Non--Equilibrium Transport in Open Quantum Systems via Dynamically Constrained non--Hermitian Boundary Domains

The accurate simulation of real--time quantum transport is notoriously difficult, requiring a consistent scheme to treat incoming and outgoing fluxes at the boundary of an open system. We demonstrate a method to converge non--equilibrium steady states using non--Hermitian source and sink potentials alongside the application of dynamic density constraints during wavefunction propagation. This scheme adds negligible cost to existing computational methods while exhibiting exceptional stability and numerical accuracy.