Energy contribution of a point interacting impurity in a Fermi gas

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 $m_c\approx 0.36$, which is the same regime for which we recently showed stability of the system.

LaTeX, 39 pages

References in corpus (7)

• Stability of a fermionic $N+1$ particle system with point interactions
• Spectral analysis of the 2+1 fermionic trimer with contact interactions
• The three-body problem in dimension one: From short-range to contact interactions
• Stability of the 2+2 fermionic system with point interactions
• Spectral Theory of the Fermi Polaron
• Stability of the two-dimensional Fermi polaron
• Remarks on the Hamiltonian for the Fermionic Unitary Gas model

Cited by in corpus (3)

• Spectral Theory of the Fermi Polaron
• High Density Limit of the Fermi Polaron with Infinite Mass
• Weak coupling limit for the ground state energy of the 2D Fermi polaron