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arXiv · 1807.06365

High Density Limit of the Fermi Polaron with Infinite Mass

Ulrich Linden·David Mitrouskas
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Abstract

We analyze the ground state energy for $N$ identical fermions in a two-dimensional box of volume $L^2$ 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 $N/L^2 \gg 1$ 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 F. Chevy 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.

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Ulrich Linden, David Mitrouskas. 2018-07-17. High Density Limit of the Fermi Polaron with Infinite Mass. https://doi.org/10.1007/s11005-019-01158-y

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