Dispersive Estimates for Harmonic Oscillator Systems

TL;DR

This paper establishes long-time dispersive estimates for a broad class of harmonic oscillator systems, extending the understanding of their dynamical behavior beyond short-time locality bounds.

Contribution

It introduces new long-time dispersive estimates for harmonic systems, contrasting with previously known short-time Lieb-Robinson bounds.

Findings

Proves long-time dispersive estimates for harmonic oscillator models.

Extends the theoretical understanding of quantum harmonic dynamics.

Provides tools for analyzing long-term behavior of harmonic systems.

Abstract

We consider a large class of harmonic systems, each defined as a quasi-free dynamics on the Weyl algebra over $\ell^2(\mathbb{Z}^d)$. In contrast to recently obtained, short-time locality estimates, known as Lieb-Robinson bounds, we prove a number of long-time dispersive estimates for these models.