Heisenberg 热核的复兴与复测地线
Resurgence and Complex Geodesics for the Heisenberg Heat Kernel
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中文总结 AI 辅助
研究各向同性 Heisenberg 群热核的复兴，通过复测地线作用与 Stokes 矩阵显式计算，揭示奇点结构与维数无关性。
中文摘要 AI 辅助
我们研究各向同性 Heisenberg 群上的复测地线作用与热核复兴。对于具有 $r>0,y\ e0$ 的实端点，通过最小鞍点 Borel 芽的解析延拓所达到的非零有限奇点恰好是有限复作用差。对于非共振端点，我们构造行有限的定向 Stokes 算子，并显式计算正射线 Stokes 矩阵及其对数；本原 alien 支撑可以严格小于完整 Borel 奇点支撑。在垂直轴附近，我们从最近的 Borel 奇点获得一致的两项大阶渐近。三次共振允许一致的 $A_2$ 合流公式。我们还识别了原始 Fourier 轮廓所选择的复兴扇区的组合。在水平端点处，正 Borel 求和是精确的。在非零各向同性复端点处，不存在有限法向轨迹，但有符号垂直作用格是完整的极限谱。作用与 Stokes 结构在各向同性 $H^n$ 上与维数无关。
英文摘要
We study complex geodesic actions and heat-kernel resurgence on isotropic Heisenberg groups. For real endpoints with $r>0,y\ne0$, the nonzero finite singularities reached by analytic continuation of the minimizing-saddle Borel germ are exactly the finite complex action differences. For nonresonant endpoints, we construct row-finite directional Stokes operators and compute the positive-ray Stokes matrix and its logarithm explicitly; the primitive alien support can be strictly smaller than the full Borel singular support. Near the vertical axis, we obtain uniform two-term large-order asymptotics from the nearest Borel singularity. Cubic resonances admit uniform $A_2$ confluence formulas. We also identify the combination of resurgent sectors selected by the original Fourier contour. Positive Borel summation is exact at horizontal endpoints. At nonzero isotropic complex endpoints, no finite normal trajectories exist, but the signed vertical action lattice is the complete limiting spectrum. The action and Stokes structures are independent of the dimension on isotropic $H^n$.
发表机构
- Beijing Institute of Mathematical Sciences and Applications（北京国际数学研究中心）
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