关于高于四阶的无交换元指数积分器正性条件不满足性
Non-satisfiability of a positivity condition for commutator-free exponential integrators of order higher than four
AI总结：
研究了无交换元指数积分器的正性条件，证明了对于抛物线问题，这种积分器的最大收敛阶为四，这与之前其他作者的猜想一致。
摘要：
我们考虑了[Alverman, A., Fehske, H.: High-order commutator-free exponential time-propagation of driven quantum systems. J. Comput. Phys. 230, 5930-5956 (2011)]中提出的无交换元指数积分器。对于抛物线问题，其well-definedness要求该积分器满足正性条件，即本质上只向前推进时间。我们证明这一要求导致实系数下的最大收敛阶为四，这与之前其他作者的猜想一致。
英文摘要：
We consider commutator-free exponential integrators as put forward in [Alverman, A., Fehske, H.: High-order commutator-free exponential time-propagation of driven quantum systems. J. Comput. Phys. 230, 5930-5956 (2011)]. For parabolic problems, it is important for the well-definedness that such an integrator satisfies a positivity condition such that essentially it only proceeds forward in time. We prove that this requirement implies maximal convergence order of four for real coefficients, which has been conjectured earlier by other authors.
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