Investigation of classical and fractional Bose–Einstein condensation for harmonic potential

Abstract

In this study, classical and fractional Gross–Pitaevskii (GP) equations were solved for harmonic potential and repulsive interactions between the boson particles using the Homotopy Perturbation Method (HPM) to investigate the ground state dynamics of Bose–Einstein Condensation (BEC). The purpose of writing fractional GP equations is to consider the system in a more realistic manner. The memory effects of non-Markovian processes involving long-range interactions between bosons with the restriction of the ergodic hypothesis and the effect of non-Gaussian distributions of bosons in the condensation can be taken into account with time fractional and space fractional GP equations, respectively. The obtained results of the fractional GP equations differ from the results of the classical one. While the Gauss distribution describing the homogeneous, reversible and unitary system is obtained from the classical GP equation, the probability density of the solution function of fractional GP equations is non-conserved. This situation describes the inhomogeneous, irreversible and non-unitary systems. ► We investigate Bose–Einstein Condensation for real systems. ► Fractional Gross–Pitaevskii equations were written using the Caputo fractional derivative operator. ► Classical and fractional Gross–Pitaevskii equations were solved with the Homotopy Perturbation Method. ► We consider that fractional Gross–Pitaevskii equations can describe the inhomogeneous, irreversible and non-unitary systems.