发表刊物：Submitted

摘要：We investigate the Widom conjecture for the spectral projection operator \(\Pi = \ind_{\{H_{\Gamma,\hbar} < \mu\}}\) of momentum-restricted Schr\"odinger operators \(H_{\Gamma,\hbar}\coloneq \text{Op}_{\hbar}(\ind_{\Gamma}(\xi))\text{Op}_{\hbar}( p(x,\xi))\text{Op}_{\hbar}(\ind_{\Gamma}(\xi))\) in $\mathbb R^n$. Using semiclassical and operator-theoretic techniques, we establish the Widom conjecture for momentum-restricted Schr\"odinger operators, obtaining precise asymptotic expansions of the corresponding trace and entropy functionals. We further derive limiting formulas for the entanglement entropy in the semiclassical regime and identify the extremal configurations among compact convex domains. In particular, we show that the limiting entropy constant admits a variational characterization over convex bodies and that the extremal values are uniquely attained by two congruent spheres, up to translation. These results provide a geometric and functional-analytic perspective on Widom-type asymptotics, linking spectral theory, convex geometry, and entropy in the semiclassical analysis of Schr\"odinger operators.

合写作者：Pan Ma, Daoyuan Zheng

论文类型：期刊论文

学科门类：理学

一级学科：数学

文献类型：J

是否译文：否