| Autor: |
L H Haddad, Lincoln D Carr |
| Jazyk: |
angličtina |
| Rok vydání: |
2015 |
| Předmět: |
|
| Zdroj: |
New Journal of Physics, Vol 17, Iss 11, p 113011 (2015) |
| Druh dokumentu: |
article |
| ISSN: |
1367-2630 |
| DOI: |
10.1088/1367-2630/17/11/113011 |
| Popis: |
We analyze the vortex solution space of the $(2+1)$ -dimensional nonlinear Dirac equation for bosons in a honeycomb optical lattice at length scales much larger than the lattice spacing. Dirac point relativistic covariance combined with s-wave scattering for bosons leads to a large number of vortex solutions characterized by different functional forms for the internal spin and overall phase of the order parameter. We present a detailed derivation of these solutions which include skyrmions, half-quantum vortices, Mermin–Ho and Anderson–Toulouse vortices for vortex winding ${\ell }=1.$ For ${\ell }\geqslant 2$ we obtain topological as well as non-topological solutions defined by the asymptotic radial dependence. For arbitrary values of ℓ the non-topological solutions include bright ring-vortices which explicitly demonstrate the confining effects of the Dirac operator. We arrive at solutions through an asymptotic Bessel series, algebraic closed-forms, and using standard numerical shooting methods. By including a harmonic potential to simulate a finite trap we compute the discrete spectra associated with radially quantized modes. We demonstrate the continuous spectral mapping between the vortex and free particle limits for all of our solutions. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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