发表机构
University of Cambridge（剑桥大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文指出传统泰勒展开诊断流体动力学收敛性可能失效，提出在壳外构成关系层面研究梯度展开，建立因果菱形收敛区域，并揭示非流体动力学谱的获取途径。
AI 中文摘要
流体动力学的收敛性通常通过将无能隙色散关系 $\omega(k)$ 在 $k=0$ 附近进行泰勒展开来研究。我们证明，这种诊断方法在任意接近流体动力学极限时都可能失效：声学模式可以在任意小的波数处碰撞，使得 $\omega(k)$ 成为非解析函数，而密度与通量之间的关系在该处仍然是解析的。我们转而直接在构成关系的层面上，在壳外（即存在外力的情况下）表述梯度展开。对于具有弛豫谱的因果理论，我们建立了在 $|i\omega|+w|ik|<1/\tau_g$ 区域内的收敛性，其中 $w$ 是最大信息速度，$1/\tau_g$ 是非流体动力学间隙。在自然的洛伦兹平面 $\{i\omega,ik\}$ 上，该区域是一个因果菱形，其边界标志着与非流体动力学模式首次可能相遇的位置。超出该区域，解析延拓通过重求和构成关系的奇点揭示了非流体动力学谱。因此，流体动力学能够意识到流体动力学之外的自由度，但这一信息只有在壳外才能完全获取。
英文摘要
The convergence of hydrodynamics is commonly investigated by Taylor-expanding the gapless dispersion relations $ω(k)$ around $k=0$. We show that this diagnostic can fail arbitrarily close to the hydrodynamic limit: sound modes can collide at arbitrarily small wave number, rendering $ω(k)$ nonanalytic, while the relationship between densities and fluxes remains analytic there. We instead formulate the gradient expansion off-shell (i.e. in the presence of external forces), directly at the level of the constitutive relations. For causal theories with relaxational spectra, we establish convergence for $|iω|+w|ik|<1/τ_g$, where $w$ is the maximal information speed and $1/τ_g$ the nonhydrodynamic gap. On the naturally Lorentzian $\{iω,ik\}$ plane, this region is a causal diamond, whose boundary marks the first possible encounter with nonhydrodynamic modes. Beyond it, analytic continuation reveals the nonhydrodynamic spectrum through singularities of the resummed constitutive relations. Thus, hydrodynamics is aware of the degrees of freedom beyond hydrodynamics, but this information becomes fully accessible only off-shell.
Comments7 pages, 3 figures (main text) + 7 pages, 3 figures (supplementary material), comments welcome!
