Stable memory kernel coupling theory for quantum dynamics: Projection-based and continued fraction methods

Area of Science:

• Quantum Mechanics
• Computational Physics
• Theoretical Chemistry

Background:

• Non-Markovian quantum dynamics describe systems with memory effects.
• Accurate simulation of these dynamics is crucial for understanding complex quantum systems.
• Existing methods may face challenges with stability and convergence.

Purpose of the Study:

• Introduce two complementary formulations for memory kernel coupling theory (MKCT).
• Develop stable and accurate methods for simulating non-Markovian quantum dynamics.
• Provide a versatile framework for computational quantum physics.

Main Methods:

• Developed a projection-based method (PMKCT) in the time domain for MKCT.
• Introduced a continued fraction representation (CF-MKCT) in the frequency domain.
• PMKCT enforces stability via orthogonal projection; CF-MKCT ensures stability by construction.

Main Results:

• PMKCT removes unstable spectral components for asymptotic stability.
• CF-MKCT achieves high accuracy with few moments (N∼8) and numerical stability.
• Inverse Fourier transform of CF-MKCT yields stable, rapidly converging time-domain solutions.
• Benchmark calculations on the spin-boson model show excellent agreement with exact results.

Conclusions:

• The combined PMKCT and CF-MKCT offer a stable, accurate, and versatile framework.
• These methods significantly advance the simulation of non-Markovian quantum dynamics.
• The approach is validated by successful application to the spin-boson model.