Based on Classical and Fractional Approach
In this study, after we have briefly introduced the standard Gross- Pitaevskii equation, we have suggested
fractional Gross-Pitaevskii to investigate the time-dependent ground state dynamics of the Bose-Einstein
condensation. We think that fractional Gross-Pitaevskii equation can include the non-Markovian process or non-
Gaussian distribution and long-range interactions of weakly interacting bosonic particle system. We are
interested in memory effect of non-Markovian process; we only focused the time-fractional Gross-Pitaevskii
equation. We have obtained solutions of the Gross-Pitaevskii equation of the integer and fractional order for
attractive and repulsive interactions in the case external trap potentials and optical lattice potential
using Homotopy Perturbation Method. We have found that the Homotopy Perturbation Method
solutions of the standard 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 solution 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 evolves with time as stretched
exponentially.
NUTKU Ferhat
Danışman : Prof. Dr. M. Çetin ARIKAN
Anabilim Dalı : Fizik
Programı (Varsa) : Katıhal Fiziği
Mezuniyet Yılı : 2013
Tez Savunma Jürisi : Prof. Dr. M. Çetin ARIKAN
Prof. Dr. Yüksel ERGÜN
Doç. Dr. Ayşe EROL
Doç. Dr. Afif SIDDIKİ
Doç. Dr. Oğuzhan GÜRLÜ
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