Abstract

In the context of the averaging method for Poisson and symplectic structures and the theory of Hannay–Berry connections, we discuss some aspects of the semiclassical quantization for a class of slow-fast Hamiltonian systems with two degrees of freedom. For a pseudodifferential Weyl operator with two small parameters corresponding to the semiclassical and adiabatic limits, we show how to construct some series of quasimodes associated to a family of Lagrangian 2-tori which are almost invariant with respect to the classical dynamics.

中文翻译：

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慢速相空间的几何和半经典量化

摘要

在泊松和辛结构的平均方法以及Hannay-Berry连接理论的背景下，我们讨论了一类具有两个自由度的慢速哈密顿系统的半经典量化的某些方面。对于具有两个与半经典和绝热极限相对应的小参数的伪微分Weyl算子，我们展示了如何构建与Lagrangian 2-tori族相关的一系列准模，这对于经典动力学几乎是不变的。