Local Quantum Friction with Pairing: Unitary Dissipation in Large Fermi Systems

We present a unitary framework for dissipative quantum dynamics that can be efficiently applied to large-scale Fermi systems. The method introduces local Hermitian operators that emulate frictional forces while strictly preserving the unitarity of time evolution. Unlike approaches based on the Lindblad equation, our formulation scales favorably with system size and can be seamlessly integrated into time-dependent density functional theory frameworks. We demonstrate that energy dissipation arises from the damping of particle currents and pairing-field fluctuations. Furthermore, we develop a variant of the scheme that allows the particle number to vary in time, enabling controlled density scans. The method is generic and versatile, as illustrated by applications to spin-imbalanced unitary Fermi gases and to nuclear matter in the neutron-star crust. The framework can be naturally extended to include stochastic noise, providing a foundation for studying fluctuation-dissipation dynamics and thermalization in strongly interacting Fermi superfluids.