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- W1497443396 abstract "Through molecular dynamics, we study the $d=2,3$ classical model of $N$ coupled rotators (inertial XY model) assuming a coupling constant which decays with distance as $r_{ij}^{-alpha}$ ($alpha ge 0$). The total energy $ $ is asymptotically $propto N {tilde N}$ with ${tilde N} equiv [N^{1-alpha/d}-(alpha/d)]/[1-alpha/d]$, hence the model is thermodynamically extensive if $alpha/d>1$ and nonextensive otherwise. We numerically show that, for energies above some threshold, the (appropriately scaled) maximum Lyapunov exponent is $propto N^{-kappa}$ where $kappa$ is an {it universal} (one and the same for $d=1,2$ and 3, and all energies) function of $alpha/d$, which monotonically decreases from 1/3 to zero when $alpha/d$ increases from 0 to 1, and identically vanishes above 1. These features are consistent with the nonextensive statistical mechanics scenario, where thermodynamic extensivity is associated with {it exponential} mixing in phase space, whereas {it weaker} (possibly {it power-law} in the present case) mixing emerges at the $N to infty$ limit whenever nonextensivity is observed." @default.
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- W1497443396 date "2000-07-06" @default.
- W1497443396 modified "2023-09-27" @default.
- W1497443396 title "Long-range interacting classical systems: universality in mixing weakening" @default.
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