Infrared behavior of interacting bosons at zero temperature

Dupuis, N.; Rançon, Adam

doi:10.1134/s1054660x11150059

“…are density and phase fluctuation operators. Green's functions in the hydrodynamic picture and the standard picture are related each other [5,19,22,23,32], giving the form…”

Section: List Of πmentioning

confidence: 99%

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

Watabe,

Ohashi

2014

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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, as well as 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 non-singular 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.

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“…Green's functions in the hydrodynamic picture and the standard picture are related each other [5,19,22,23,32], giving the form…”

Section: Appendix B: Popov's Hydrodynamic Theorymentioning

confidence: 99%

“…Here, G AB with A, B = π, ϕ is the non-perturbed correlation function for the hydrodynamic variables, given by [5,19,22,23,32]…”

Section: Appendix B: Popov's Hydrodynamic Theorymentioning

confidence: 99%

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

Watabe

¹

,

Ōhashi

²

2014

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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, as well as 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 non-singular 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.

show abstract

“…Notify that the diagrammatic contribution employed in this paper satisfies exact identities. Since the lowest contribution of the regular part shows the infrared divergence χ 0 R (p) ∝ −T /|p| at nonzero temperatures [49][50][51], the off-diagonal self-energy satisfies the Nepomnyashchii-Nepomnyashchii identity Σ 12 (0) = Σ 12,c (0) = 0 [52], which leads the infrared divergence of the longitudinal susceptibility caused by the higher order phase-phase correlation [49][50][51][53][54][55]. Because of the same reason of the infrared divergence, the density vertices also satisfy the exact identity Υ(0) = Υ † (0) = 0 [52].…”

mentioning

confidence: 99%

Hidden multiparticle excitation in a weakly interacting Bose-Einstein condensate

Watabe

¹

2018

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We investigate multiparticle excitation effect on a collective density excitation as well as a singleparticle excitation in a weakly interacting Bose-Einstein condensate (BEC). We find that although the weakly interacting BEC offers weak multiparticle excitation spectrum at low temperatures, this multiparticle excitation effect may not remain hidden, but emerges as bimodality in the density response function through the single-particle excitation. Identification of spectra in the BEC between the single-particle excitation and the density excitation is also assessed at nonzero temperatures, which has been known to be unique nature in the BEC at absolute zero temperature.

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Infrared behavior of interacting bosons at zero temperature

Cited by 6 publications

References 28 publications

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

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

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

Hidden multiparticle excitation in a weakly interacting Bose-Einstein condensate

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