### 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 |
---|---|

Pages (from-to) | 1247-1270 |

Number of pages | 24 |

Journal | Annals of Physics |

Volume | 323 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2008 May |

### Fingerprint

### 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

**Quantum field theoretical analysis on unstable behavior of Bose-Einstein condensates in optical lattices.** / Kobayashi, K.; Mine, Makoto; Okumura, M.; Yamanaka, Yoshiya.

Research output: Contribution to journal › Article

*Annals of Physics*, vol. 323, no. 5, pp. 1247-1270. https://doi.org/10.1016/j.aop.2007.09.002

}

TY - JOUR

T1 - Quantum field theoretical analysis on unstable behavior of Bose-Einstein condensates in optical lattices

AU - Kobayashi, K.

AU - Mine, Makoto

AU - Okumura, M.

AU - Yamanaka, Yoshiya

PY - 2008/5

Y1 - 2008/5

N2 - 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.

AB - 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.

KW - 03.75.Kk

KW - 03.75.Lm

KW - 11.10.-z

KW - Bose-Einstein condensation

KW - Dynamical instability

KW - Optical lattice

KW - Quantum field theory

UR - http://www.scopus.com/inward/record.url?scp=41849083086&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=41849083086&partnerID=8YFLogxK

U2 - 10.1016/j.aop.2007.09.002

DO - 10.1016/j.aop.2007.09.002

M3 - Article

VL - 323

SP - 1247

EP - 1270

JO - Annals of Physics

JF - Annals of Physics

SN - 0003-4916

IS - 5

ER -