Interplay of Nonlinearity and Strength of Coupling in Classical Open Systems

At the classical level, the theory of open system dynamics is characterised by Fluctuation Dissipation Relations (FDR) and Generalised Langevin Equation (GLE). The presence of system nonlinearities has been studied extensively to understand many phenomena in open physical and chemical systems. Here, we show the interplay between the coupling of a probe system and a nonlinear thermal environment, the latter requiring a perturbative treatment due to lack of exact solutions. On one hand, a weak system-bath coupling study reveals the robustness of FDR at zeroeth order with perturbative corrections. The motion is described by an effective GLE with dissipation functions showing non-trivial temperature dependence. The other limit, ie. the strong coupling scenario, drastically extends the standard FDR and breaks time-translation invariance of the noise-correlations. Moreover, the GLE provides non-linear velocity-dependent damping kernels leading to new dynamical fixed points perturbed via nonlinear, nonlocal noise.

References:
1. Bhadra et al., Journal of Stat. Mech, 2016, doi:10.1088/1742-5468/2016/04/043404
2. Bhadra et al., arXiv:1710:10691