Energy localization in pumped systems

Considering a local nonlinear oscillator interacting with a chain of coupled Linear oscillators, we demonstrate that the dynamics of the local oscillator is characterized by a frequency-dependent damping constant, related to the frequency-dependent density of states of the linear modes. Further, we demonstrate how this intrinsic damping provides possibilities for multiple steady states of the nonlinear oscillator, and how these steady states may create local potentials for electrons that are adiabatically coupled with the linear modes. Finally, the implications on coarse-grained mode-ling of hard, softy and biological matter are discussed.