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Impact of Quantum Fluctuations on the Modulational Instability of a Modified Gross-Pitaevskii Equation with Two-Body Interaction
Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaounde I, Yaounde, Cameroon
Departement de Physique de l' Universite des Sciences et Techniques de Masuku, B.P. 943 Franceville, Gabon
Ecole Normale Superieure, B.P. 2889 Libreville, Gabon
Max Planck Institute for the Physics of Complex Systems, Dresden, Germany
Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaounde I, Yaounde, Cameroon
- 1 Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaounde I, Yaounde, Cameroon
- 2 Departement de Physique de l' Universite des Sciences et Techniques de Masuku, B.P. 943 Franceville, Gabon
- 3 Ecole Normale Superieure, B.P. 2889 Libreville, Gabon
- 4 Max Planck Institute for the Physics of Complex Systems, Dresden, Germany
- 5 Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaounde I, Yaounde, Cameroon
Applied Mathematics·Volume 03 (2012)·Pages 844–850·Published 28 August 2012·DOI10.4236/am.2012.38125
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Abstract
Modulational instability conditions for the generation of localized structures in the context of matter waves in Bose-Einstein condensates are investigated analytically and numerically. The model is based on a modified Gross-Pitaevskii equation, which account for the energy dependence of the two-body scattering amplitude. It is shown that the modified term due to the quantum fluctuations modify significantly the modulational instability gain. Direct numerical simulations of the full modified Gross-Pitaevskii equation are performed, and it is found that the modulated plane wave evolves into a train of pulses, which is destroyed at longer times due to the effects of quantum fluctuations.
KeywordsModulational InstabilityModified Gross-Pitaevskii EquationQuantum Fluctuations
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