2026-10-22 · arXiv Quantum Physics
arXiv:2609.18806v2 Announce Type: replace
Abstract: Higher-order time-convolutionless (TCL) master equations provide systematic corrections for non-Markovian dynamics in open quantum systems, but their time-ordered integrals become increasingly costly to evaluate. Direct quadrature of the Hadamard-reduced sixth-order (TCL6) generator at all $N_t$ sampled times requires $O(N_t^3)$ operations at fixed system dimension. We derive an exact reduction for a finite-dimensional system coupled through one Hermitian operator to a stationary centered Gaussian bath. By separating operator coefficients from scalar time-dependent spectral densities, the complete TCL6 time series is reduced to cumulative sums and first-order recurrences, one-dimensional causal convolutions, and an exact dyadic recursion for interlocked sums. With the algorithm, evaluating the complete TCL6 time series requires $O(N_t\log^2N_t)$ operations. These reductions enable fast, practical simulations of non-Markovian dynamics involving multiphonon and multiphoton processes in open quantum systems.
原文链接：https://arxiv.org/abs/2609.18806
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