Physics
Scientific paper
Nov 1990
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990phya..169...73k&link_type=abstract
Physica A, Volume 169, Issue 1, p. 73-94.
Physics
23
Scientific paper
Time-dependent solutions to the gravitational N-body problem are unstable in the sense that small initial perturbations tend to be amplified exponentially. This fact, well known from numerical simulations, was ``explained'' by Gurzadyan and Savvidy, who argued that this instability implies that an N-body system will tend to ``mix'' on a time scale τGS ~ N1/3tD, where tD is a typical crossing time. It is shown here that the prediction of Gurzadyan and Savvidy of a ``mixing'' is right, but that, allowing correctly for the large scale bulk forces present in a self-gravitating system, one anticipates that the effects of this ``mixing'' should be manifest already on a much shorter time scale ~tD. It is argued that the result of this ``coarse-grained'' mixing on a time scale ~tD should be consistent, at least broadly, with the expected outcome of an epoch of ``violent relaxation''. It is also emphasized that this time scale τ must be interpreted in an appropriate ``average'' sense since, as has been observed, e.g., by R.H. Miller, there exist (admittedly special) perturbations which can be amplified on time scales as short as N-1/2tD.
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