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Updated: May 7, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
Stable memory kernel coupling theory for quantum dynamics: Projection-based and continued fraction methods
Wei Liu1, Rui-Hao Bi1, Yu Su2
1Department of Chemistry, School of Science and Research Center for Industries of the Future, Westlake University, Hangzhou, Zhejiang 310030, China.
Abstract:
We introduce two complementary formulations within memory kernel coupling theory (MKCT) for non-Markovian quantum dynamics: a projection-based method (PMKCT) in the time domain and a continued fraction representation (CF-MKCT) in the frequency domain. The PMKCT operates on the matrix representation of MKCT and enforces asymptotic stability by removing unstable spectral components through orthogonal projection. The CF-MKCT yields a rapidly convergent representation, achieving high accuracy with only N ∼ 8 moments while preserving numerical stability by construction; the inverse Fourier transformation back to the time domain naturally yields a stable solution and converges rapidly with relatively few moments. Together, these two formulations provide a stable, accurate, and versatile framework for simulating non-Markovian quantum dynamics. Benchmark calculations on the spin-boson model with Ohmic spectral densities show excellent agreement with numerically exact results.
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