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.
Ulfa et al. (Thu,) studied this question.
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