Issue |
EPL
Volume 94, Number 5, June 2011
|
|
---|---|---|
Article Number | 56002 | |
Number of page(s) | 6 | |
Section | Condensed Matter: Structural, Mechanical and Thermal Properties | |
DOI | https://doi.org/10.1209/0295-5075/94/56002 | |
Published online | 25 May 2011 |
Relativistic linear stability equations for the nonlinear Dirac equation in Bose-Einstein condensates
Department of Physics, Colorado School of Mines - Golden, CO 80401, USA
a
haddad@mines.edu
b
lcarr@mines.edu
Received:
8
January
2011
Accepted:
19
April
2011
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 Schrödinger 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.
PACS: 67.85.-d – Ultracold gases, trapped gases / 03.65.Vf – Phases: geometric; dynamic or topological / 05.45.-a – Nonlinear dynamics and chaos
© EPLA, 2011
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