A microscopic theory of the interacting bose system

Vitaly V. Kocharovsky, Vl. V. Kocharovsky

Jorge Alberto Carballo

C. J. Pethick, H. Smith

Willy Bierter, Harry L. Morrison

Philippe Nozières, David Pines

In this chapter, the authors turn their attention to microscopic theories of interacting Bose systems, that class of theories which begin with a given law of interaction between the particles, and derive the various properties of the system therefrom. Microscopic theory does not provide a quantitative description of liquid He II. Indeed, there exists a satisfactory microscopic theory of an interacting boson system in only two limiting cases, those of: Weak repulsive interactions between the bosons; and a dilute gas with arbitrary repulsive interaction between the particles. One sees how the macroscopic occupation of a single quantum state dictates the structure of the microscopic description of system behavior. The Hamiltonian serves as a starting Hamiltonian in authors consideration of microscopic theory; they show that the existence of macroscopic occupation of a single quantum state leads to an effective Hamiltonian which looks rather different.

Shosuke Sasaki, K. Matsuda

A new theory of the interacting bose system is proposed. In contrast with the Bogoliubov theory, the condensate in the present theory is composed of the interacting dressed atoms and the total number of the dressed atoms is conserved. The second-order corrections to the ground-state energy and the excitation energy are evaluated to be found that the results in the present theory coincide with those obtained by Sunakawa et al. On the basis of this situation, it is shown that the present formalism is essentially equivalent to the theory of Sunakawa et al.