论文标题
Frisch - parisi形式主义，用于Schrödinger方程的波动
The Frisch--Parisi formalism for fluctuations of the Schrödinger equation
论文作者
论文摘要
当初始基准趋向于Dirac Comb时，我们考虑$ \ Mathbb {r} $中Schrödinger方程$ u $的解决方案。令$ h _ {\ text {p}，δ}（t）$为$ \ int \ lvert x \ rvert x \ rvert^{2Δ} \ lvert u（x，x，x，x，t）\ rvert^2 \，dx $，dx $的波动。我们证明Frisch-Parisi形式主义对$H_δ（T）= \ int _ {[0，T]} H _ {\ Text {p}，δ}（2S）\，ds $，这在道德上是Riemann的无分量曲线曲线$ r r $。我们的动机是了解与$ r $有关的多边形丝的涡旋丝方方程的演变。
We consider the solution of the Schrödinger equation $u$ in $\mathbb{R}$ when the initial datum tends to the Dirac comb. Let $h_{\text{p}, δ}(t)$ be the fluctuations in time of $\int\lvert x\rvert^{2δ}\lvert u(x,t)\rvert^2\,dx$, for $0 < δ< 1$, after removing a smooth background. We prove that the Frisch--Parisi formalism holds for $H_δ(t) = \int_{[0,t]}h_{\text{p}, δ}(2s)\,ds$, which is morally a simplification of the Riemann's non-differentiable curve $R$. Our motivation is to understand the evolution of the vortex filament equation of polygonal filaments, which are related to $R$.
