论文标题
schr {Ö} dinger方程的可观察性和可控性
Observability and Controllability for the Schr{ö}dinger Equation on Quotients of Groups of Heisenberg Type
论文作者
论文摘要
我们提供了必要和足够的条件，以使Schr \''Odinger方程涉及涉及Nilmanifold的次宽曲板，通过将Heisenberg类型的商通过其一个离散的子组之一获得的尼尔曼堡类型获得的商品获得。这类Nilpotent Lie clote是一组分层式的lie sequient of Schriptient of sep of sep of sep schript cons of sep of sup of of sepell of of of of of of of of of of of sep of sepell of of of of of of of of of of of of of。与通常的椭圆形schr \''odinger方程（例如在扁平托里或负弯曲的歧管上）相反，存在最小的可控时间。证明中使用的主要工具是（可估算的）半古典措施，该测量是通过使用表示理论和我们在海森伯格类型组的背景下引入的半古典波数据包的概念。
We give necessary and sufficient conditions for the controllability of a Schr\''odinger equation involving the sub-Laplacian of a nilmanifold obtained by taking the quotient of a group of Heisenberg type by one of its discrete sub-groups.This class of nilpotent Lie groups is a major example of stratified Lie groups of step 2. The sub-Laplacian involved in these Schr\''odinger equations is subelliptic, and, contrarily to what happens for the usual elliptic Schr\''odinger equation for example on flat tori or on negatively curved manifolds, there exists a minimal time of controllability. The main tools used in the proofs are (operator-valued) semi-classical measures constructed by use of representation theory and a notion of semi-classical wave packets that we introduce here in the context of groups of Heisenberg type.
