The Nonlinear Dirac Equation in Bose-Einstein Condensates: Foundation and Symmetries

Details The Nonlinear Dirac Equation in Bose-Einstein Condensates: Foundation and Symmetries The Nonlinear Dirac Equation in Bose-Einstein Condensates: Foundation and Symmetries

2008-03-20

arxiv.org/abs/0803.3039v1

Physica D: Nonlinear Phenomena, v. 238, p. 1413 (2009)

Physics

Condensed Matter

Other Condensed Matter

11 pages, 1 figure

Scientific paper

10.1016/j.physd.2009.02.001

We show that Bose-Einstein condensates in a honeycomb optical lattice are described by a nonlinear Dirac equation in the long wavelength, mean field limit. Unlike nonlinear Dirac equations posited by particle theorists, which are designed to preserve the principle of relativity, i.e., Poincar\'e covariance, the nonlinear Dirac equation for Bose-Einstein condensates breaks this symmetry. We present a rigorous derivation of the nonlinear Dirac equation from first principles. We provide a thorough discussion of all symmetries broken and maintained.

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