Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2003-12-20
Nonlinear Sciences
Chaotic Dynamics
12 pages revtex, 5 figures, accepted by Physical Review E
Scientific paper
10.1103/PhysRevE.70.016207
In this paper, we demonstrate how the Lyapunov exponents close to zero of a system of many hard spheres can be described as Goldstone modes, by using a Boltzmann type of approach. At low densities, the correct form is found for the wave number dependence of the exponents as well as for the corresponding eigenvectors in tangent-space. The predicted values for the Lyapunov exponents belonging to the transverse mode are within a few percent of the values found in recent simulations, the propagation velocity for the longitudinal mode is within 1%, but the value for the Lyapunov exponent belonging to the longitudinal mode deviates from the simulations by 30%. For higher densities, the predicted values deviate more from the values calculated in the simulations. These deviations may be due to contributions from ring collisions and similar terms, which, even at low densities, can contribute to the leading order.
Beijeren Henk van
de Wijn Astrid S.
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