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

@misc{citeulike:2601217, abstract = {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.}, archivePrefix = {arXiv}, author = {Haddad, L. H. and Carr, L. D.}, citeulike-article-id = {2601217}, citeulike-linkout-0 = {http://arxiv.org/abs/0803.3039}, citeulike-linkout-1 = {http://arxiv.org/pdf/0803.3039}, day = {20}, eprint = {0803.3039}, keywords = {becs, dirac-equation, nonlinearity, symmetries}, month = {Mar}, posted-at = {2009-06-06 17:23:10}, priority = {2}, title = {The Nonlinear Dirac Equation in Bose-Einstein Condensates: Foundation and Symmetries}, url = {http://arxiv.org/abs/0803.3039}, year = {2008} }

TY - ELEC ID - citeulike:2601217 L3 - citeulike-article-id:2601217 N2 - 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. TI - The Nonlinear Dirac Equation in Bose-Einstein Condensates: Foundation and Symmetries KW - becs KW - dirac-equation KW - nonlinearity KW - symmetries AU - Haddad, LH AU - Carr, LD PY - 2008/Mar/20/ UR - http://arxiv.org/abs/0803.3039 ER -