On the physics of weakly-interacting dilute Bose-gas in 2D

This colloquium surveys a number of theoretical problems and open questions in the field of two-dimensional dilute Bose gases with weak repulsive interactions. In contrast to three dimensions, in two dimensions the formation of long-range order is prohibited by the Bogoliubov-Hohenberg theorem, and Bose-Einstein condensation is not expected to occur. Nevertheless, experimental indications supporting the formation of a condensate in low-dimensional systems have recently been obtained. This unexpected behavior appears to be due to the nonuniformity introduced into a system by the external trapping potential. Theoretical predictions, made for homogeneous systems, require therefore careful reexamination. A number of popular theoretical treatments of the dilute weakly interacting Bose gas are presented and their regions of applicability are discussed. The possibility of Bose-Einstein condensation in a two-dimensional gas, the validity of the perturbative $t$ -matrix approximation, and the diluteness condition are issues also discussed in detail.This colloquium surveys a number of theoretical problems and open questions in the field of two-dimensional dilute Bose gases with weak repulsive interactions. In contrast to three dimensions, in two dimensions the formation of long-range order is prohibited by the Bogoliubov-Hohenberg theorem, and Bose-Einstein condensation is not expected to occur. Nevertheless, experimental indications supporting the formation of a condensate in low-dimensional systems have recently been obtained. This unexpected behavior appears to be due to the nonuniformity introduced into a system by the external trapping potential. Theoretical predictions, made for homogeneous systems, require therefore careful reexamination. A number of popular theoretical treatments of the dilute weakly interacting Bose gas are presented and their regions of applicability are discussed. The possibility of Bose-Einstein condensation in a two-dimensional gas, the validity of the perturbative $t$-matrix approximation, and the diluteness condition are issues also discussed in detail.

arXiv:cond-mat/0506034Reviews of Modern PhysicsOct 4, 2006156 citations

Ground-State Properties of a Dilute Two-Dimensional Bose Gas

V. Pastukhov

arXiv:1803.05242Journal of Low Temperature PhysicsOct 12, 20187 citations

Susceptibilities of the Higgs Mode in a 2D dilute Bose gas

Ji-Chong Yang, Yu Shi

We investigate the spectral functions of the Higgs mode in a 2D Bose gas by using $O(2)$ model in the zero temperature limit. Our calculation is done up to the full 2-loop contributions as well as some higher order contributions. The peaks show up in the spectral functions of both the longitudinal and the scalar susceptibilities. We point out that the zero temperature limit of $O(2)$ model cannot explain the disappearance of the response at the weak interaction limit, and that to use the longitudinal or scalar susceptibility is irrelevant to the visibility of the Higgs mode. A possible lower peak at about $2m_{\sigma}$ is also noted.We investigate the spectral functions of the Higgs mode in a 2D Bose gas by using $O(2)$ model in the zero temperature limit. Our calculation is done up to the full 2-loop contributions as well as some higher order contributions. The peaks show up in the spectral functions of both the longitudinal and the scalar susceptibilities. We point out that the zero temperature limit of $O(2)$ model cannot explain the disappearance of the response at the weak interaction limit, and that to use the longitudinal or scalar susceptibility is irrelevant to the visibility of the Higgs mode. A possible lower peak at about $2m_{\sigma}$ is also noted.

Apr 26, 20180 citations

Instability in a dilute 2D interacting Bose system

William J. Mullin, Markus Holzmann, Franck Laloë

Jan 1, 20000 citations

t

-matrix approximation, and the diluteness condition are issues also discussed in detail.

We investigate the spectral functions of the Higgs mode in a 2D Bose gas by using

O(2)

model in the zero temperature limit. Our calculation is done up to the full 2-loop contributions as well as some higher order contributions. The peaks show up in the spectral functions of both the longitudinal and the scalar susceptibilities. We point out that the zero temperature limit of

O(2)

model cannot explain the disappearance of the response at the weak interaction limit, and that to use the longitudinal or scalar susceptibility is irrelevant to the visibility of the Higgs mode. A possible lower peak at about

2m_{\sigma}

is also noted.