2012/03/15 by N. Uzar, Neslihan Üzar, D. Han +7
Computer Science · Mathematics · Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Other Condensed Matter (cond-mat.other) #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Spectroscopy and Quantum Chemical Studies #Strong Light-Matter Interactions #cond-mat.other #math-ph #math.MP #nlin.SI #quant-ph
paper · pdf · doi:10.48550/arxiv.1203.3352
29 page 12 figures
arxiv created 2012/03/15 · openalex publication_date 2012/03/15 · arxiv updated 2012/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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) =±sin2x by using Homotopy Perturbation Method. We have found that the Homotopy Perturbation Method solutions of the Gross-Pitaevskii equation for these 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.