### Abstract

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 language | English |
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Pages (from-to) | 1247-1270 |

Number of pages | 24 |

Journal | Annals of Physics |

Volume | 323 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2008 May |

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### Keywords

- 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)

### Cite this

*Annals of Physics*,

*323*(5), 1247-1270. https://doi.org/10.1016/j.aop.2007.09.002