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

Uzar N., Ballikaya S.

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, cilt.392, sa.8, ss.1733-1741, 2013 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 392 Sayı: 8
  • Basım Tarihi: 2013
  • Doi Numarası: 10.1016/j.physa.2012.11.039
  • Dergi Adı: PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1733-1741
  • Anahtar Kelimeler: Bose-Einstein condensation, Gross-Pitaevskii equation, Homotopy perturbation method, Caputo fractional derivative operator, HOMOTOPY PERTURBATION METHOD, GAS
  • İstanbul Üniversitesi Adresli: Evet

Özet

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. (c) 2012 Elsevier B.V. All rights reserved.