We develop a stochastic Schrödinger equation (SSE) framework to simulate the real-time dynamics of Anderson-Holstein (AH) impurities coupled to a continuous Fermionic bath. The bath degrees of freedom are incorporated through fluctuating terms determined by exact system-bath correlations, which is derived in an ab initio manner. We show that such an SSE treatment provides a middle ground between numerically expansive microscopic simulations and macroscopic master equations. Computationally, the SSE model enables efficient numerical methods for propagating stochastic trajectories. We demonstrate that this approach not only naturally provides microscopically detailed information unavailable from reduced models but also captures effects beyond master equations, thus serving as a promising tool to study open quantum dynamics emerging in physics and chemistry.
Microscopic master equations have gained traction for the dissipative treatment of molecular spin and solid-state systems for quantum technologies. Single particle approximations are often invoked to treat these systems, which can lead to unphysical evolution when combined with master equation approaches. We present a mathematical constraint on the system-environment parameters to ensure that microscopically-derived Markovian master equations preserve fermionic,
N-representable statistics when applied to reduced systems. We demonstrate these constraints for the recently derived unified master equation and universal Lindblad equation, along with the Redfield master equation for cases when positivity issues are not present. For operators that break the constraint, we explore the addition of Pauli factors to recover
N-representability. This work promotes feasible applications of novel microscopic master equations for realistic chemical systems.
An effective boson Hamiltonian is derived from the original Hamiltonian of a many-fermion system. The results show that when the intrinsic motion of bosons is collective and the excitation energies of the system are small, the effective boson-boson interaction can be reduced to a two-body interaction while for odd systems or systems with uncorrelated fermions, there is an additional two-body boson-fermion interaction. Both these interactions can be calculated from the original fermion-fermion ones. Thus, the microscopic foundation of the interacting boson model is established without recourse to mapping procedures.NUCLEAR STRUCTURE Interacting boson model, boson fermion hybrid representation, microscopic foundation.