Hidden multiparticle excitation in a weakly interacting Bose-Einstein condensate

Abstract

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.

Identities and Many-Body Approaches in Bose-Einstein Condensates

“…where f 0 | = (0, 1, 1, 0) and |f 0 = (0, 1, 1, 0) T . This regular part does not show the infrared divergence and converges to [15][16][17]…”

“…This section focuses on many-body approaches at nonzero temperatures, such as the random-phase approximation, and the many-body T -matrix theory. [15][16][17] For simplicity, we take the convention V = = k B = 1 in this section. It may be convenient to construct building blocks for many-body contributions from the single-particle Green's function in the Hartree-Fock-Bogoliubov-Popov approximation (Shohno model), 10 given by g(p) = g 11 g 12…”

“…where ⊗ is the Kronecker product. Since the normal and anomalous Green's function has the opposite sign in the low-energy regime, i.e., g ij (p) ≃ (−1) i+j mc 2 0 /(ω 2 − c 2 0 p 2 ), where the Bogoliubov phonon sound speed is c 0 = U n 0 /m, the infrared divergence of this correlation function Π has a simple structure, which can be extracted by the following matrix [15][16][17]…”

“…The correlation function Π R ≡ Π − Π IR converges to a finite value in the lowenergy limit. Using this correlation function Π, the four point vertex Γ and the regular part of the density response function χ R are respectively given by [15][16][17]…”

“…7 Finally, we discuss many-body approaches satisfying these identities. [15][16][17] Development of approximation frameworks for BEC is not completed, in the sense that there is not a practical approximation satisfying all the exact relations in BECs. We hope that this paper helps to guide readers towards theories on BECs, and is useful for developing them.…”