The nonlinear Dirac equation in Bose-Einstein condensates: II. Relativistic soliton stability analysis

The nonlinear Dirac equation in Bose-Einstein condensates: II. Relativistic soliton stability analysis

The nonlinear Dirac equation for Bose-Einstein condensates (BECs) in honeycomb optical lattices gives rise to relativistic multi-component bright and dark soliton solutions. Using the relativistic linear stability equations, the relativistic generalization of the Boguliubov-de Gennes equations, we c...

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Bibliographic Details
Published in:New journal of physics 2015-06, Vol.17 (6), p.63034, Article 063034
Main Authors: Haddad, L H, D Carr, Lincoln
Format: Article
Language:eng
Subjects:
05.45.-a
67.85.Hj
67.85.Jk
Bose-Einstein condensate
Bose-Einstein condensates
Chemical potential
Dirac equation
Domain walls
Excitation
Magnons
Nonlinear analysis
Nonlinearity
Notches
Numerical analysis
Optical lattices
Organic chemistry
Physics
Quantum phenomena
Relativism
Relativistic effects
Solitary waves
soliton
Stability analysis
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Summary:The nonlinear Dirac equation for Bose-Einstein condensates (BECs) in honeycomb optical lattices gives rise to relativistic multi-component bright and dark soliton solutions. Using the relativistic linear stability equations, the relativistic generalization of the Boguliubov-de Gennes equations, we compute soliton lifetimes against quantum fluctuations and classify the different excitation types. For a BEC of atoms, we find that our soliton solutions are stable on time scales relevant to experiments. Excitations in the bulk region far from the core of a soliton and bound states in the core are classified as either spin waves or as a Nambu-Goldstone mode. Thus, solitons are topologically distinct pseudospin- domain walls between polarized regions of . Numerical analysis in the presence of a harmonic trap potential reveals a discrete spectrum reflecting the number of bright soliton peaks or dark soliton notches in the condensate background. For each quantized mode the chemical potential versus nonlinearity exhibits two distinct power law regimes corresponding to the free-particle (weakly nonlinear) and soliton (strongly nonlinear) limits.
ISSN:1367-2630
1367-2630