期刊
PHYSICAL REVIEW A
卷 86, 期 5, 页码 -出版社
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevA.86.053633
关键词
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资金
- NSF [PHY-0653183, PHY-1005543]
- ERC Project FERLODIM [228177]
- European Research Council (ERC) [228177] Funding Source: European Research Council (ERC)
We derive exact general relations between various observables for N bosons with zero-range interactions, in two or three dimensions, in an arbitrary external potential. Some of our results are analogous to relations derived previously for two-component fermions and involve derivatives of the energy with respect to the two-body s-wave scattering length a. Moreover, in the three-dimensional case, where the Efimov effect takes place, the interactions are characterized not only by a, but also by a three-body 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 three-body loss rate always present in experiments (due to three-body recombination to deeply bound diatomic molecules), at least in the limit where the so-called inelasticity parameter eta is small enough. As an application, we obtain, within the zero-range model and to first order in eta, an analytic expression for the three-body 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.
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