Susceptibility of quasiclassical Brownian motion in harmonic nonlinear potentials

TL;DR

This paper derives exact equations for the response and susceptibility of a Brownian particle in nonlinear harmonic potentials, introducing a recursion method to solve complex nonlinear differential equations in quantum bath systems.

Contribution

It presents a novel recursion method to solve nonlinear response equations for a Brownian particle in quantum harmonic oscillator baths with nonlinear potentials.

Findings

Derived exact response equations for nonlinear harmonic potentials.

Introduced a recursion method for solving nonlinear differential equations.

Analyzed the nonlinear damped Duffing equation for the system.

Abstract

This work sets the exact equations for the quasiclassical response function and susceptibility of a Brownian particle immersed in a bath of quantum harmonic oscillators driving by nonlinear harmonic potentials. A delta force perturbation gives rise to a response whose susceptibility is the combination of a linear term, own of the harmonic oscillator, plus a nonlinear one involving an integral \textcolor{black}{equation. It is provided a recursion method to find its solutions based on functional equations in the Banach space.} The ODE for the response function is a highly nonlinear damped non-autonomous Duffing equation for which the aforementioned method is used to get its solution.