115 citations · 221 across the 12 of their papers we have counts for
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The nonlinear Dirac equation in Bose-Einstein condensates: Superfluid fluctuations and emergent theories from relativistic linear stability equations
L. H. Haddad, Lincoln D. Carr
We present the theoretical and mathematical foundations of stability analysis for a Bose-Einstein condensate (BEC) at Dirac points of a honeycomb optical lattice. The combination o…
The nonlinear Dirac equation in Bose-Einstein condensates: Vortex solutions and spectra in a weak harmonic trap
L. H. Haddad, Lincoln D. Carr
We analyze the vortex solution space of the -dimensional nonlinear Dirac equation for bosons in a honeycomb optical lattice at length scales much larger than the lattice sp…
The nonlinear Dirac equation in Bose-Einstein condensates: II. Relativistic soliton stability analysis
L. H. Haddad, Lincoln D. Carr
The nonlinear Dirac equation for Bose-Einstein condensates in honeycomb optical lattices gives rise to relativistic multi-component bright and dark soliton solutions. Using the rel…
The nonlinear Dirac equation in Bose-Einstein condensates: I. Relativistic solitons in armchair nanoribbon optical lattices
L. H. Haddad, C. M. Weaver, Lincoln D. Carr
We present a thorough analysis of soliton solutions to the quasi-one-dimensional nonlinear Dirac equation (NLDE) for a Bose-Einstein condensate in a honeycomb lattice with armchair…
The nonlinear Dirac equation: Preparation and stability of relativistic vortices in Bose-Einstein condensates
L. H. Haddad, K. M. O'Hara, Lincoln D. Carr
We propose a detailed experimental procedure for preparing relativistic vortices, governed by the nonlinear Dirac equation, in a two-dimensional Bose-Einstein condensate (BEC) in a…
Relativistic linear stability equations for the nonlinear Dirac equation in Bose-Einstein condensates
L. H. Haddad, L. D. Carr
We present relativistic linear stability equations (RLSE) for quasi-relativistic cold atoms in a honeycomb optical lattice. These equations are derived from first principles and pr…