Ground State Energy of the Low Density Bose Gas

Elliolt H. Lieb, Jakob Yngvason

Alessandro Giuliani, Robert Seiringer

Élliott H. Lieb, A.Y. Sakakura

Foldy, and later Girardeau, calculated the ground-state energy of a charged Bose gas at high density. We rederive the common first term obtained by these authors by using a nonperturbation method developed previously. Our aims are: (i) to establish the validity of this common result, which has not been proved; (ii) to establish the validity and usefulness of our nonperturbation method. We also show that our method will give the correct functional dependence of the ground-state energy on the density at low density, although the exact coefficient must await a numerical computation.

Alexander A. Ovchinnikov

We propose a new method to describe the interacting Bose gas at zero temperature. For the three-dimensional system the correction to the ground-state energy in density is reproduced. For a two-dimensional dilute Bose gas the ground-state energy in the leading order in the parameter mod ln p alpha 2 mod -1 where alpha is the scattering length is obtained.

Phan Thành Nam, Julien Ricaud, Arnaud Triay

We consider the low density Bose gas in the thermodynamic limit with a three-body interaction potential. We prove that the leading order of the ground state energy of the system is determined completely in terms of the scattering energy of the interaction potential. The corresponding result for two-body interactions was proved in seminal papers of Dyson [Phys. Rev. 106, 20–26 (1957)] and of Lieb and Yngvason [Phys. Rev. Lett. 80, 2504–2507 (1998)].

Rudi Weikard, Gilbert Weinstein