Quantum field theoretical description of unstable behavior of trapped Bose-Einstein condensates with complex eigenvalues of Bogoliubov-de Gennes equations
- Department of Physics, Waseda University, Tokyo 169-8555 (Japan)
- Department of Applied Physics, Waseda University, Tokyo 169-8555 (Japan)
- Department of Materials Science and Engineering, Waseda University, Tokyo 169-8555 (Japan)
The Bogoliubov-de Gennes equations are used for a number of theoretical works on the trapped Bose-Einstein condensates. These equations are known to give the energies of the quasi-particles when all the eigenvalues are real. We consider the case in which these equations have complex eigenvalues. We give the complete set including those modes whose eigenvalues are complex. The quantum fields which represent neutral atoms are expanded in terms of the complete set. It is shown that the state space is an indefinite metric one and that the free Hamiltonian is not diagonalizable in the conventional bosonic representation. We introduce a criterion to select quantum states describing the metastablity of the condensate, called the physical state conditions. In order to study the instability, we formulate the linear response of the density against the time-dependent external perturbation within the regime of Kubo's linear response theory. Some states, satisfying all the physical state conditions, give the blow-up and damping behavior of the density distributions corresponding to the complex eigenmodes. It is qualitatively consistent with the result of the recent analyses using the time-dependent Gross-Pitaevskii equation.
- OSTI ID:
- 21077643
- Journal Information:
- Annals of Physics (New York), Vol. 322, Issue 10; Other Information: DOI: 10.1016/j.aop.2007.01.008; PII: S0003-4916(07)00015-2; Copyright (c) 2007 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
- Country of Publication:
- United States
- Language:
- English
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