Susceptibility of quasiclassical Brownian motion in harmonic nonlinear potentials

• URL: http://arxiv.org/abs/2012.04033v1
• Date: Mon, 7 Dec 2020 20:16:27 GMT
• Title: Susceptibility of quasiclassical Brownian motion in harmonic nonlinear potentials
• Authors: Pedro J. Colmenares
• Abstract summary: 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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