The nonlinear Dirac equation in Bose-Einstein condensates: Foundation and symmetries

被引：89

作者：

Haddad, L. H. ^{[1
]}

Carr, L. D. ^{[1
]}

机构：

[1] Colorado Sch Mines, Dept Phys, Golden, CO 80401 USA

来源：

PHYSICA D-NONLINEAR PHENOMENA | 2009年 / 238卷 / 15期

基金：

美国国家科学基金会;

关键词：

Nonlinear Dirac equation; Nonlinear Schrodinger equation; Bose-Einstein condensates; Ultra-cold atoms; Optical lattices; Graphene; GRAPHENE; SOLITONS; FERMIONS; STATES;

D O I：

10.1016/j.physd.2009.02.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that Bose-Einstein condensates in a honeycomb optical lattice can he 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., Poincare 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. (C) 2009 Elsevier B.V. All rights reserved.

引用

页码：1413 / 1421

页数：9

共 51 条

[1] Optical solitary waves in two- and three-dimensional nonlinear photonic band-gap structures [J].