论文标题
Berezin-toeplitz操作员的量子繁殖
Quantum propagation for Berezin-Toeplitz operators
论文作者
论文摘要
我们描述了带有实用值主符号的Berezin-Toeplitz运算符产生的量子传播器的渐近行为。在自主情况下，我们还为与操作员相关的平滑光谱投影仪提供精确的渐近造型。这使我们引入了与沉浸式Lagrangian Submanifolds相关的量子状态。这些描述涉及两个起源的几何量，分别来自哈密顿量流向前束和规范束的升力。后者是本文的主要贡献，并与痕量公式中出现的马斯洛夫指数相连，这将在即将发表的论文中进行解释。
We describe the asymptotic behaviour of the quantum propagator generated by a Berezin-Toeplitz operator with real-valued principal symbol. We also give precise asymptotics for smoothed spectral projectors associated with the operator in the autonomous case; this leads us to introducting quantum states associated with immersed Lagrangian submanifolds. These descriptions involve geometric quantities of two origins, coming from lifts of the Hamiltonian flow to the prequantum bundle and the canonical bundle respectively. The latter are the main contribution of this article and are connected to the Maslov indices appearing in trace formulas, as will be explained in a forthcoming paper.
