• DOI:10.1007/s11005-019-01158-y
• Corpus ID: 119654660

High density limit of the Fermi polaron with infinite mass

@article{Linden2018HighDL,
  title={High density limit of the Fermi polaron with infinite mass},
  author={Ulrich Linden and David Mitrouskas},
  journal={Letters in Mathematical Physics},
  year={2018},
  pages={1-21}
}

• U. Linden, D. Mitrouskas
• Published 17 July 2018
• Physics
• Letters in Mathematical Physics

We analyze the ground state energy for N identical fermions in a two-dimensional box of volume $$L^2$$L2 interacting with an external point scatterer. Since the point scatterer can be considered as an impurity particle of infinite mass, this system is a limit case of the Fermi polaron. We prove that its ground state energy in the limit of high density $$N/L^2\gg 1$$N/L2≫1 is given by the polaron energy. The polaron energy is an energy estimate based on trial states up to first order in particle-hole expansion, which was proposed by Chevy (Phys Rev A 74:063628, 2006) in the physics literature. The relative error in our result is shown to be small uniformly in L. Hence, we do not require a gap of fixed size in the spectrum of the Laplacian on the box. The strategy of our proof relies on a twofold Birman–Schwinger type argument applied to the many-particle Hamiltonian of the system.