Lieb-Robinson Bounds for the Toda Lattice

TL;DR

This paper derives Lieb-Robinson bounds for the Toda lattice, showing velocity dependence on initial conditions and extending results to related hierarchies and perturbations.

Contribution

It establishes locality estimates for the Toda lattice, including velocity dependence on initial conditions and applicability to hierarchies and perturbations.

Findings

Lieb-Robinson bounds are proven for the Toda lattice.

The velocity depends on initial conditions, unlike harmonic models.

Results extend to Toda and Kac-van Moerbeke hierarchies and certain perturbations.

Abstract

We establish locality estimates, known as Lieb-Robinson bounds, for the Toda lattice. In contrast to harmonic models, the Lieb-Robinson velocity for these systems do depend on the initial condition. Our results also apply to the entire Toda as well as the Kac-van Moerbeke hierarchy. Under suitable assumptions, our methods also yield a finite velocity for certain perturbations of these systems.