Differential Equation Based Path Integral for Open Quantum Systems

We propose the differential equation based path integral method to simulate real-time evolution of open quantum systems. In this method, a system partial equations is derived on continuation classical numerical called iterative quasi-adiabatic propagator (i-QuAPI). While resulting has infinite equations, we introduce reasonable closure obtain series finite New schemes can be by discretizing these equations. It numerically verified that in certain cases, selecting appropriate systems and applying suitable schemes, memory cost required i-QuAPI significantly reduced.