On the existence of the dynamics for anharmonic quantum oscillator systems

Bruno Nachtergaele; Benjamin Schlein; Robert Sims; Shannon Starr; Valentin Zagrebnov

doi:10.1142/S0129055X1000393X

On the existence of the dynamics for anharmonic quantum oscillator systems

Bruno Nachtergaele
, Benjamin Schlein
, Robert Sims
, Shannon Starr
, Valentin Zagrebnov

Mathematics

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

27 Scopus citations

Abstract

We construct a W*-dynamical system describing the dynamics of a class of anharmonic quantum oscillator lattice systems in the thermodynamic limit. Our approach is based on recently proved Lieb-Robinson bounds for such systems on finite lattices [19].

Original language	English (US)
Pages (from-to)	207-231
Number of pages	25
Journal	Reviews in Mathematical Physics
Volume	22
Issue number	2
DOIs	https://doi.org/10.1142/S0129055X1000393X
State	Published - Mar 2010

Keywords

Anharmonic lattice
Infinite-system dynamics
Thermodynamic limit

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1142/S0129055X1000393X

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title = "On the existence of the dynamics for anharmonic quantum oscillator systems",

abstract = "We construct a W*-dynamical system describing the dynamics of a class of anharmonic quantum oscillator lattice systems in the thermodynamic limit. Our approach is based on recently proved Lieb-Robinson bounds for such systems on finite lattices [19].",

keywords = "Anharmonic lattice, Infinite-system dynamics, Thermodynamic limit",

author = "Bruno Nachtergaele and Benjamin Schlein and Robert Sims and Shannon Starr and Valentin Zagrebnov",

note = "Funding Information: The work reported in this paper was supported by the National Science Foundation: B.N. under Grants \#DMS-0605342 and \#DMS-0757581, R.S. under Grant \#DMS-0757424, and S.S. under Grant \#DMS-0757327 and \#DMS-0706927. The authors would also like to acknowledge the hospitality of the Department of Mathematics at U.C. Davis where a part of this work was completed.",

year = "2010",

month = mar,

doi = "10.1142/S0129055X1000393X",

language = "English (US)",

volume = "22",

pages = "207--231",

journal = "Reviews in Mathematical Physics",

issn = "0129-055X",

publisher = "World Scientific",

number = "2",

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TY - JOUR

T1 - On the existence of the dynamics for anharmonic quantum oscillator systems

AU - Nachtergaele, Bruno

AU - Schlein, Benjamin

AU - Sims, Robert

AU - Starr, Shannon

AU - Zagrebnov, Valentin

N1 - Funding Information: The work reported in this paper was supported by the National Science Foundation: B.N. under Grants #DMS-0605342 and #DMS-0757581, R.S. under Grant #DMS-0757424, and S.S. under Grant #DMS-0757327 and #DMS-0706927. The authors would also like to acknowledge the hospitality of the Department of Mathematics at U.C. Davis where a part of this work was completed.

PY - 2010/3

Y1 - 2010/3

N2 - We construct a W*-dynamical system describing the dynamics of a class of anharmonic quantum oscillator lattice systems in the thermodynamic limit. Our approach is based on recently proved Lieb-Robinson bounds for such systems on finite lattices [19].

AB - We construct a W*-dynamical system describing the dynamics of a class of anharmonic quantum oscillator lattice systems in the thermodynamic limit. Our approach is based on recently proved Lieb-Robinson bounds for such systems on finite lattices [19].

KW - Anharmonic lattice

KW - Infinite-system dynamics

KW - Thermodynamic limit

UR - https://www.scopus.com/pages/publications/77951550444

UR - https://www.scopus.com/pages/publications/77951550444#tab=citedBy

U2 - 10.1142/S0129055X1000393X

DO - 10.1142/S0129055X1000393X

M3 - Article

AN - SCOPUS:77951550444

SN - 0129-055X

VL - 22

SP - 207

EP - 231

JO - Reviews in Mathematical Physics

JF - Reviews in Mathematical Physics

IS - 2

ER -

On the existence of the dynamics for anharmonic quantum oscillator systems

Abstract

Keywords

ASJC Scopus subject areas

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