Aspects of cold bosonic atoms with a large scattering length

We investigate various aspects of cold bosonic atoms with strong interactions described by a large scattering length alpha. The one-particle-irreducible (1PI) effective action, a functional of a classical atom field that encodes information of quantum effects, is extended to a functional also of a classical dimer field. This equivalent 1PI effective action is more convenient for describing processes involving the loosely-bound diatomic molecules associated with a large positive scattering length. We introduce an approximation to the 1PI effective action in which it is truncated to include 1-body and 2-body terms exactly while higher-body terms are neglected. Using this approximation, we study the properties of a strongly interacting system of bosonic atoms at zero temperature, including the static homogeneous states and the quasi-particle spectrum. The truncated 1PI effective action has a well-defined unitary limit as alpha → +/- infinity in which the properties of the static homogeneous state are determined by the atom number density only. It predicts a quantum phase transition between a phase with a dimer condensate and a phase with a mixture of atom and dimer condensates. We also apply factorization to the break-up and recombination processes for loosely-bound molecules composed of atoms with a large scattering length alpha. If these processes involve atoms with relative momenta much larger than h/|a|, the leading contributions to their rates can be separated into products of short-distance factors that are insensitive to alpha and long-distance factors that are insensitive to the range of the interaction. In the scaling region of the collision energy E, the resulting rates scale as inverse powers of E and do not depend on the scattering length.