The Magnus expansion is an efficient alternative to solving similarity renormalization group (SRG) flow equations with high-order, memory-intensive ordinary differential equation solvers. The numerical simplifications it offers for operator evolution are particularly valuable for in-medium SRG calculations, though challenges remain for difficult problems involving intruder states. Here we test the Magnus approach in an analogous but more accessible situation, which is the free-space SRG treatment of the spurious bound states arising from a leading-order chiral effective field theory (EFT) potential with very high cutoffs. We show that the Magnus expansion passes these tests and then use the investigations as a springboard to address various aspects of operator evolution that have renewed relevance in the context of the scale and scheme dependence of nuclear processes. These aspects include SRG operator flow with band- versus block-diagonal generators, universality for chiral EFT Hamiltonians and associated operators with different regularization schemes, and the impact of factorization arising from scale separation. Implications for short-range correlations physics and the possibilities for reconciling high- and low-resolution treatments of nuclear structure and reactions are discussed.

中文翻译：

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相似重整化群和马格努斯展开的算子演化

Magnus 展开是使用高阶、内存密集型常微分方程求解器求解相似重整化群 (SRG) 流方程的有效替代方法。它为算子演化提供的数值简化对于介质中 SRG 计算特别有价值，尽管涉及入侵者状态的难题仍然存在挑战。在这里，我们在一个类似但更容易理解的情况下测试 Magnus 方法，这是对由具有非常高截止值的前导手性有效场理论 (EFT) 势产生的伪束缚态的自由空间 SRG 处理。我们证明 Magnus 扩展通过了这些测试，然后将调查用作跳板来解决算子进化的各个方面，这些方面在核过程的规模和方案依赖性的背景下重新具有相关性。这些方面包括带带对角线生成器的 SRG 算子流、手性 EFT 哈密顿算子的通用性和具有不同正则化方案的相关算子，以及因尺度分离引起的因式分解的影响。讨论了对短程相关物理学的影响以及协调核结构和反应的高分辨率和低分辨率处理的可能性。手性 EFT 哈密顿算符和具有不同正则化方案的相关算子的普遍性，以及因尺度分离引起的因式分解的影响。讨论了对短程相关物理学的影响以及协调核结构和反应的高分辨率和低分辨率处理的可能性。手性 EFT 哈密顿算符和具有不同正则化方案的相关算子的普遍性，以及因尺度分离引起的因式分解的影响。讨论了对短程相关物理学的影响以及协调核结构和反应的高分辨率和低分辨率处理的可能性。