Abstract
Synergetics deals with complicated systems consisting of very many subsystems. As one of Haken’s famous examples [1-4] let us consider the laser systems. Here a few light modes are coupled to the many active atoms (subsystems) in the laser cavity. A total description of such a system would require very many variables. In general such a detailed microscopic description is not needed. Instead we are only interested in a few relevant variables, which describe the system on a macroscopic scale. In the laser the few light modes are such relevant macroscopic variables.
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References
H. Haken: Z. Physik 181, 96 (1964)
H. Haken: Laser Theory, Encyclopedia of Physics, Vol. XXV/2c Springer, Berlin (1970)
H. Haken: Rev. Mod. Phys. 47, 67 (1975)
H. Haken: Synergetics, An Introduction 3rd ed. Springer Series in Synergetics, Vol. 1, Springer, Berlin (1983)
H. Risken: The Fokker-Planck Equation, Springer Series in Synergetics, Vol. 18, Springer, Berlin (1984)
O. Perron: Die Lehre von den Kettenbrüchen, Vols. I and II, Teubner Stuttgart (1977)
W. B. Jones, W.J. Thron: Continued Fractions, Encyclopedia of Mathematics and its Applications, Vol. 11, Addison-Wesley, Reading, MA (1980)
P. Hänggi, F. Rösel, D. Trautmann: Z. Naturforsch. 33a, 402 (1978)
H. Haken: Advanced Synergetics, Springer Series in Synergetics Vol. 20, Springer, Berlin (1983)
H. Risken, H.D. Vollmer: Z. Physik B39, 89 and 339 (1980)
I. S. Gradshteyn, I. M. Ryzhik: Tables of Integrals, Series and Products, Academic Press, New York (1965)
H. Denk, M. Riederle: J. Approx. Theory 35, 355 (1982)
H. A. Kramers: Physica 7, 284 (1940)
H. Risken, H.D. Vollmer: Z. Physik B33, 297 (1979)
H. D. Vollmer, H. Risken: Z. Physik B34, 313 (1979)
K. Voigtlaender, H. Risken: J. Stat. Phys. 10, 397 (1985)
M. Büttiker, R. Landauer: Phys. Rev. B30, 1551 (1984)
H. Risken, K. Voigtlaender: J. Stat. Phys. 11, 825 (1985)
M. Mörsch, H. Risken, H.D. Vollmer: Z. Physik B49, 47 (1982)
P. Jung, H. Risken: Z. Physik B61, 367 (1985)
P. Jung, H. Risken: Phys. Lett. 103A, 38 (1984)
H. J. Breymeyer, H. Risken, H.D. Vollmer, W. Wonneberger: Appi. Phys. B28, 335 (1982)
W. Schleich, C.S. Cha, J.D. Cresser: Phys. Rev. A29, 230 (1984)
H. Haug, S.W. Koch, R. Neumann, H.E. Schmidt: Z. Physik B49, 79 (1982)
P. Zoller, G. Alber, R. Salvador: Phys. Rev. A24, 398 (1981)
M. Dörfle, A. Schenzle: Z. Physik B65, 113 (1986)
P. D. Drummond, D.F. Walls: J. Phys. A13, 725 (1980)
K. Vogel, H. Risken: in preparation
H. Denk: Ph. D. Thesis, Ulm (1984)
Th. Leiber: Diploma Thesis, Ulm (1985)
A., Allegrini, E. Arimondo, A. Bambini: Phys. Rev. A15, 718 (1977)
C. Durst, E. Sigmund, P. Reineker, A. Scheuing: J. Phys. C: Solid State Phys. 19, 2701 (1986)
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Risken, H. (1987). Solutions of Fokker-Planck Equations in Terms of Matrix Continued Fractions. In: Graham, R., Wunderlin, A. (eds) Lasers and Synergetics. Springer Proceedings in Physics, vol 19. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-72758-0_11
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DOI: https://doi.org/10.1007/978-3-642-72758-0_11
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