Periodic coherent states decomposition and quantum dynamics on the flat torus

TL;DR

This paper develops a decomposition of functions into coherent states on the flat torus and explores its invariance under quantum dynamics governed by semiclassical elliptic pseudodifferential operators.

Contribution

It introduces a new coherent states decomposition for functions on the flat torus and analyzes its invariance under specific quantum dynamics.

Findings

Coherent states decomposition for functions on the flat torus.

Invariance of the decomposition under quantum dynamics.

Application to semiclassical elliptic pseudodifferential operators.

Abstract

We provide a result on the coherent states decomposition for functions in $L^2 (\Bbb T^n)$ where $\Bbb T^n := (\Bbb R / 2\pi \Bbb Z)^n$. 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.