Self-consistent perturbation expansion for Bose-Einstein condensates satisfying Goldstone's theorem and conservation laws
- Department of Physics, Hokkaido University, Sapporo 060-0810 (Japan)
Quantum-field-theoretic descriptions of interacting condensed bosons have suffered from the lack of self-consistent approximation schemes satisfying Goldstone's theorem and dynamical conservation laws simultaneously. We present a procedure to construct such approximations systematically by using either an exact relation for the interaction energy or the Hugenholtz-Pines relation to express the thermodynamic potential in a Luttinger-Ward form. Inspection of the self-consistent perturbation expansion up to the third order with respect to the interaction shows that the two relations yield a unique identical result at each order, reproducing the conserving-gapless mean-field theory [T. Kita, J. Phys. Soc. Jpn. 74, 1891 (2005)] as the lowest-order approximation. The uniqueness implies that the series becomes exact when infinite terms are retained. We also derive useful expressions for the entropy and superfluid density in terms of Green's function and a set of real-time dynamical equations to describe thermalization of the condensate.
- OSTI ID:
- 21294536
- Journal Information:
- Physical Review. B, Condensed Matter and Materials Physics, Vol. 80, Issue 21; Other Information: DOI: 10.1103/PhysRevB.80.214502; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1098-0121
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
SUPERCONDUCTIVITY AND SUPERFLUIDITY
APPROXIMATIONS
BOSE-EINSTEIN CONDENSATION
CONDENSATES
CONSERVATION LAWS
DISTURBANCES
ENTROPY
EQUATIONS
FREE ENERGY
GOLDSTONE BOSONS
GREEN FUNCTION
INTERACTIONS
MEAN-FIELD THEORY
PERTURBATION THEORY
QUANTUM FIELD THEORY
SUPERFLUIDITY
THERMALIZATION