Microscopic derivation of driving-resonance scales

Derive the microscopic origins and numerical prefactors of the low- and high-boundary-driving resonance scales in the strongly interacting boundary-driven Fermi-Hubbard chain from the underlying many-body dynamics.

Background

The paper identifies two current resonances as functions of the boundary driving rate in the strongly interacting Fermi-Hubbard chain. The low-driving resonance scales with the superexchange energy as approximately $2J_{\mathrm{ex}}/N$, whereas the high-driving resonance scales with the interaction energy stored in a doublon-rich domain as approximately $NU/2$.

The authors provide phenomenological interpretations for these scales: the low-driving resonance is associated with the onset of a subdiffusive regime and the superexchange scale, while the high-driving resonance is associated with collective reorganization and dissolution of the doublon-rich domain. A first-principles derivation of these scales and their numerical coefficients from the full many-body dynamics remains unresolved.