Formation of fractal structure in many-body systems with attractive power-law potentials.

ABSTRACT

We study the formation of fractal structure in one-dimensional many-body systems with attractive power-law potentials. Numerical analysis shows that the range of the index of the power for which fractal structure emerges is limited. Dependence of the growth rate on wave number and power-index is obtained by linear analysis of the collisionless Boltzmann equation, which supports the numerical results.