Open quantum systems with nonlinear environmental backactions: Extended dissipaton theory versus core-system hierarchy construction

TL;DR

This paper advances quantum dissipation theories by developing extended dissipaton equations of motion and core-system hierarchies for systems with quadratic environmental couplings, enabling accurate thermodynamic relations and efficient simulations.

Contribution

It introduces extended DEOM and core-system hierarchy methods for quadratic environment couplings, enhancing numerical efficiency and visualization of solvation dynamics.

Findings

Extended DEOM reproduces Jarzynski and Crooks relations accurately.

Core-system hierarchy aids in visualizing solvation dynamics.

Extended DEOM is more numerically efficient.

Abstract

In this paper, we present a comprehensive account of quantum dissipation theories with the quadratic environment couplings. The theoretical development includes the Brownian solvation mode embedded hierarchical quantum master equations, a core-system hierarchy construction that verifies the extended dissipaton equation of motion (DEOM) formalism [R. X. Xu et al., J. Chem. Phys. 148, 114103 (2018)]. Developed are also the quadratic imaginary-time DEOM for equilibrium and the {\lambda} (t)-DEOM for nonequilibrium thermodynamics problems. Both the celebrated Jarzynski equality and Crooks relation are accurately reproduced, which in turn confirms the rigorousness of the extended DEOM theories. While the extended DEOM is more numerically efficient, the core-system hierarchy quantum master equation is favorable for ''visualizing'' the correlated solvation dynamics.