Multiple-time-scale analysis for pinned breathers in Bose-Hubbard chains

Research output: Contribution to journalArticle

Abstract

Localized and pinned discrete breathers in Bose-Einstein condensates in optical lattices or in arrays of optical waveguides oscillate with frequencies which are much higher than those present in the spectrum of the background. Hence, the interaction between localized breathers and their surroundings is extremely weak leading to a multiple-time-scale perturbation expansion. We identify the leading order in the asymptotic expansion of the breather amplitude which does not average to zero after one full oscillation. The reduced model predicts a lower bound of the breather drift times and explains the topological differences between breathers in dimers, trimers, and in spatially extended one-dimensional lattices even in the presence of transport from boundary heat-baths. These analytical boundaries hold true for lattices of any length, due to the highly localized nature of breathers.
LanguageEnglish
Article number022212
Number of pages11
JournalPhysical Review E
Volume99
Issue number2
DOIs
Publication statusPublished - 19 Feb 2019

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Multiple Time Scales
Breathers
expansion
trimers
Bose-Einstein condensates
optical waveguides
baths
Discrete Breathers
Optical Lattice
dimers
Heat Bath
Perturbation Expansion
Optical Waveguides
Bose-Einstein Condensate
Reduced Model
Dimer
perturbation
heat
oscillations
Asymptotic Expansion

Keywords

  • discrete breathers
  • Bose-Einstein condensates
  • rare events

Cite this

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title = "Multiple-time-scale analysis for pinned breathers in Bose-Hubbard chains",
abstract = "Localized and pinned discrete breathers in Bose-Einstein condensates in optical lattices or in arrays of optical waveguides oscillate with frequencies which are much higher than those present in the spectrum of the background. Hence, the interaction between localized breathers and their surroundings is extremely weak leading to a multiple-time-scale perturbation expansion. We identify the leading order in the asymptotic expansion of the breather amplitude which does not average to zero after one full oscillation. The reduced model predicts a lower bound of the breather drift times and explains the topological differences between breathers in dimers, trimers, and in spatially extended one-dimensional lattices even in the presence of transport from boundary heat-baths. These analytical boundaries hold true for lattices of any length, due to the highly localized nature of breathers.",
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Multiple-time-scale analysis for pinned breathers in Bose-Hubbard chains. / Chirondojan, Liviu F.; Oppo, Gian-Luca.

In: Physical Review E, Vol. 99, No. 2, 022212, 19.02.2019.

Research output: Contribution to journalArticle

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