Perturbative computation of nonlinear harvesting through a path integral approach

Abstract

Statistical field theories provide powerful tools to study complex dynamical systems. In this work those tools are used to analyze the dynamics of a kinetic energy harvester, which is modeled by a system of coupled stochastic nonlinear differential equations and driven by colored noise. Using the Martin-Siggia-Rose response fields we analytically approach the problem through path integrals in the phase space and represent the moments that correspond to physical observables through Feynman diagrams. This analysis method is tested by comparing the solution to the linear case with previous analytical results. Through a perturbative expansion it is calculated how the nonlinearity affects, to the first order, the energy harvest supporting the results through numerical simulations.