01649nas a2200193   4500000000100000000000100001008004100002260000700043100002000050700002400070700002300094700001500117700001900132245007900151856003800230490000800268520116500276022001401441       2025                            d  c091 aSubhajit Sarkar1 aGabriela Wójtowicz1 aBartłomiej Gardas1 aMarek Rams1 aMichael Zwolak00aApproaching the scaling limit of transport through lattices with dephasing  uhttps://doi.org/10.1063/5.02832820 v1633 a<p>We examine the stationary-state equations for lattices with generalized Markovian dephasing and relaxation. When the Hamiltonian is quadratic, the single-particle correlation matrix has a closed system of equations even in the presence of these two processes. The resulting equations have a vectorized form related to, but distinct from, Lyapunov’s equation. We present an efficient solution that helps to achieve the scaling limit, e.g., of the current decay with lattice length. As an example, we study the super-diffusive-to-diffusive transition in a lattice with long-range hopping and dephasing. The approach enables calculations with up to 104 sites, representing an increase of 10 to 40 times over prior studies. This enables a more precise extraction of the diffusion exponent, enhances agreement with theoretical results, and supports the presence of a phase transition. There is a wide range of problems that have Markovian relaxation, noise, and driving. They include quantum networks for machine-learning-based classification and extended reservoir approaches for transport. The results here will be useful for these classes of problems.</p>
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