Lieb-Robinson Bounds for the Toda Lattice
arXiv:1204.5278 · doi:10.1007/s10955-012-0554-2
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 (23)
- An Area Law for One Dimensional Quantum Systems
- Lieb-Schultz-Mattis in Higher Dimensions
- Spectral Gap and Exponential Decay of Correlations
- Lieb-Robinson Bounds and the Exponential Clustering Theorem
- Topological quantum order: stability under local perturbations
- Propagation of Correlations in Quantum Lattice Systems
- A short proof of stability of topological order under local perturbations
- Automorphic Equivalence within Gapped Phases of Quantum Lattice Systems
- Lieb-Robinson Bound and Locality for General Markovian Quantum Dynamics
- Lieb-Robinson Bounds for Harmonic and Anharmonic Lattice Systems
- Dynamical Localization in Disordered Quantum Spin Systems
- A Multi-Dimensional Lieb-Schultz-Mattis Theorem
- Information propagation for interacting particle systems
- Long-Time Asymptotics of the Toda Lattice for Decaying Initial Data Revisited
- On the Existence of the Dynamics for Anharmonic Quantum Oscillator Systems
- Lieb-Robinson bounds for commutator-bounded operators
- Algebro-Geometric Quasi-Periodic Finite-Gap Solutions of the Toda and Kac-van Moerbeke Hierarchies
- On the propagation of a perturbation in an anharmonic system
- Lieb-Robinson bounds for classical anharmonic lattice systems
- On the Spatial Asymptotics of Solutions of the Toda Lattice
- On the Equivalence of Different Lax Pairs for the Kac-van Moerbeke Hierarchy
- Dispersive Estimates for Harmonic Oscillator Systems
- Unique continuation for discrete nonlinear wave equations
Cited by in corpus (4)
- Quasi-Locality Bounds for Quantum Lattice Systems. Part I. Lieb-Robinson Bounds, Quasi-Local Maps, and Spectral Flow Automorphisms
- Simulating Bosonic Baths with Error Bars
- Classical Lieb-Robinson Bound for Estimating Equilibration Timescales of Isolated Quantum Systems
- On the evolution of scattering data under perturbations of the Toda lattice