Periodic coherent states decomposition and quantum dynamics on the flat torus

Abstract

We provide a result on the coherent states decomposition for functions in $L^2({\mathbb{T}}^n)$ where ${\mathbb{T}}^n:=(\mathbb{R}/2\pi \mathbb{Z}{)}^n$. Suddenly, we study such a decomposition with respect to the quantum dynamics related to semiclassical elliptic Pseudodifferential operators, and we prove a related invariance result.