Quantum Open System Dynamics in a Nonlinear Environment

The Caldeira-Leggett model has been a paradigm for studying open quantum systems for decades via path-integral methods and subsequent works by Zurek has shown its application in understanding the phenomenon of decoherence. Recently, it has been shown that at the classical level, intrinsic nonlinearity of the environment leads to significant changes in correlations and Langevin dynamics of an open system. The quantum counterpart of such a model, employing a canonical formalism, leads to corrections of the standard Quantum Fluctuation Dissipation Relations (FDR) for a Bosonic bath at finite temperatures. The nonlinearity bears the signature of self interaction of the bath modes. On the other hand, a Feynman-Vernon path-integral evaluation of the problem using perturbative expansion reveals a Quantum Master Equation approximated at suitable limits. The effect on decoherence and dissipation can be surmised from this equation and predictions for realistic self-interacting baths can be made. The issue of system-bath coupling strength also shows different characteristics at weak and strong parameter values.

1. Annals of Physics 149, 374-456 (1983)
2. Journal of Stat. Mech., 043404 (2016)