Some remarks on semi-classical analysis on two-step Nilmanifolds

TL;DR

This paper explores semi-classical analysis on two-step nilmanifolds, examining how geometric properties influence the behavior of eigenfunction densities and their weak limits in this setting.

Contribution

It develops a semi-classical framework for two-step nilmanifolds and investigates the impact of geometry on eigenfunction density limits.

Findings

Properties of weak limits of eigenfunction densities are characterized.

Geometry significantly influences the semi-classical behavior.

Results extend understanding of semi-classical analysis in nilpotent Lie group settings.

Abstract

In this paper, we present recent results about the developement of a semiclassical approach in the setting of nilpotent Lie groups and nilmanifolds. We focus on two-step nilmanifolds and exhibit some properties of the weak limits of sequence of densities associated with eigenfunctions of a sub-Laplacian. We emphasize the influence of the geometry on these properties.