Green's-function formalism for a condensed Bose gas consistent with infrared-divergent longitudinal susceptibility and Nepomnyashchii-Nepomnyashchii identity

Shohei Watabe, Yoji Ohashi

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Abstract

We present a Green's-function formalism for an interacting Bose-Einstein condensate (BEC) satisfying the two required conditions: (i) the infrared-divergent longitudinal susceptibility with respect to the BEC order parameter, and (ii) the Nepomnyashchii-Nepomnyashchii identity stating the vanishing off-diagonal self-energy in the low-energy and low-momentum limit. These conditions cannot be described by the ordinary mean-field Bogoliubov theory, the many-body T-matrix theory, or the random-phase approximation with the vertex correction. In this paper, we show that these required conditions can be satisfied, when we divide many-body corrections into singular and nonsingular parts, and separately treat them as different self-energy corrections. The resulting Green's function may be viewed as an extension of the Popov's hydrodynamic theory to the region at finite temperatures. Our results would be useful in constructing a consistent theory of BECs satisfying various required conditions, beyond the mean-field level.

Original languageEnglish
Article number013603
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Volume90
Issue number1
DOIs
Publication statusPublished - 2014 Jul 3

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ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

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