Bifurcation analysis of a two-component Bose-Einstein condensate

Yuen Cheng Kuo, Wen Wei Lin, Shih-Feng Shieh

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

In this paper, we prove that the solution curve of the ground/positive bound states of a two-component Bose-Einstein condensate undergoes supercritical pitchfork bifurcations at some finite values of the inter-component scattering length. The ground state solutions bifurcate into two symmetric solutions with respect to some suitable axis on the symmetric domain, when a two-component BEC has equal intra- and inter-component scattering lengths. Furthermore, we show that the ground/positive bound states repel each other and form segregated nodal domains when the repulsive scattering length goes to infinity. Numerical results of bifurcation diagrams and the forms of ground/positive bound state solutions for a two-component BEC with various trap potentials are presented.

Original languageEnglish
Pages (from-to)311-346
Number of pages36
JournalPhysica D: Nonlinear Phenomena
Volume211
Issue number3-4
DOIs
Publication statusPublished - 2005 Nov 15

Fingerprint

Bose-Einstein condensates
scattering
infinity
diagrams
traps
ground state
curves

Keywords

  • Bose-Einstein condensate
  • Gross-Pitaevskii equation
  • Nonlinear Schrödinger equation
  • Pitchfork bifurcation

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

Cite this

Bifurcation analysis of a two-component Bose-Einstein condensate. / Kuo, Yuen Cheng; Lin, Wen Wei; Shieh, Shih-Feng.

In: Physica D: Nonlinear Phenomena, Vol. 211, No. 3-4, 15.11.2005, p. 311-346.

Research output: Contribution to journalArticle

Kuo, Yuen Cheng ; Lin, Wen Wei ; Shieh, Shih-Feng. / Bifurcation analysis of a two-component Bose-Einstein condensate. In: Physica D: Nonlinear Phenomena. 2005 ; Vol. 211, No. 3-4. pp. 311-346.
@article{a1f89d4e0a4142aea23b501645abbef3,
title = "Bifurcation analysis of a two-component Bose-Einstein condensate",
abstract = "In this paper, we prove that the solution curve of the ground/positive bound states of a two-component Bose-Einstein condensate undergoes supercritical pitchfork bifurcations at some finite values of the inter-component scattering length. The ground state solutions bifurcate into two symmetric solutions with respect to some suitable axis on the symmetric domain, when a two-component BEC has equal intra- and inter-component scattering lengths. Furthermore, we show that the ground/positive bound states repel each other and form segregated nodal domains when the repulsive scattering length goes to infinity. Numerical results of bifurcation diagrams and the forms of ground/positive bound state solutions for a two-component BEC with various trap potentials are presented.",
keywords = "Bose-Einstein condensate, Gross-Pitaevskii equation, Nonlinear Schr{\"o}dinger equation, Pitchfork bifurcation",
author = "Kuo, {Yuen Cheng} and Lin, {Wen Wei} and Shih-Feng Shieh",
year = "2005",
month = "11",
day = "15",
doi = "10.1016/j.physd.2005.09.003",
language = "English",
volume = "211",
pages = "311--346",
journal = "Physica D: Nonlinear Phenomena",
issn = "0167-2789",
publisher = "Elsevier",
number = "3-4",

}

TY - JOUR

T1 - Bifurcation analysis of a two-component Bose-Einstein condensate

AU - Kuo, Yuen Cheng

AU - Lin, Wen Wei

AU - Shieh, Shih-Feng

PY - 2005/11/15

Y1 - 2005/11/15

N2 - In this paper, we prove that the solution curve of the ground/positive bound states of a two-component Bose-Einstein condensate undergoes supercritical pitchfork bifurcations at some finite values of the inter-component scattering length. The ground state solutions bifurcate into two symmetric solutions with respect to some suitable axis on the symmetric domain, when a two-component BEC has equal intra- and inter-component scattering lengths. Furthermore, we show that the ground/positive bound states repel each other and form segregated nodal domains when the repulsive scattering length goes to infinity. Numerical results of bifurcation diagrams and the forms of ground/positive bound state solutions for a two-component BEC with various trap potentials are presented.

AB - In this paper, we prove that the solution curve of the ground/positive bound states of a two-component Bose-Einstein condensate undergoes supercritical pitchfork bifurcations at some finite values of the inter-component scattering length. The ground state solutions bifurcate into two symmetric solutions with respect to some suitable axis on the symmetric domain, when a two-component BEC has equal intra- and inter-component scattering lengths. Furthermore, we show that the ground/positive bound states repel each other and form segregated nodal domains when the repulsive scattering length goes to infinity. Numerical results of bifurcation diagrams and the forms of ground/positive bound state solutions for a two-component BEC with various trap potentials are presented.

KW - Bose-Einstein condensate

KW - Gross-Pitaevskii equation

KW - Nonlinear Schrödinger equation

KW - Pitchfork bifurcation

UR - http://www.scopus.com/inward/record.url?scp=27644464896&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=27644464896&partnerID=8YFLogxK

U2 - 10.1016/j.physd.2005.09.003

DO - 10.1016/j.physd.2005.09.003

M3 - Article

AN - SCOPUS:27644464896

VL - 211

SP - 311

EP - 346

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

IS - 3-4

ER -