具有圆锥奇点的平面上的超疤痕准模
Superscarred quasimodes on flat surfaces with conical singularities
摘要：
我们构造了平移曲面上Laplace-Beltrami算子的连续拟模族。我们将我们的结果应用到有理多边形量子台球，从而构建了一个连续的家庭的拟模的Neumann拉普拉斯算子在这样的域的谱宽度${\mathcal{O}}_\varepsilon(λ^{3/8+\varepsilon})$。我们证明了与这个准模族相关联的半经典测度在动量空间上投影为Dirac测度的有限和，因此，它们满足Bogomolny和Schmit关于有理多边形的superscar猜想.
英文摘要：
We construct a continuous family of quasimodes for the Laplace-Beltrami operator on a translation surface. We apply our result to rational polygonal quantum billiards and thus construct a continuous family of quasimodes for the Neumann Laplacian on such domains with spectral width ${\mathcal{O}}_\varepsilon(λ^{3/8+\varepsilon})$. We show that the semiclassical measures associated with this family of quasimodes project to a finite sum of Dirac measures on momentum space, hence, they satisfy Bogomolny and Schmit's superscar conjecture for rational polygons.
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