Nonstandard mixing in the standard map

Details Nonstandard mixing in the standard map Nonstandard mixing in the standard map

2001-08-29

arxiv.org/abs/cond-mat/0108501v2

Physics

Condensed Matter

Statistical Mechanics

latex, 11 pages, 5 figures

Scientific paper

The standard map is a paradigmatic one-parameter (noted $a$) two-dimensional conservative map which displays both chaotic and regular regions. This map becomes integrable for $a=0$. For $a \ne 0$ it can be numerically shown that the usual, Boltzmann-Gibbs entropy $S_1(t)=-\sum_{i} p_i(t)\ln{p_i(t)}$ exhibits a {\it linear} time evolution whose slope hopefully converges, for very fine graining, to the Kolmogorov-Sinai entropy. However, for increasingly small values of $a$, an increasingly large time interval emerges, {\it before} that stage, for which {\it linearity} with $t$ is obtained only for the generalized nonextensive entropic form $S_q(t)=\frac{1-\sum_{i}[p_i(t)]^{q}}{q-1}$ with $q = q^*\simeq 0.3$. This anomalous regime corresponds in some sense to a power-law (instead of exponential) mixing. This scenario might explain why in isolated classical long-range $N$-body Hamiltonians, and depending on the initial conditions, a metastable state (whose duration diverges with $1/N\to 0$) is observed before it crosses over to the BG regime.

Affiliated with

Also associated with

No associations

Rating

Nonstandard mixing in the standard map does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Nonstandard mixing in the standard map, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Nonstandard mixing in the standard map will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-594854