Lyapunov modes in soft-disk systems
  Lyapunov modes are periodic spatial perturbations of phase-space states of many-particle systems, which are associated with the small positive or negative Lyapunov exponents. Although familiar for hard-particle systems in one, two, and three dimensions, they have been difficult to find for soft-particles. We present computer simulations for soft-disk systems in two dimensions and demonstrate the existence of the modes, where also Fourier-transformation methods are employed. We discuss some of their properties in comparison with equivalent hard-disk results. The whole range of densities corresponding to fluids is considered. We show that it is not possible to represent the modes by a two-dimensional vector field of the position perturbations alone (as is the case for hard disks), but that the momentum perturbations are simultaneously required for their characterization. 
Christina Forster and Harald A. Posch