. L. D. Landau, E. M. Lifshitz: In Course of Theoretical Physics, Vol. 6: Fluid Mechanics (Pergamon Press, London-New York-Paris-Los Angeles 1959)Google Scholar
  21. Chia-Shun-Yih: Fluid Mechanics (McGraw Hill, New York 1969)Google Scholar
  22. G. K. Batchelor: An Introduction to Fluid Dynamics (University Press, Cambridge 1970)Google Scholar
  23. S. Chandrasekhar: Hydrodynamic and Hydromagnetic Stability (Clarendon Press, Oxford 1961)zbMATHGoogle Scholar
  24. C. C. Lin: Hydrodynamic Stability (University Press, Cambridge 1967)Google Scholar
  25. H. Haken: Phys. Lett. 46A, 193 (1973) and in particular Rev. Mod. Phys. 47,67 (1976)ADSGoogle Scholar
  26. R. Graham: Phys. Rev. Lett. 31, 1479 (1973); Phys. Rev. 10, 1762 (1974)ADSCrossRefGoogle Scholar
  27. A. Wunderlin: Thesis, Stuttgart University (1975)Google Scholar
  28. A. Schlüter, D. Lortz, F. Busse: J. Fluid Mech. 23, 129 (1965)MathSciNetADSzbMATHCrossRefGoogle Scholar
  29. F. H. Busse: J. Fluid Mech. 30, 625 (1967)ADSzbMATHCrossRefGoogle Scholar
  30. A. C. Newell, J. A. Whitehead: J. Fluid Mech. 38, 279 (1969)ADSzbMATHCrossRefGoogle Scholar
  31. R. C. Diprima, H. Eckhaus, L. A. Segel: J. Fluid Mech. 49, 705 (1971)ADSzbMATHCrossRefGoogle Scholar
  32. F. H. Busse: J. Fluid Mech. 52, 1, 97 (1972)ADSzbMATHCrossRefGoogle Scholar
  33. D. Ruelle, F. Takens: Comm. Math. Phys. 20,167 (1971)MathSciNetADSzbMATHCrossRefGoogle Scholar
  34. J. B. McLaughlin, P. C. Martin: Phys. Rev. A 12, 186 (1975)ADSGoogle Scholar
  35. Fluctuations, Instabilities and Phase Transitions, ed. by T. Riste (Plenum Press, New York 1975)Google Scholar
  36. J. B. Gunn: Solid State Commun. 1, 88 (1963)ADSCrossRefGoogle Scholar
  37. J. B. Gunn: IBM J. Res. Develop. 8, 141 (1964)CrossRefGoogle Scholar
  38. H. Thomas: In Synergetics, ed. by H. Haken (Teubner, Stuttgart 1973)Google Scholar
  39. K. Nakamura: J. Phys. Soc. Jap. 38, 46 (1975)ADSCrossRefGoogle Scholar
  40. J. M. T. Thompson, G. W. Hunt: A General Theory of Elastic Stability (Wiley, London 1973)zbMATHGoogle Scholar
  41. K. Huseyin: Nonlinear Theory of Elastic Stability (Nordhoff, Leyden 1975)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1977

Authors and Affiliations

  • Hermann Haken
    • 1
  1. 1.Institut für Theoretische PhysikUniversität StuttgartStuttgart 80Germany

Personalised recommendations