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This work sets the exact equations for the quasiclassical response functionand susceptibility of a Brownian particle immersed in a bath of quantumharmonic oscillators driving by nonlinear harmonic potentials. A delta forceperturbation gives rise to a response whose susceptibility is the combinationof a linear term, own of the harmonic oscillator, plus a nonlinear oneinvolving an integral \textcolor{black}{equation. It is provided a recursionmethod to find its solutions based on functional equations in the Banachspace.} The ODE for the response function is a highly nonlinear dampednon-autonomous Duffing equation for which the aforementioned method is used toget its solution.

Susceptibility of quasiclassical Brownian motion in harmonic nonlinear potentials