Abstract
Starting with this lecture, we turned our attention to the case of an interacting gas. This lesson was devoted to the low-temperature regime, for which the state of the gas can be described as a "quasi-condensate", i.e. a condensate with a fluctuating phase. We adopted a description of the atomic fluid in terms of the classical field, which brought significant simplifications compared to the fully quantum description. However, we have shown that this description in terms of the classical field still contains an essential "quantum element", the quantization of velocity circulation. This plays a central role in lecture 4, where we look at the physics of wormholes. In lecture 3, we focused on "soft" gas excitations, i.e. phonons, which are predominant at low temperatures. Our key result was to show that the repulsive interactions between atoms that underlie this phonon physics induce a long-range quasi-order in the gas, with an algebraic decay of the one-body correlation function G1(r). This result is radically different from that found for a perfect gas in the previous lecture, where we showed that G1(r) always decays exponentially with distance in the absence of interactions.
