@article{bibcite_16091,
  author = {Subhajit Sarkar and Gabriela W{\'o}jtowicz and Bart{\l}omiej Gardas and Marek Rams and Michael Zwolak},
  title = {Approaching the scaling limit of transport through lattices with dephasing},
  abstract = {<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{\textquoteright}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>
},
  year = {2025},
  journal = {The Journal of Chemical Physics},
  volume = {163},
  month = {09},
  issn = {0021-9606},
  url = {https://doi.org/10.1063/5.0283282},
  doi = {10.1063/5.0283282},
  language = {eng},
}