Local Quantum Cooling for Large Fermi Systems with Pairing

We present a framework for local quantum cooling that can be efficiently applied to large-scale Fermi systems. The method introduces local Hermitian operators as a cooling potential while strictly preserving the unitarity of time evolution. Our formulation scales favorably with system size and can be seamlessly integrated into time-dependent density-functional theory frameworks. We demonstrate that energy cooling 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 thermalization in strongly interacting Fermi superfluids.