Real-Time Path Integral Methods, Quantum Master Equations, and Classical vs Quantum Memory.

Area of Science:

• Quantum dynamics
• Computational chemistry
• Theoretical physics

Background:

• Generalized quantum master equations (GQME) describe open quantum systems.
• Memory kernels are crucial for accurately capturing system-bath interactions.
• Path integral methods offer alternative approaches to quantum dynamics.

Purpose of the Study:

• To investigate the accuracy of quasi-adiabatic propagator path integral (QuAPI) and quantum-classical path integral (QCPI) methods for generating GQME memory kernels.
• To compare the memory kernel lengths obtained from QuAPI and QCPI with the Feynman-Vernon influence functional.
• To assess the ability of these methods to capture long-timescale dynamics.

Main Methods:

• Implementation of QuAPI and QCPI for generating memory kernels.
• Solution of GQME using QuAPI-generated kernels.
• Iterative QuAPI and QCPI calculations.
• Comparison of memory kernel lengths and simulation results.

Main Results:

• The memory kernel length in system-bath models equals the time nonlocality of the Feynman-Vernon influence functional.
• GQME solutions with QuAPI kernels match iterative QuAPI calculations.
• Iterative QCPI calculations yield shorter memory lengths than GQME kernels.
• QCPI effectively treats classical memory effects and some quantum contributions.

Conclusions:

• QuAPI accurately generates GQME memory kernels, yielding identical results to iterative QuAPI.
• QCPI offers computational advantages by reducing memory length through pretreatment of classical and some quantum memory effects.
• Trajectory-based QCPI simulations can capture long-timescale structural changes beyond the scope of master equation treatments.