@article{72457e72169f4e649596abecfa0d6c40,

title = "Quantum field theoretical analysis on unstable behavior of Bose-Einstein condensates in optical lattices",

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 Schr{\"o}dinger equation.",

keywords = "03.75.Kk, 03.75.Lm, 11.10.-z, Bose-Einstein condensation, Dynamical instability, Optical lattice, Quantum field theory",

author = "K. Kobayashi and M. Mine and M. Okumura and Y. Yamanaka",

note = "Funding Information: M.M. is supported partially by the Grant-in-Aid for The 21st Century COE Program (Physics of Self-organization Systems) at Waseda University. This work is partly supported by a Grant-in-Aid for Scientific Research (C) (No. 17540364) from the Japan Society for the Promotion of Science, for Young Scientists (B) (No. 17740258) and for Priority Area Research (B) (No. 13135221) both from the Ministry of Education, Culture, Sports, Science and Technology, Japan. The authors thank the Yukawa Institute for Theoretical Physics at Kyoto University for offering us the opportunity to discuss this work during the YITP workshop YITP-W-06-07, Thermal Quantum Field Theories and Their Applications. ",

year = "2008",

month = may,

doi = "10.1016/j.aop.2007.09.002",

language = "English",

volume = "323",

pages = "1247--1270",

journal = "Annals of Physics",

issn = "0003-4916",

publisher = "Academic Press Inc.",

number = "5",

}