Abstract
We give a lower bound on the ground state energy of a system of two fermions of one species interacting with two fermions of another species via point interactions. We show that there is a critical mass ratio m2 ≈ 0.58 such that the system is stable, i.e., the energy is bounded from below, for \(m \in [m_{2}, m_{2}^{-1}]\). So far it was not known whether this 2 + 2 system exhibits a stable region at all or whether the formation of four-body bound states causes an unbounded spectrum for all mass ratios, similar to the Thomas effect. Our result gives further evidence for the stability of the more general N + M system.
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Financial support by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 694227), and by the Austrian Science Fund (FWF), project Nr. P27533-N27, is gratefully acknowledged.
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Moser, T., Seiringer, R. Stability of the 2 + 2 Fermionic System with Point Interactions. Math Phys Anal Geom 21, 19 (2018). https://doi.org/10.1007/s11040-018-9275-3
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DOI: https://doi.org/10.1007/s11040-018-9275-3