Stochastic Systems

  • L. E. Reichl
Part of the Institute for Nonlinear Science book series (INLS)

Abstract

Until now in this book, we have focused on the transition in the dynamical behavior of conservative classical and quantum systems (the transition to chaos) which occurs when constants of the motion are destroyed by internal resonances. There is now some evidence that similar behavior may occur in stochastic systems as well. In this chapter we shall describe some of these preliminary results.

Keywords

Stochastic System Langevin Equation Brownian Rotor Random Matrix Theory Complex Eigenvalue 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Chen, Z.-Y. (1990): Phys. Rev. A42 5837.ADSCrossRefGoogle Scholar
  2. Gardiner, C.W. (1983): Handbook of Stochastic Methods (Springer-Verlag, Berlin)MATHCrossRefGoogle Scholar
  3. Ginibre, J. (1965): J. Math. Phys. 6 440.MathSciNetADSMATHCrossRefGoogle Scholar
  4. Grobe, R., Haake, F., and Sommers, H.-J., (1988): Phys. Rev. Lett. 61 1899.MathSciNetADSCrossRefGoogle Scholar
  5. Haake, F. (1990): The Quantum Signatures of Chaos (Springer-Verlag, Berlin).Google Scholar
  6. Leonard, D. and Reichl, L.E. (1990): J. Chem. Phys. 92 6004.ADSCrossRefGoogle Scholar
  7. Ramshaw, J.D. and Lindenberg, K. (1986): J. Stat. Phys. 45 295.MathSciNetADSCrossRefGoogle Scholar
  8. Reichl, L.E., Chen, Z.-Y., and Millonas, M.M. (1989): Phys. Rev. Lett. 63 2013.ADSCrossRefGoogle Scholar
  9. Reichl, L.E., Chen, Z.-Y., and Millonas, M.M. (1990): Phys. Rev. A41 1874.MathSciNetADSCrossRefGoogle Scholar
  10. van Kampen, N.G. (1981): Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam).MATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • L. E. Reichl
    • 1
  1. 1.Center for Statistical Mechanics and Complex Systems, Department of PhysicsUniversity of Texas at AustinAustinUSA

Personalised recommendations