Exact Solutions for Equations of Bose-Fermi Mixtures in One-Dimensional Optical Lattice
We present two new families of stationary solutions for equations of Bose-Fermi mixtures with an elliptic function potential with modulus k. We also discuss particular cases when the quasiperiodic solutions become periodic ones. In the limit of a sinusoidal potential (k → 0) our solutions model a qu...
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| Datum: | 2007 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут математики НАН України
2007
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| Schriftenreihe: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/147363 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Exact Solutions for Equations of Bose-Fermi Mixtures in One-Dimensional Optical Lattice / N.A. Kostov, V.S. Gerdjikov, T.I. Valchev // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 27 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | We present two new families of stationary solutions for equations of Bose-Fermi mixtures with an elliptic function potential with modulus k. We also discuss particular cases when the quasiperiodic solutions become periodic ones. In the limit of a sinusoidal potential (k → 0) our solutions model a quasi-one dimensional quantum degenerate Bose-Fermi mixture trapped in optical lattice. In the limit k → 1 the solutions are expressed by hyperbolic function solutions (vector solitons). Thus we are able to obtain in an unified way quasi-periodic and periodic waves, and solitons. The precise conditions for existence of every class of solutions are derived. There are indications that such waves and localized objects may be observed in experiments with cold quantum degenerate gases. |
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