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Understanding transport in interacting quantum many-body systems is a central challenge in condensed matter and statistical physics. Numerical studies typically rely on two main approaches: Dynamics of linear-response functions in closed systems and Markovian dynamics governed by master equations for boundary-driven open systems. While the equivalence of their dynamical behavior has been explored in recent studies [1], a systematic comparison of the transport coefficients obtained from these two classes of methods remains an open question. Here [2], we address this gap by comparing and contrasting the dc diffusion constant $\mathcal{D}_{\text{dc}}$ computed from the aforementioned two approaches. We find a clear mismatch between the two, with $\mathcal{D}_{\text{dc}}$ exhibiting a strong dependence on the system-bath coupling for the boundary-driven technique, highlighting fundamental limitations of such a method in calculating the transport coefficients related to the asymptotic dynamical behavior of the system. We trace the origin of this mismatch to the incorrect order of limits of time $t \rightarrow \infty$ and system size $L\rightarrow \infty$, which we argue to be intrinsic to boundary-driven setups. As a practical resolution, we advocate computing only time-dependent transport coefficients within the boundary-driven framework, which show excellent agreement with those obtained from the Kubo formalism based on closed-system dynamics, up to a time scale set by the system size. This leads us to interpret the sensitivity of the dc diffusion constant on the system-bath coupling strength in an open system as a potential diagnostic for finite-size effects.
[1] T. Heitmann, J. Richter, F. Jin, S. Nandy, Z. Lenarčič, J. Herbrych, K. Michielsen, H. De Raedt, J. Gemmer, R. Steinigeweg, Phys. Rev. B 108, L201119 (2023).
[2] M. Kempa, M. Kraft, S. Nandy, J. Herbrych, J. Wang, J. Gemmer, R. Steinigeweg, arXiv:2507.16528.
