Lyapunov instabilities of Lennard-Jones fluids

Abstract

Recent work on many-particle systems reveals the existence of regular collective perturbations corresponding to the smallest positive Lyapunov exponents (LEs), called hydrodynamic Lyapunov modes. Until now, however, these modes have been found only for hard-core systems. Here we report results on Lyapunov spectra and Lyapunov vectors (LVs) for Lennard-Jones fluids. By considering the Fourier transform of the coordinate fluctuation density u((alpha)) (x,t) , it is found that the LVs with lambda approximately equal to 0 are highly dominated by a few components with low wave numbers. These numerical results provide strong evidence that hydrodynamic Lyapunov modes do exist in soft-potential systems, although the collective Lyapunov modes are more vague than in hard-core systems. In studying the density and temperature dependence of these modes, it is found that, when the value of the Lyapunov exponent lambda((alpha)) is plotted as function of the dominant wave number k(max) of the corresponding LV, all data from simulations with different densities and temperatures collapse onto a single curve. This shows that the dispersion relation lambda((alpha)) vs k(max) for hydrodynamical Lyapunov modes appears to be universal for the low-density cases studied here. Despite the wavelike character of the LVs, no steplike structure exists in the Lyapunov spectrum of the systems studied here, in contrast to the hard-core case. Further numerical simulations show that the finite-time LEs fluctuate strongly. We have also investigated localization features of LVs and propose a length scale to characterize the Hamiltonian spatiotemporal chaotic states.