Bosonic quantum transport with power-law coupling: Single-particle versus many-body treatment

¹ Department of Physics, Faculty of Mathematics and Natural Science, Jakarta State University, East Jakarta 13220, Indonesia
² Research Center for Quantum Physics, National Research and Innovation Agency (BRIN), South Tangerang 15314, Indonesia
³ Asia Pacific Center for Theoretical Physics, Pohang Science and Technology University, Pohang 37673, South Korea

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Published online: 2 July 2026

Abstract

Simulating boundary-driven quantum transport in open systems is quadratically more complex compared to an isolated quantum system, which already contains exponentially growing time-complexity as the number of sites grows. To efficiently solve the Lindblad master equation, one may restrict attention to the single-excitation problem, effectively mapping the problem to a tight-binding model or retain the many-body description by working with the covariance matrix via the Lyapunov equation. We show numerically for bosonic systems that these two approaches do not agree in general, except in a specific limit that is rarely stated explicitly: the dilute limit where the injection rate is much smaller than the extraction rate. We identify the regime for when each the single-particle sector is applicable.