Relativistic linear stability equations for the nonlinear Dirac equation in Bose-Einstein condensates

Details Relativistic linear stability equations for the nonlinear Dirac equation in Bose-Einstein condensates Relativistic linear stability equations for the nonlinear Dirac equation in Bose-Einstein condensates

2010-06-19

arxiv.org/abs/1006.3893v3

Europhys.Lett.94:56002,2011

Physics

Condensed Matter

Quantum Gases

6 pages, 3 figures

Scientific paper

10.1209/0295-5075/94/56002

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 provide a method for computing stabilities of arbitrary localized solutions of the nonlinear Dirac equation (NLDE), a relativistic generalization of the nonlinear Schr\"odinger equation. We present a variety of such localized solutions: skyrmions, solitons, vortices, and half-quantum vortices, and study their stabilities via the RLSE. When applied to a uniform background, our calculations reveal an experimentally observable effect in the form of Cherenkov radiation. Remarkably, the Berry phase from the bipartite structure of the honeycomb lattice induces a boson-fermion transmutation in the quasi-particle operator statistics.

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