Universal behaviour of four-boson systems from a functional renormalisation group
arXiv:1304.5454 · doi:10.1103/PhysRevA.88.043613
Abstract
We apply a functional renormalisation group to systems of four bosonic atoms close to the unitary limit. We work with a local effective action that includes a dynamical trimer field and we use this field to eliminate structures that do not correspond to the Faddeev-Yakubovsky equations. In the physical limit, we find three four-body bound states below the shallowest three-body state. The values of the scattering lengths at which two of these states become bound are in good agreement with exact solutions of the four-body equations and experimental observations. The third state is extremely shallow. During the evolution we find an infinite number of four-body states based on each three-body state which follow a double-exponential pattern in the running scale. None of the four-body states shows any evidence of dependence on a four-body parameter.
9 pages, 3 figures, details of flow equations and more explanation added
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- Nuclear Physics Around the Unitarity Limit
- Renormalization group study of Bose polarons
- Topological origin of universal few-body clusters in Efimov physics
- Four-boson bound states from a functional renormalisation group
- Functional renormalisation group approach to the finite-temperature Bose polaron