arXiv:0904.2717 · Colloquium Mathematicum

Dynamics and Lieb–Robinson estimates for lattices of interacting anharmonic oscillators

Laurent Amour, Pierre Lévy-Bruhl, Jean Nourrigat

Published Jan 1, 2010• 21 citations

Abstract

For a class of infinite lattices of interacting anharmonic oscillators, we study the existence of the dynamics, together with Lieb-Robinson bounds, in a suitable algebra of observables.

DOI: 10.4064/cm118-2-17

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arXiv:0904.2717 · Colloquium Mathematicum

Dynamics and Lieb–Robinson estimates for lattices of interacting anharmonic oscillators

Laurent Amour, Pierre Lévy-Bruhl, Jean Nourrigat

Published Jan 1, 2010• 21 citations

arXiv HTML PDF

Abstract

For a class of infinite lattices of interacting anharmonic oscillators, we study the existence of the dynamics, together with Lieb-Robinson bounds, in a suitable algebra of observables.

DOI: 10.4064/cm118-2-17

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Bruno Nachtergaele

We present a recent result on the existence of the dynamics in the thermodynamic limit of a class of anharmonic quantum oscillator lattices, which was obtained using Lieb--Robinson bounds.

arXiv:0909.2845International Congress on Mathematical Physics (ICMP)Mar 1, 20100 citations

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\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.