Twin-Space Representation of Classical Mapping Model in the Constraint Phase Space Representation: Numerically Exact Approach to Open Quantum Systems

TL;DR

This paper introduces an exact trajectory-based phase space method using twin-space formulation and classical mapping to accurately simulate open quantum system dynamics in condensed phases.

Contribution

It develops a novel twin-space (TS) formulation combined with classical mapping models to improve numerical convergence and accuracy in open quantum system simulations.

Findings

Accurately reproduces population dynamics of benchmark models.

Yields nonlinear spectra consistent with hierarchical equations of motion.

Addresses long-time convergence issues in condensed phase simulations.

Abstract

The constraint coordinate-momentum \textit{phase space} (CPS) has recently been developed to study nonadiabatic dynamics in gas-phase and condensed-phase molecular systems. Although the CPS formulation is exact for describing the discrete (electronic/ vibrational/spin) state degrees of freedom (DOFs), when system-bath models in condense phase are studied, previous works often employ the discretization of environmental bath DOFs, which breaks the time irreversibility and may make it difficult to obtain numerically converged results in the long-time limit. In this paper, we develop an exact trajectory-based phase space approach by adopting the twin-space (TS) formulation of quantum statistical mechanics, in which the density operator of the reduced system is transformed to the wavefunction of an expanded system with twice the DOFs. The classical mapping model (CMM) is then used to map the Hamiltonian of the expanded system to its equivalent classical counterpart on CPS. To demonstrate the applicability of the TS-CMM approach, we compare simulated population dynamics and nonlinear spectra for a few benchmark condensed phase system-bath models with those obtained from the hierarchical equations of motion method, which shows that our approach yields accurate dynamics of open quantum systems.