Higher-order solutions to non-Markovian quantum dynamics via hierarchical functional derivative

TL;DR

This paper introduces a hierarchical functional derivative method for efficiently solving non-Markovian quantum dynamics in open systems, providing explicit equations and exact solutions for certain models.

Contribution

The authors develop a systematic hierarchical functional derivative approach that simplifies solving non-Markovian quantum trajectories, including exact solutions for specific models.

Findings

Hierarchical equations terminate at a finite order for certain models

Explicit expressions for arbitrary order HFD equations are derived

The method efficiently captures non-Markovian quantum dynamics

Abstract

Solving realistic quantum systems coupled to an environment is a challenging task. Here we develop a hierarchical functional derivative (HFD) approach for efficiently solving the non-Markovian quantum trajectories of an open quantum system embedded in a bosonic bath. An explicit expression for arbitrary order HFD equation is derived systematically. Moreover, it is found that for an analytically solvable model, this hierarchical equation naturally terminates at a given order and thus becomes exactly solvable. This HFD approach provides a systematic method to study the non-Markovian quantum dynamics of an open system coupled to a bosonic environment.