Energy Contribution of a Point-Interacting Impurity in a Fermi Gas

  • Thomas Moser
  • Robert SeiringerEmail author
Open Access


We give a bound on the ground-state energy of a system of N non-interacting fermions in a three-dimensional cubic box interacting with an impurity particle via point interactions. We show that the change in energy compared to the system in the absence of the impurity is bounded in terms of the gas density and the scattering length of the interaction, independently of N. Our bound holds as long as the ratio of the mass of the impurity to the one of the gas particles is larger than a critical value \({m^{**}}\approx 0.36\), which is the same regime for which we recently showed stability of the system.



Open access funding provided by Institute of Science and Technology (IST Austria). We would like to thank Ulrich Linden for many helpful discussions. 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. P 27533-N27, is gratefully acknowledged.


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Authors and Affiliations

  1. 1.IST AustriaKlosterneuburgAustria

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