Bose condensation of weakly interacting massLESS particles

Benjamin Hinrichs, Jonas Lampart

In the Bogoliubov–Fröhlich model, we prove that an impurity immersed in a Bose–Einstein condensate forms a stable quasi-particle when the total momentum is less than its mass times the speed of sound. The system thus exhibits superfluid behavior, as this quasi-particle does not experience friction. We do not assume any infrared or ultraviolet regularization of the model, which contains massless excitations and point-like interactions.

C. G. Townsend, N. J. van Druten, Michael R. Andrews +4 more

Fabrizio Tafuri, C. A. Perroni, G. De Filippis

Takafumi Kita

We theoretically study the properties of Nambu-Goldstone bosons in an interacting single-component Bose-Einstein condensate (BEC). We first point out that the proofs of Goldstone's theorem by Goldstone, et al. [Phys. Rev. {\bf 127} (1962) 965] may be relevant to distinct massless modes of the BEC: whereas the first proof deals with the poles of the single-particle Green's function $\hat{G}$, the second one concerns those of the two-particle Green's function. Thus, there may be multiple Nambu-Goldstone bosons even in the single-component BEC with broken U(1) symmetry. The second mode turns out to have an infinite lifetime in the long-wavelength limit in agreement with the conventional viewpoint. In contrast, the first mode from $\hat{G}$, i.e., the Bogoliubov mode in the weak-coupling regime, is shown to be a "bubbling" mode fluctuating temporally out of and back into the condensate. The substantial lifetime originates from an "improper" structure of the self-energy inherent in the BEC, which has been overlooked so far and will be elucidated here, and removes various infrared divergences pointed out previously.

Lukong Cornelius Fai

This chapter examines a simple example of a quantum liquid that is a weakly nonideal gas. In this case, the interaction among gas particles is relatively small. The chapter examines a weakly interacting Bose gas at almost zero temperature. Interactions in atomic gases are usually very weak, but they can have important effects. It shows that the interactions among gas particles are repulsive. This implies that the scattering amplitude is positive. It is important to note that for the case of a Bose gas, the assumption is connected with the fact that even for infinitesimal attractive forces, a Bose gas cannot remain dilute at low temperatures. All particles in the condensate are in the ground state of an ideal Bose gas. This is for the zero-state energy. The gas is often said to be in the condensate or the condensed state. The diagonalization is done by introducing the canonical transformation known as a Bogoliubov transformation.

Joseph V. Pulé