Quantum field theoretical analysis on unstable behavior of Bose-Einstein condensates in optical lattices

K. Kobayashi, Makoto Mine, M. Okumura, Yoshiya Yamanaka

Research output: Contribution to journalArticle


We study the dynamics of Bose-Einstein condensates flowing in optical lattices on the basis of quantum field theory. For such a system, a Bose-Einstein condensate shows an unstable behavior which is called the dynamical instability. The unstable system is characterized by the appearance of modes with complex eigenvalues. Expanding the field operator in terms of excitation modes including complex ones, we attempt to diagonalize the unperturbative Hamiltonian and to find its eigenstates. It turns out that although the unperturbed Hamiltonian is not diagonalizable in the conventional bosonic representation the appropriate choice of physical states leads to a consistent formulation. Then we analyze the dynamics of the system in the regime of the linear response theory. Its numerical results are consistent with those given by the discrete nonlinear Schrödinger equation.

Original languageEnglish
Pages (from-to)1247-1270
Number of pages24
JournalAnnals of Physics
Issue number5
Publication statusPublished - 2008 May



  • 03.75.Kk
  • 03.75.Lm
  • 11.10.-z
  • Bose-Einstein condensation
  • Dynamical instability
  • Optical lattice
  • Quantum field theory

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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