In this paper we analyze the evolution of the time averaged energy densities associated with a family of solutions to a Schrödinger equation on a Lie group of Heisenberg type. We use a semi-classical approach adapted to the stratified structure of the group and describe the semi-classical measures (also called quantum limits) that are associated with this family. This allows us to prove an Egorov’s type Theorem describing the quantum evolution of a pseudodifferential semi-classical operator through the semi-group generated by a sub-Laplacian.

中文翻译：

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海森堡型群的量子演化和亚拉普拉斯算子

在本文中，我们分析了与海森堡类型李群上薛定谔方程的一系列解相关的时间平均能量密度的演变。我们使用适用于该族群分层结构的半经典方法，并描述与该族相关的半经典度量（也称为量子限制）。这使我们能够证明描述伪微分半经典算子通过亚拉普拉斯算子生成的半群的量子演化的叶戈罗夫类型定理。