Minimal Model for an Energy Cascades in Driven Nonequilibrium Systems

Complex systems that are fed energy at their constituent-level frequently exhibit self-organizational and emergent properties. The external driving can be periodic, but more commonly it comes in the form of noise. Here we show how a spatially extended layer of charged particles exhibits intermittent switching between crystalline and gas-like states. The particles are driven by individual charge fluctuations which feed energy into one vibrational degree of freedom. A small amount of disorder leads to recurrent energy cascades (melting) in the system. Using normal mode analysis, we show that the fraction of vertical vibrational modes with low participation ratio determine the response of the system to the noisy driving. We propose a minimal model of the transfer of the kinetic energy between vertical and horizontal degrees of freedom using modified Lotka-Volterra equations. The model reproduces all of the salient features of the energy cascades observed in the experiment and simulation. Similar to the Reynolds number in fluid flow, we characterize a dimensionless number that is the ratio of the energy input and dissipation. Intermittent energy cascades are observed for a narrow range of this number, in striking resemblance to transition to turbulence in pipe flow.