Title:	Perturbation theory for stochastic nonlinear oscillators and Feynman diagram
Authors:	Pal, Akshay Bhattacharjee, Jayanta, K
Keywords:	Non linear oscillators Stochastic processes Feynman Diagrams Linear response theory Langevin Equation
Issue Date:	Dec-2023
Publisher:	Elsevier
Citation:	Annals of Physics, 2023, Vol.459, p169495
Abstract:	We show that a systematic perturbation theory for the class of stochastically driven nonlinear oscillator ̈ 𝑥 + 2𝛤 ̇ 𝑥 + 𝜔20 𝑥 + 𝜇𝑥2 + 𝜆𝑥3 = 𝑓(𝑡) where f(t) is a Gaussian white noise can be effectively developed by writing down the relevant Feynman diagrams using response function and correlation functions. For 𝜇 = 0, we find that the response function acquires a non- Lorentzian shape at 𝑂(𝜆2). This is a qualitative shift in the response. For 𝜆 << 1 and 𝜇 ≠ 0, we show that a particle located at the minimum of a potential well can cross the barrier within a perturbative approach.
Description:	Restricted Access. An open-access version is available at arXiv.org (one of the alternative locations)
URI:	http://hdl.handle.net/2289/8210
ISSN:	0003-4916 (print) 1096-035X (online)
Alternative Location:	http://arxiv.org/abs/ https://doi.org/10.1016/j.aop.2023.169495 http://adsabs.harvard.edu/abs/
Copyright:	2023, The Publisher
Appears in Collections:	Research Papers (TP)

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