发表机构
Niels Bohr International Academy, Niels Bohr Institute, University of Copenhagen（哥本哈根大学尼尔斯玻尔研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
Magnus是一个开源Python代码，利用Magnus展开高效计算任意哈密顿量、任意味数和任意物质分布下的中微子振荡概率，在高精度下比现有代码更快，并自动选择最廉价的路径。
AI 中文摘要
解释中微子振荡测量结果需要计算一个以某种味产生的中微子被探测为另一种味的概率。在真空中和恒定密度物质中，该概率具有精确公式。当密度沿路径变化时（如在地球、太阳或超新星中），则不存在精确公式。在这种情况下，通常的方法要么用恒定密度阶梯代替物质分布，其误差仅随阶梯宽度的平方下降；要么使用通用求解器积分演化方程，而该求解器必须缩短步长以满足更严格的容差。两者在高精度下都会变慢，然而分析需要在许多能量、方向和参数值下计算概率。每个新实验或模型通常需要编写和验证新的求解器。我们提出Magnus，一个开源Python代码，避免了这些限制。它使用Magnus展开，其误差随步长的高次幂下降，其成本由密度变化的快慢决定，而非路径包含的振荡次数。Magnus接受任意密度分布、任意味数和任意厄米哈密顿量，例如非标准相互作用、惰性中微子、洛伦兹不变性破坏和赝狄拉克中微子所对应的哈密顿量。如果存在更便宜的方法，它会自动采用。例如，在密度缓慢变化的地方（如太阳内部），它跟随瞬时本征态，并仅在共振处应用展开。除了振荡概率，Magnus还返回相位平均概率，这些概率描述了太阳和天体物理中微子。一个典型概率计算只需几毫秒，批量扫描每点便宜一到两个数量级。在我们比较的公开代码中，Magnus在变化物质分布上高精度计算时速度最快。Magnus将研究新实验或模型的努力从编写求解器转移到指定其物理上。
英文摘要
Interpreting neutrino oscillation measurements requires computing the probability that a neutrino born with one flavor is detected with another. In vacuum and in matter of constant density, this probability has exact formulas. Where the density varies along the path, as in the Earth, the Sun, or a supernova, it does not. There, the usual approaches either replace the profile by constant-density steps, whose error falls only as the square of their width, or integrate the evolution equation with a general-purpose solver, which must shorten its steps to meet a tighter tolerance. Both become slow at high accuracy, yet an analysis needs the probability at many energies, directions, and parameter values. Each new experiment or model often requires writing and validating a new solver. We present Magnus, an open-source Python code that avoids these limitations. It uses the Magnus expansion, whose error falls as a high power of its step width and whose cost is set by how fast the density varies, not by how many oscillations the path holds. Magnus accepts any density profile, any number of flavors, and any Hermitian Hamiltonian, such as those of non-standard interactions, sterile neutrinos, Lorentz-invariance violation, and pseudo-Dirac neutrinos. Where a cheaper route exists, it takes it automatically. For example, where the density varies slowly, as in the Sun, it follows the instantaneous eigenstates and applies the expansion only at resonances. Besides oscillating probabilities, Magnus returns phase-averaged ones, which describe solar and astrophysical neutrinos. A typical probability takes a few milliseconds, and batched scans are one to two orders of magnitude cheaper per point. Among the public codes we compared, Magnus is the fastest at high accuracy on a varying profile. Magnus shifts the effort of studying a new experiment or model from writing a solver to specifying its physics.
Comments92 pages, 43 figures, plus code listings and appendices. Full documentation: https://mbustama.github.io/Magnus/
