Lieb-Robinson Bounds for the Toda Lattice

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.

References in corpus (6)

• Lieb-Robinson Bounds and the Exponential Clustering Theorem
• Propagation of Correlations in Quantum Lattice Systems
• Lieb-Robinson Bounds for Harmonic and Anharmonic Lattice Systems
• A Multi-Dimensional Lieb-Schultz-Mattis Theorem
• Long-Time Asymptotics of the Toda Lattice for Decaying Initial Data Revisited
• On the Equivalence of Different Lax Pairs for the Kac-van Moerbeke Hierarchy