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arXiv:1807.00739 · Annales Henri Poincaré

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

Thomas Moser, Robert Seiringer

Published Jan 8, 2019• 5 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1007/s00023-018-00757-0

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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∗∗≈0.36{m^{**}}\approx 0.36m∗∗≈0.36 , which is the same regime for which we recently showed stability of the system.
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