JMP Nameplate
  • Volume/Page
  • Keyword
  • DOI
  • Citation
  • Advanced
   
 
 
 

Flickr Twitter UniPHY Group iResearch App Facebook

Journal of Mathematical Physics / Volume 53 / Issue 1 / ARTICLES / Statistical Physics

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

View MapView Map

(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

RELATED DATABASES

To view database links for this article, you need to log in.

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

For access to fully linked references, you need to log in.
    Bravyi, S., Hastings, M., and Michalakis, S., “Topological quantum order: Stability under local perturbations,” J. Math. Phys. 51, 093512 (2010)JMAPAQ000051000009093512000001.

    Hastings, M., “Lieb-Schultz-Mattis in higher dimensions,” Phys. Rev. B 69, 104431 (2004).


For access to citing articles, you need to log in.


Figures (1)

Access to article objects (figures, tables, multimedia) requires a subscription; log in to view available files.
(Access to supplementary files, where available, is free for this journal.)



Close

Google Calendar

ADVERTISEMENT

Your Recent History Recent History Help

Recently Viewed

  1. Dispersive estimates for harmonic oscillator systems
  2. Classical ladder operators, polynomial Poisson algebras, and classification of superintegrable systems
  3. Quasi-coherent states for harmonic oscillator with time-dependent parameters
  4. The gap equation for spin-polarized fermions
  5. Twisted hierarchies associated with the generalized sine-Gordon equation
Go to AIP Home
Copyright © American Institute of Physics
close