Une transition liquide-gaz pour des bosons en interaction attractive à une dimension

We consider a one-dimensional system of N bosons interacting via an attractive Dirac delta function potential. We place the bosonic quantum particles at thermal equilibrium in a box of length L with periodic boundary conditions. At large N and for L much larger than the diameter of a two-particle bound state, we predict by numerical and analytical studies of a simple model derived from first principles that the system exhibits a first-order phase transition in a high temperature, non-degenerate regime. The higher-temperature phase is an almost pure atomic gas, with a small fraction of dimers, a smaller fraction of trimers, etc. The lower-temperature phase is a mesoscopic or macroscopic bound state that collects all the particles of the system, with the exception of a small gaseous fraction composed mainly of atoms. We term this phase, which is the quantum equivalent of the classical bright soliton, a liquid.