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

Wei Liu1, Rui-Hao Bi1, Yu Su2

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Summary
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We present two new methods, projection-based (PMKCT) and continued fraction (CF-MKCT), for simulating non-Markovian quantum dynamics. These stable and accurate techniques offer a versatile framework for complex quantum system analysis.

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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.