Chaotic and regular behaviours of classical and fractional Gross–Pitaevskii equations including two-body, three-body and higher-order interactions

Üzar N.

Pramana - Journal of Physics, cilt.97, sa.1, 2023 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 97 Sayı: 1
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1007/s12043-022-02497-7
  • Dergi Adı: Pramana - Journal of Physics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, Civil Engineering Abstracts
  • Anahtar Kelimeler: 02.60.Cb, 05.30.Jp, 05.45.-a, 05.45.Df, Chaos, fractional Gross–Pitaevskii equations, harmonic potential, higher-order interaction, optical lattice potential, three-body interaction
  • İstanbul Üniversitesi Adresli: Evet

Özet

© 2023, Indian Academy of Sciences.This study investigates the chaotic and regular behaviours of classical and fractional Gross–Pitaevskii equations (GPE) for interacting boson systems under combined harmonic and optical lattice potentials by Poincaré section of phase space, Lyapunov exponents, power spectrum and bifurcation analysis techniques. Also, the effects of system parameters on the system behaviour are discussed. After certain values of the harmonic potential (for β= 0.001 and above), it is seen that the classical GP equation with two-body interaction shows shock wave-like dynamics. In addition, it is found that the harmonic potential is dominant where only binary interaction and three types of interactions exist for β= 0.001 and above. While the boson system exhibits a regular/ quasiperiodic behaviour for a small order of fractional derivative operator, it displays a chaotic structure as it approaches the value of 2.