Partition-free approach to open quantum systems in harmonic environments: an exact stochastic Liouville equation

TL;DR

This paper introduces an exact, partition-free method for modeling the evolution of open quantum systems coupled to harmonic environments, using a novel stochastic Liouville equation that generalizes previous models.

Contribution

The authors develop a new exact differential equation framework for open quantum systems that does not require initial partitioning, extending previous models to more general initial conditions.

Findings

Derivation of the Extended Stochastic Liouville-von Neumann equation

Applicable to systems with equilibrated initial conditions

Potential for efficient numerical simulations

Abstract

We present a partition-free approach to the evolution of density matrices for open quantum systems coupled to a harmonic environment. The influence functional formalism combined with a two-time Hubbard-Stratonovich transformation allows us to derive a set of exact differential equations for the reduced density matrix of an open system, termed the Extended Stochastic Liouville-von Neumann equation. Our approach generalises previous work based on Caldeira-Leggett models and a partitioned initial density matrix. This provides a simple, yet exact, closed-form description for the evolution of open systems from equilibriated initial conditions. The applicability of this model and the potential for numerical implementations are also discussed.