dc.contributor.author | AYDINER, EKREM | |
dc.date.accessioned | 2021-03-03T16:38:25Z | |
dc.date.available | 2021-03-03T16:38:25Z | |
dc.date.issued | 2012 | |
dc.identifier.citation | AYDINER E., "Solutions of the Gross-Pitaevskii and time-fractional Gross-Pitaevskii equations for different potentials with Homotopy Perturbation Method", arXiv, cilt.1, sa.1, ss.1-10, 2012 | |
dc.identifier.other | vv_1032021 | |
dc.identifier.other | av_4549fe57-1ec3-4a93-9504-7b9e845c159e | |
dc.identifier.uri | http://hdl.handle.net/20.500.12627/50251 | |
dc.identifier.uri | http://arxiv.org/abs/1203.3352 | |
dc.description.abstract | In this study, after we have briefly introduced the standard Gross-Pitaevskii equation, we have suggested fractional Gross-Pitaevskii equations to investigate the time-dependent ground state dynamics of the Bose-Einstein condensation of weakly interacting bosonic particle system which can includes non-Markovian processes or non-Gaussian distributions and long-range interactions. Only we focused the time-fractional Gross-Pitaevskii equation and have obtained solutions of the standard Gross-Pitaevskii and time-fractional Gross-Pitaevskii equations for attractive and repulsive interactions in the case external trap potentials $V(x)=0$ and optical lattice potential $V(x) =\pm\sin^{2}x$ by using Homotopy Perturbation Method. We have found that the Homotopy Perturbation Method solutions of the Gross-Pitaevskii equation forthese potentials and interactions are the same analytical results of it. Furthermore we have also found that solutions of the time-fractional Gross-Pitaevskii equation for these potentials and interactions can be given in terms of Mittag-Leffler function. The solutions of the time-fractional Gross-Pitaevskii equation provide that the time evolution of the ground state dynamics of Bose-Einstein condensation of bosonic particles deviates exponential form, and evolutes with time as stretched exponentially. | |
dc.language.iso | eng | |
dc.subject | Fizik | |
dc.subject | Temel Bilimler (SCI) | |
dc.subject | Temel Bilimler | |
dc.title | Solutions of the Gross-Pitaevskii and time-fractional Gross-Pitaevskii equations for different potentials with Homotopy Perturbation Method | |
dc.type | Makale | |
dc.relation.journal | arXiv | |
dc.contributor.department | İstanbul Üniversitesi , Fen Fakültesi , Fizik Bölümü | |
dc.identifier.volume | 1 | |
dc.identifier.issue | 1 | |
dc.identifier.startpage | 1 | |
dc.identifier.endpage | 10 | |
dc.contributor.firstauthorID | 572101 | |