Linear response of phase-space trajectories to shearing

The influence of the Lyapunov instability on a trajectory in phase space is investigated numerically for a Lennard-Jones fluid under a constant shear rate γ. The time dependence of the distance d(t,γ;Γ) between two individual trajectories, starting at the same phase point Γ, but moving either with or without an imposed shear, can be described by d(t,γ;Γ)=Aγ exp(t/${\mathrm{\tau }}_{\mathrm{L}}$), where ${\mathrm{\tau }}_{\mathrm{L}}$ is the inverse of the largest Lyapunov exponent of the system without shear. A possible explanation of this behavior and the consequences for the validity of linear-response theory are discussed.