Lieb-Robinson Bounds for the Toda Lattice

Umar Islambekov; Robert Sims; Gerald Teschl

doi:10.1007/s10955-012-0554-2

Lieb-Robinson Bounds for the Toda Lattice

Umar Islambekov
, Robert Sims
, Gerald Teschl

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

5 Scopus citations

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.

Original language	English (US)
Pages (from-to)	440-479
Number of pages	40
Journal	Journal of Statistical Physics
Volume	148
Issue number	3
DOIs	https://doi.org/10.1007/s10955-012-0554-2
State	Published - Aug 2012

Keywords

Lieb-Robinson bound
Toda lattice

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s10955-012-0554-2

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title = "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.",

keywords = "Lieb-Robinson bound, Toda lattice",

author = "Umar Islambekov and Robert Sims and Gerald Teschl",

note = "Funding Information: R. S. and U. I. were supported, in part, by NSF grants DMS-0757424 and DMS-1101345. G. T. was supported by the Austrian Science Fund (FWF) under Grant No. Y330.",

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doi = "10.1007/s10955-012-0554-2",

language = "English (US)",

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journal = "Journal of Statistical Physics",

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T1 - Lieb-Robinson Bounds for the Toda Lattice

AU - Islambekov, Umar

AU - Sims, Robert

AU - Teschl, Gerald

N1 - Funding Information: R. S. and U. I. were supported, in part, by NSF grants DMS-0757424 and DMS-1101345. G. T. was supported by the Austrian Science Fund (FWF) under Grant No. Y330.

PY - 2012/8

Y1 - 2012/8

N2 - 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.

AB - 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.

KW - Lieb-Robinson bound

KW - Toda lattice

UR - https://www.scopus.com/pages/publications/84865431011

UR - https://www.scopus.com/pages/publications/84865431011#tab=citedBy

U2 - 10.1007/s10955-012-0554-2

DO - 10.1007/s10955-012-0554-2

M3 - Article

AN - SCOPUS:84865431011

SN - 0022-4715

VL - 148

SP - 440

EP - 479

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 3

ER -

Lieb-Robinson Bounds for the Toda Lattice

Abstract

Keywords

ASJC Scopus subject areas

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