Semiclassical analysis on compact nilmanifolds

TL;DR

This paper develops semi-classical analysis techniques on compact nilmanifolds, exploring quantum limits for sub-Laplacians and Rockland operators, contributing to understanding quantum behavior in these geometric settings.

Contribution

It introduces semi-classical analysis on compact nilmanifolds and investigates quantum limits for sub-Laplacians and Rockland operators, a novel extension in this area.

Findings

Properties of quantum limits for sub-Laplacians established

Semi-classical limits characterized on nilmanifolds

Analysis applicable to positive Rockland operators

Abstract

In this paper, we define and study semi-classical analysis and semi-classical limits on compact nil-manifolds. As an application, we obtain properties of quantum limits for sub-Laplacians in this context, and more generally for positive Rockland operators.