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Butkovskii O.Ya., Kravtsov Yu.A.

Spontaneous symmetry breaking and predictability
for nonadiabatic transition

O.Ya. Butkovskii tex2html_wrap_inline2366 , Yu.A. Kravtsov tex2html_wrap_inline2370
tex2html_wrap_inline2366 Vladimir State Tech. Univ.;
tex2html_wrap_inline2370 Space Res. Inst., Russ. Acad. Sci.

The problem of symmetry breaking under bifurcation transition is investigated. It is shown that the one of two final states which are usually assumed to be equiprobable may be realized with a probability close to unity if transition is caring out with a finite speed. The probability of the final state depends on the relationship between speed of the transition and the noise level in the system.

By the example of the logistic map there was numerically investigated the transition through the first doubling period bifurcation. It was revealed that the probability of transition into the determined final state may vary from unity, what corresponds to the fast noiseless transition with symmetry breaking, to probability 1/2, when the transition is rather slow and results in symmetrical distribution over possible states.

The transition with symmetry breaking is shown to be separated from the equiprobable states by a rather narrow border, which is totally determined by the relationship between the transition speed and the noise level. A number of physical situations are considered for the illustration of the bifurcation paradox.



Book of abstracts
ICND-96