Crossover between equilibrium and shear-controlled dynamics in sheared liquids

We present a numerical simulation study of a simple monatomic Lennard-Jones liquid under shear flow, as a function of both temperature T and shear rate (gamma) over dot. By investigating different observables we find that (i) there exists a line, T-(gamma) over dot, in the (T-(gamma) over dot) plane that sharply marks the border between an "equilibrium" and a "shear-controlled" region for both the dynamic and the thermodynamic quantities; and (ii) along this line the structural relaxation time, tau(alpha)(T-(gamma) over dot), is proportional to (gamma) over dot(-1), i.e., to the typical time scale introduced by the shear flow. Above T-(gamma) over dot, the liquid dynamics is unaffected by the shear flow, while below T-(gamma) over dot both T and (gamma) over dot control the particle motion.