%0 Journal Article
%T Semiclassical quantisation for a bosonic atom-molecule conversion system
%A Eva-Maria Graefe
%A Maria Graney
%A Alexander Rush
%J Physics
%D 2015
%I arXiv
%R 10.1103/PhysRevA.92.012121
%X We consider a simple quantum model of atom-molecule conversion where bosonic atoms can combine into diatomic molecules and vice versa. The many-particle system can be expressed in terms of the generators a deformed $SU(2)$ algebra, and the mean-field dynamics takes place on a deformed version of the Bloch sphere, a teardrop shaped surface with a cusp singularity. We analyse the mean-field and many-particle correspondence, which shows typical features of quantum-classical correspondence. We demonstrate that semiclassical methods can be employed to recover full many-particle features from the mean-field description in cold atom systems with atom-molecule conversion, and derive an analytic expression for the many-particle density of states in the limit of large particle numbers.
%U http://arxiv.org/abs/1505.03351v2