Fast Evaluation of the Sixth-Order Time-Convolutionless (TCL6) Master-Equation Generator
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 Nt sampled times requires O(Nt3) 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(Ntlog2Nt) operations. These reductions enable fast, practical simulations of non-Markovian dynamics involving multiphonon and multiphoton processes in open quantum systems.
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BibTeX
@misc{chen2026fast,
title = {{Fast Evaluation of the Sixth-Order Time-Convolutionless (TCL6) Master-Equation Generator}},
author = {Jiahao Chen and Sirui Chen and Dragomir Davidovic},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.18806},
eprint = {2609.18806},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18806},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fast Evaluation of the Sixth-Order Time-Convolutionless (TCL6) Master-Equation Generator
AU - Jiahao Chen
AU - Sirui Chen
AU - Dragomir Davidovic
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2609.18806
UR - https://arxiv.org/abs/2609.18806
AB - 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_tlog^2N_t) operations. These reductions enable fast, practical simulations of non-Markovian dynamics involving multiphonon and multiphoton processes in open quantum systems.
ER -