标题： 接触度量结构的量子遍历性 显示英文标题

标题： Quantum ergodicity for contact metric structures

摘要： 本文致力于在Reeb流是遍历的假设下，证明接触度量流形上子拉普拉斯算子本征函数的量子遍历性（QE）定理。 为此，我们依赖于为一般过滤流形开发的半经典伪微分演算，并将其专门应用于接触流形的设置。 我们的策略类似于对Born-Oppenheimer近似的实现，因为我们依赖于在演算中构造与子拉普拉斯算子交换的微局部投影算子，称为Landau投影算子。 然后表明，子拉普拉斯算子在每个Landau投影算子的值域上有效作用，如同Reeb向量场所做的那样。 一旦建立了微局部Weyl定律，证明的其余部分就遵循经典的QE路径。 显示英文摘要

摘要： This paper is dedicated to the proof of a Quantum Ergodicity (QE) theorem for the eigenfunctions of subLaplacians on contact metric manifolds, under the assumption that the Reeb flow is ergodic. To do so, we rely on a semiclassical pseudodifferential calculus developed for general filtered manifolds that we specialize to the setting of contact manifolds. Our strategy is then reminiscent of an implementation of the Born-Oppenheimer approximation as we rely on the construction of microlocal projectors in our calculus which commute with the subLaplacian, called Landau projectors. The subLaplacian is then shown to act effectively on the range of each Landau projector as the Reeb vector field does. The remainder of the proof follows the classical path towards QE, once microlocal Weyl laws have been established.