Pushing the limits of the reaction-coordinate mapping

Correa, Luis A.; Xu, Buqing; Morris, Benjamin; Adesso, Gerardo

Abstract

The reaction-coordinate mapping is a useful technique to study complex quantum dissipative dynamics into structured environments. In essence, it aims to mimic the original problem by means of an “augmented system,” which includes a suitably chosen collective environmental coordinate—the “reaction coordinate.” This composite then couples to a simpler “residual reservoir” with short-lived correlations. If, in addition, the residual coupling is weak, a simple quantum master equation can be rigorously applied to the augmented system, and the solution of the original problem just follows from tracing out the reaction coordinate. But, what if the residual dissipation is strong? Here, we consider an exactly solvable model for heat transport—a two-node linear “quantum wire” connecting two baths at different temperatures. We allow for a structured spectral density at the interface with one of the reservoirs and perform the reaction-coordinate mapping, writing a perturbative master equation for the augmented system. We find that (a) strikingly, the stationary state of the original problem can be reproduced accurately by a weak-coupling treatment even when the residual dissipation on the augmented system is very strong, (b) the agreement holds throughout the entire dynamics under large residual dissipation in the overdamped regime; and (c) such a master equation can grossly overestimate the stationary heat current across the wire, even when its nonequilibrium steady state is captured faithfully. These observations can be crucial when using the reaction-coordinate mapping to study the largely unexplored strong-coupling regime in quantum thermodynamics.

Citation

Correa, L. A., Xu, B., Morris, B., & Adesso, G. (2019). Pushing the limits of the reaction-coordinate mapping. Journal of Chemical Physics, 151(9), Article 094107. https://doi.org/10.1063/1.5114690

• Journal Article Type: Article
• Acceptance Date: Aug 11, 2019
• Online Publication Date: Sep 6, 2019
• Publication Date: Sep 7, 2019
• Deposit Date: Sep 13, 2019
• Publicly Available Date: Sep 7, 2020
• Journal: The Journal of Chemical Physics
• Print ISSN: 0021-9606
• Electronic ISSN: 1089-7690
• Publisher: American Institute of Physics
• Peer Reviewed: Peer Reviewed
• Volume: 151
• Issue: 9
• Article Number: 094107
• DOI: https://doi.org/10.1063/1.5114690
• Keywords: Physical and Theoretical Chemistry; General Physics and Astronomy
• Public URL: https://nottingham-repository.worktribe.com/output/2613856
• Publisher URL: https://aip.scitation.org/doi/10.1063/1.5114690
• Additional Information: This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Pushing the limits of the reaction-coordinate mapping, Luis A. Correa, Buqing Xu, Benjamin Morris, and Gerardo Adesso, ; The Journal of Chemical Physics 151:9 and may be found at https://aip.scitation.org/doi/abs/10.1063/1.5114690.