System-reservoir theory with anharmonic baths: a perturbative approach

作者：Bhadra Chitrak; Banerjee Dhruba^*

来源：Journal of Statistical Mechanics: Theory and Experiment , 2016, 2016(4): 043404.

DOI：10.1088/1742-5468/2016/04/043404

• nonlinear dynamics
• correlation functions
• stochastic particle dynamics (theory)

In this paper we develop the formalism of a general system coupled to a reservoir (the words 'bath' and 'reservoir' will be used interchangeably) consisting of nonlinear oscillators, based on perturbation theory at the classical level, by extending the standard Zwanzig approach of elimination of bath degrees of freedom order by order in perturbation. We observe that the fluctuation dissipation relation (FDR) of the second kind in its standard form for harmonic baths gets modified due to the nonlinearity and this is manifested through higher powers of k(B)T in the expression for two-time noise correlation. On the flip side, this very modification allows us to define a dressed (renormalized) system-bath coupling that depends on the temperature and the nonlinear parameters of the bath in such a way that the structure of the FDR (of the second kind) is maintained. As an aside, we also observe that the first moment of the noise arising from a nonlinear bath can be non-zero, even in the absence of any external drive, if the reservoir potential is asymmetric with respect to one of its minima, about which one builds up the perturbation theory.

• 出版日期2016-4