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Journal of Mathematical Physics / Volume 53 / Issue 1 / ARTICLES / Statistical Physics
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J. Math. Phys. 53, 013302 (2012); http://dx.doi.org/10.1063/1.3677978 (24 pages)

Dispersive estimates for harmonic oscillator systems

Vita Borovyk1 and Robert Sims2

1Department of Mathematical Sciences, University of Cincinnati, Cincinnati, Ohio 45221, USA
2Department of Mathematics, University of Arizona, Tucson, Arizona 85721, USA

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(Received 12 September 2011; accepted 27 December 2011; published online 23 January 2012)

We consider a large class of harmonic systems, each defined as a quasi-free dynamics on the Weyl algebra over ℓ2(mathd). 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.

© 2012 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. MODELS AND RESULTS
    1. Weyl algebras and a quasi-free dynamics
    2. Harmonic evolutions in infinite volume
    3. Main results
  3. PROOF OF THEOREMS 2.1 AND 2.2
  4. PROOF OF THEOREM 2.3
    1. The main estimates
    2. On the Morse lemma for γ

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KEYWORDS and PACS

Keywords

algebra, harmonic oscillators, statistical mechanics

PACS

  • 05.20.-y

    Classical statistical mechanics

  • 03.65.Ge

    Solutions of wave equations: bound states

  • 02.10.-v

    Logic, set theory, and algebra

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3677978

PUBLICATION DATA

ISSN

0022-2488 (print)  
1089-7658 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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Figures (click on thumbnails to view enlargements)

FIG.1
Decay of ‖[τt(W(δ0)), W(δx)]‖.

FIG.1 Download High Resolution Image (.zip file) | Export Figure to PowerPoint



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