Lyapunov instability and collective tangent space dynamics of fluids

Abstract

The phase space trajectories of many body systems charateristic of simple fluids are highly unstable. We quantify this instability by a set of Lyapunov exponents, which are the rates of exponential divergence, or convergence, of initial (infinitesimal) perturbations along carefully selected directions in phase space. It is demonstrated that the perturbation associated with the maximum Lyapunov exponent is localized in space. This localization persists in the large-particle limit, regardless of the interaction potential. The perturbations belonging to the smallest positive exponents, however, are sensitive to the potential. For hard particles they form well-defined long-wavelength modes. The modes could not be observed for systems interacting with a soft potential due to surprisingly large fluctuations of the local time-dependent exponents.