发表机构
Instituto Galego de Física de Altas Enerxías, Universidade de Santiago de Compostela; High Energy Physics Research Unit, Faculty of Science, Chulalongkorn University; Theoretische Natuurkunde, Vrije Universiteit Brussel (VUB) & International Solvay Institutes（加利西亚高能物理研究所，圣地亚哥-德孔波斯特拉大学; 朱拉隆功大学理学院高能物理研究组; 布鲁塞尔自由大学理论物理系及国际索尔维研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究证明在具有随机非线性耦合的无限维共振哈密顿系统中，即使仅保留无穷小比例的耦合，也能通过相位对齐和幂律谱形成实现相干能量级联，并揭示相位锁定机制，表明无序相互作用可维持跨尺度相干输运。
AI 中文摘要
熟悉的波动力学理论围绕湍流能量级联展开，其特点是各个简正模式的随机相位。相比之下，近年来的研究揭示了能量传递由相位相干动力学介导的湍流级联。此类相干级联此前已在具有严格控制的模式相互作用代数结构的确定性系统中得到证实，例如非线性薛定谔方程。在此，我们证明相位相干级联的存在对于模式耦合的实质性改变具有鲁棒性。我们证明，在具有完全共振简正模式谱和随机非线性耦合的无限维共振哈密顿系统中，一个结构化的耦合子集——占总耦合的无穷小比例——足以支持以相位对齐、幂律谱形成为特征，并伴随Sobolev范数无界增长或有限时间爆破解的相干级联。数值模拟进一步证明了相干级联从随机初始数据通过相位锁定过程涌现，提示了其在更广泛的初始数据和系统中出现的机制。因此，我们表明无序的模式相互作用可以维持而非阻碍跨越任意远尺度的相干能量输运。
英文摘要
The familiar wave kinetic theory revolves around turbulent energy cascades characterized by random phases of the individual normal modes. By contrast, recent years have revealed turbulent cascades where the transfer of energy is mediated by phase-coherent dynamics. Such coherent cascades have been previously established in deterministic systems with a tightly controlled algebraic structure of the mode interactions, such as nonlinear Schrödinger equations. Here, we show that the presence of phase-coherent cascades is robust with respect to substantial alterations of the mode couplings. We prove that, in infinite-dimensional resonant Hamiltonian systems with fully resonant normal mode spectra and random nonlinear couplings, a structured subset of couplings --- an infinitesimal fraction of the total --- suffices to support coherent cascades characterized by phase alignment, the formation of power-law spectra, and either unbounded growth of Sobolev norms or a finite-time blow-up. Numerical simulations further demonstrate the emergence of coherent cascades from random initial data through a process of phase locking, suggesting a mechanism for their emergence in broader classes of initial data and systems. We thus show that disordered mode interactions can sustain, rather than block, coherent energy transport across arbitrarily distant scales.
