A qualitative study of noise and quantum fluctuations in classical chaotic systems
The effects of noise and quantum fluctuations on chaotic behavior in classical dynamical systems is studied. Using a characterization of chaos due to R.C. Churchill, G. Pecilli, and D.L. Rod, and the idea of a quantum effective potential, it is shown that quantum fluctuations raise the energy threshold for the occurrence of chaos in the Henon-Heiles system and the four-leg potential. Further, using tests for chaotic behavior first developed by V. Melnikov, the quantum effective potential is used to study the effects of quantum fluctuations on the chaotic behavior of a periodically forced scalar field in a Robertson-Walker universe. Also, a new approach to studying noise in chaotic discrete dynamical systems is put forward in this work. It consists of exploiting directly the symbol space isomorphism by adding the noise term onto the shift map itself. It is shown that this noise term has the effect of suppressing the homoclinic sequences at large time, thus destroying the chaos. Lastly, using a generalization of the Melnikov method due to P. Holmes and S. Wiggins, chaotic behavior is shown to exist in the squeezed double-well potential. Due to the symmetry of this potential, quantum fluctuations around the instanton path can be renormalized back into the classical action. This has the effect of lowering the threshold of chaotic behavior.
- Research Organization:
- Texas Univ., Austin, TX (United States)
- OSTI ID:
- 5597274
- Country of Publication:
- United States
- Language:
- English
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