When do perturbative approaches accurately capture the dynamics of complex quantum systems?

Amir Fruchtman,Neill Lambert,Erik M Gauger

doi:10.1038/srep28204

Abstract

Understanding the dynamics of higher-dimensional quantum systems embedded in a complex environment remains a significant theoretical challenge. While several approaches yielding numerically converged solutions exist, these are computationally expensive and often provide only limited physical insight. Here we address the question: when do more intuitive and simpler-to-compute second-order perturbative approaches provide adequate accuracy? We develop a simple analytical criterion and verify its validity for the case of the much-studied FMO dynamics as well as the canonical spin-boson model.

Highlights

Recent years have seen remarkable experimental progress in probing and controlling increasingly larger quantum systems in condensed matter systems[1,2,3]
An important question to address is: when is an approach that is perturbative to second order in the coupling strength ‘good enough’ for capturing the essentials of the dynamics on a qualitative, or even quantitative, level? Here, we develop a criterion for predicting when such an approach is expected to perform well
We consider two different weak-coupling techniques: time convolutionless (TCL) master equations[4] and a second method based on the phase-space representation of the full density matrix[10] (P-mat)

Summary

Introduction

Recent years have seen remarkable experimental progress in probing and controlling increasingly larger quantum systems in condensed matter systems[1,2,3] In this setting it is often not possible to consider the environment as only having a very small perturbative influence on the system of interest. We apply both approaches to the canonical spin boson model[11] as well as the much studied FMO complex[12,13,14,15,16,17] The latter has received a significant amount of attention and is a prime example of the complicated interplay between coherent dynamics interwoven with significant environmental influences. We note that the FMO problem has previously been tackled with weak-coupling techniques[9,15,18,19,20,21], but here we use a novel method and introduce a rigorous criterion for when such approaches are permissible

Methods

Results

Conclusion