Estimating the Lieb-Robinson velocity for classical anharmonic lattice systems

Hillel Raz; Robert Sims

doi:10.1007/s10955-009-9839-5

Estimating the Lieb-Robinson velocity for classical anharmonic lattice systems

Hillel Raz, Robert Sims

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

We estimate the Lieb-Robsinon velocity, also known as the group velocity, for a system of harmonic oscillators and a variety of anharmonic perturbations with mainly short-range interactions. Such bounds demonstrate a quasi-locality of the dynamics in the sense that the support of the time evolution of a local observable remains essentially local. Our anharmonic estimates are applicable to a special class of observables, the Weyl functions, and the bounds which follow are not only independent of the volume but also the initial condition.

Original language	English (US)
Pages (from-to)	79-108
Number of pages	30
Journal	Journal of Statistical Physics
Volume	137
Issue number	1
DOIs	https://doi.org/10.1007/s10955-009-9839-5
State	Published - Oct 2009

Keywords

Anharmonic
Classical dynamics
Group velocity
Lieb-Robinson
Locality bounds

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s10955-009-9839-5

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title = "Estimating the Lieb-Robinson velocity for classical anharmonic lattice systems",

abstract = "We estimate the Lieb-Robsinon velocity, also known as the group velocity, for a system of harmonic oscillators and a variety of anharmonic perturbations with mainly short-range interactions. Such bounds demonstrate a quasi-locality of the dynamics in the sense that the support of the time evolution of a local observable remains essentially local. Our anharmonic estimates are applicable to a special class of observables, the Weyl functions, and the bounds which follow are not only independent of the volume but also the initial condition.",

keywords = "Anharmonic, Classical dynamics, Group velocity, Lieb-Robinson, Locality bounds",

author = "Hillel Raz and Robert Sims",

note = "Funding Information: Acknowledgements Both authors would like to thank Bruno Nachtergaele and Benjamin Schlein for their insight and useful discussions. The authors would like to acknowledge the hospitality of the Erwin Schr{\"o}dinger Institute, and specifically the organizers of the Summer School on Current topics in Mathematical Physics, where work on this project began. This article is based on work supported in part by the US National Science Foundation. In particular, R.S. was supported under grant # DMS-0757424, and H.R. received support from NSF grants # DMS-0605342, # DMS-07-57581 and VIGRE grant # DMS-0636297.",

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doi = "10.1007/s10955-009-9839-5",

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AU - Sims, Robert

N1 - Funding Information: Acknowledgements Both authors would like to thank Bruno Nachtergaele and Benjamin Schlein for their insight and useful discussions. The authors would like to acknowledge the hospitality of the Erwin Schrödinger Institute, and specifically the organizers of the Summer School on Current topics in Mathematical Physics, where work on this project began. This article is based on work supported in part by the US National Science Foundation. In particular, R.S. was supported under grant # DMS-0757424, and H.R. received support from NSF grants # DMS-0605342, # DMS-07-57581 and VIGRE grant # DMS-0636297.

PY - 2009/10

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N2 - We estimate the Lieb-Robsinon velocity, also known as the group velocity, for a system of harmonic oscillators and a variety of anharmonic perturbations with mainly short-range interactions. Such bounds demonstrate a quasi-locality of the dynamics in the sense that the support of the time evolution of a local observable remains essentially local. Our anharmonic estimates are applicable to a special class of observables, the Weyl functions, and the bounds which follow are not only independent of the volume but also the initial condition.

AB - We estimate the Lieb-Robsinon velocity, also known as the group velocity, for a system of harmonic oscillators and a variety of anharmonic perturbations with mainly short-range interactions. Such bounds demonstrate a quasi-locality of the dynamics in the sense that the support of the time evolution of a local observable remains essentially local. Our anharmonic estimates are applicable to a special class of observables, the Weyl functions, and the bounds which follow are not only independent of the volume but also the initial condition.

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KW - Classical dynamics

KW - Group velocity

KW - Lieb-Robinson

KW - Locality bounds

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Estimating the Lieb-Robinson velocity for classical anharmonic lattice systems

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Keywords

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