J. Stat. Phys. 148, 440-479 (2012) [DOI: 10.1007/s10955-012-0554-2]

Lieb-Robinson Bounds for the Toda Lattice

Umar Islambekov, Robert Sims, and Gerald Teschl

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.

MSC2000: Primary 37K10, 37K55; Secondary 37K60, 37K45
Keywords: Toda lattice, Lieb-Robinson bound

TeX file (117k) or pdf file (422k)