General relations for quantum gases in two and three dimensions. II. Bosons and mixtures
Abstract
We derive exact general relations between various observables for N bosons with zerorange interactions, in two or three dimensions, in an arbitrary external potential. Some of our results are analogous to relations derived previously for twocomponent fermions and involve derivatives of the energy with respect to the twobody swave scattering length a. Moreover, in the threedimensional case, where the Efimov effect takes place, the interactions are characterized not only by a, but also by a threebody parameter R_{t}. We then find additional relations which involve the derivative of the energy with respect to R_{t}. In short, this derivative gives the probability of finding three particles close to each other. Although it is evaluated for a totally lossless model, it also gives the threebody loss rate always present in experiments (due to threebody recombination to deeply bound diatomic molecules), at least in the limit where the socalled inelasticity parameter η is small enough. As an application, we obtain, within the zerorange model and to first order in η, an analytic expression for the threebody loss rate constant for a nondegenerate Bose gas at thermal equilibrium with infinite scattering length. We also discuss the generalization to arbitrary mixtures of bosons and/or fermions.
 Publication:

Physical Review A
 Pub Date:
 November 2012
 DOI:
 10.1103/PhysRevA.86.053633
 arXiv:
 arXiv:1210.1784
 Bibcode:
 2012PhRvA..86e3633W
 Keywords:

 67.85.d;
 Ultracold gases trapped gases;
 Condensed Matter  Quantum Gases
 EPrint:
 Published version, augmented by (i) a note in section III on the universal correction to the ground state energy of the 2D weakly interacting Bose gas due to a nonzero interaction range and (ii) a note in section IV.C on the decay rate due to threebody losses of an Efimov trimer close to the atomdimer dissociation threshold