On the memory kernel and the reduced system propagator.

Area of Science:

• Theoretical chemistry
• Condensed matter physics
• Quantum dynamics

Background:

• The Nakajima-Zwanzig-Mori (NZM) and Tokuyama-Mori (TM) approaches are established methods for describing open quantum systems.
• Calculating the memory kernel is crucial for both formalisms but can be computationally demanding.
• Existing methods often require high-order system-bath observables, limiting their applicability.

Purpose of the Study:

• To establish a direct relationship between the memory kernel in the NZM approach and the reduced system propagator in the TM approach.
• To develop a simplified and robust formalism for computing the memory kernel.
• To facilitate the use of numerically exact solvers for memory kernel calculations.

Main Methods:

• Relating the memory kernel of the NZM approach to the reduced system propagator of the TM approach.
• Developing a generalized system-bath model.
• Applying the formalism to a model system with electron-electron and electron-phonon couplings.

Main Results:

• A direct connection between the NZM memory kernel and the TM reduced system propagator was established.
• The proposed formalism simplifies the computation of the memory kernel.
• The method circumvents the need for high-order system-bath observables.

Conclusions:

• The established connection offers a robust and straightforward method for memory kernel computation.
• This work streamlines the application of numerically exact solvers for complex quantum systems.
• The findings are demonstrated for a driven, non-equilibrium model system with significant couplings.