利用光散射计算黎曼零点
Computing Riemann zeros with light scattering
AI总结：
本研究利用经典光散射构建黎曼zeta函数计算平台，证明黎曼假设在Born近似下对应半无限光学散射体的完美无反射条件，并通过分析渐近行为验证有效性，在经典物理与黎曼零点间建立新桥梁。
摘要：
在无序中寻找隐藏的秩序是材料科学、波物理学和数学的共同兴趣所在。黎曼假设陈述了黎曼zeta函数非平凡零点的位置，初步刻画了素数看似随机分布中的统计秩序。这一著名猜想激发了与物理学不同分支的各种联系，近期涉及非厄米物理、量子场论、囚禁离子量子比特和超均匀性。在此，我们利用经典光散射开发了黎曼zeta函数的计算平台。我们证明，黎曼假设在Born近似下为半无限光学散射体在完美无反射条件下的势能图景提供了依据。为检验基于散射的计算的有效性，我们研究了随散射体数量增加和多重散射出现时，受抑反射的渐近行为。该结果在经典物理与黎曼零点之间架起了另一座桥梁，展示了受数论启发的波器件设计。
英文摘要：
Finding hidden order within disorder is a common interest in material science, wave physics, and mathematics. The Riemann hypothesis, stating the locations of nontrivial zeros of the Riemann zeta function, tentatively characterizes statistical order in the seemingly random distribution of prime numbers. This famous conjecture has inspired various connections with different branches of physics, recently with non-Hermitian physics, quantum field theory, trapped-ion qubits, and hyperuniformity. Here we develop the computing platform for the Riemann zeta function by employing classical scattering of light. We show that the Riemann hypothesis suggests the landscape of semi-infinite optical scatterers for the perfect reflectionless condition under the Born approximation. To examine the validity of the scattering-based computation, we investigate the asymptotic behaviours of suppressed reflections with the increasing number of scatterers and the emergence of multiple scattering. The result provides another bridge between classical physics and the Riemann zeros, exhibiting the design of wave devices inspired by number theory.
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