Interaction effects in the weakly repulsive Bose gas: Two studies

R. E. Barfknecht, Angela Foerster, Nikolaj Thomas Zinner

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.

Liu Hui

The low-temperature properties of a weakly interacting Bose gas in weak magnetic field are studied by using the conclusion of a weakly interacting Bose gas in external potential.The expressions of total energy and heat capacity are given analytically.The effects of the interparticle interactions as well as magnetic field on the thermodynamic properties of the system are discussed.It is shown that repulsion(attraction) can make the spatial distribution of particle number and energy concentrate(disperse) and the chemical potential,total energy,heat capacity of system increase(decrease).While strengthen magnetic field,the spatial distribution of particle number and energy will tend to disperse and the effects of interaction on it will be weaken.The effects of interaction on the different eigenvalue exist different individual behaviors.

Renu Bala, K. N. Pathak

Jean Zinn‐Justin

Abstract Chapter 20 examines effects of weak repulsive interactions in a Bose–Einstein condensate and the transition from Bose–Einstein condensate to superfluid phase transition. Renormalization group methods are used and a universal amplitude is calculated by non–perturbative methods. After the discovery of the predicted Bose–Einstein condensation, which is a property of free bosons, an interesting issue was the effects of weak repulsive interactions. In this chapter, it is shown that, near the transition temperature, the initial non–relativistic field theory can be replaced by a relativistic effective Euclidean field theory known to describe a superfluid phase transition (a dimensional reduction). These theoretical considerations are illustrated by an evaluation of the universal variation of the transition temperature at weak coupling. For this purpose, the O(2) symmetry of the model is generalized to O(N) symmetry, and large N techniques are used.