Path integral description and direct interaction approximation for elastic plate turbulence

In this work, we apply the Martin-Siggia-Rose path integral formalism to equations of a thin elastic plate. Using diagrammatic technique, obtain direct interaction approximation (DIA) describe evolutions correlation function and response fields. Consistent with previous results, show that DIA for plates can be derived from non-markovian stochastic process in weakly nonlinear limit, lead kinetic equation wave turbulence theory. We expect approach will allow better understanding statistical properties open new avenues breakdown plates.