Wave turbulence and the kinetic equation beyond leading order
We derive a scheme by which to solve the Liouville equation perturbatively in the nonlinearity, which we apply to weakly nonlinear classical field theories. Our solution is a variant of the Prigogine diagrammatic method, and is based on an analogy between the Liouville equation in infinite volume and scattering in quantum mechanics, described by the Lippmann-Schwinger equation. The motivation for our work is wave turbulence: a broad class of nonlinear classical field theories are believed to ha…