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})=A{γ} exp(t/τL), where τL 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.