article published yes David Johannes Mitrouskas author cbddacee-2b11-11eb-a02e-a2e14d04e52d RoSe department We analyze the ground state energy of N fermions in a two-dimensional box interacting with an impurity particle via two-body point interactions. We show that for weak coupling, the ground state energy is asymptotically described by the polaron energy, as proposed by F. Chevy in the physics literature. The polaron energy is the solution of a nonlinear equation involving the Green’s function of the free Fermi gas and the binding energy of the two-body point interaction. We provide quantitative error estimates that are uniform in the thermodynamic limit. https://research-explorer.ista.ac.at/download/19660/19676/2025_ArchiveRatioMechanics_Mitrouskas.pdf application/pdfno Springer Nature2025 eng 0003-9527 1432-0673 00148277050000110.1007/s00205-025-02098-9 2493 D. J. Mitrouskas, “The weakly coupled two-dimensional Fermi polaron,” <i>Archive for Rational Mechanics and Analysis</i>, vol. 249, no. 3. Springer Nature, 2025. Mitrouskas DJ. The weakly coupled two-dimensional Fermi polaron. <i>Archive for Rational Mechanics and Analysis</i>. 2025;249(3). doi:<a href="https://doi.org/10.1007/s00205-025-02098-9">10.1007/s00205-025-02098-9</a> Mitrouskas, David Johannes. “The Weakly Coupled Two-Dimensional Fermi Polaron.” <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature, 2025. <a href="https://doi.org/10.1007/s00205-025-02098-9">https://doi.org/10.1007/s00205-025-02098-9</a>. Mitrouskas, D. J. (2025). The weakly coupled two-dimensional Fermi polaron. <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature. <a href="https://doi.org/10.1007/s00205-025-02098-9">https://doi.org/10.1007/s00205-025-02098-9</a> Mitrouskas DJ. 2025. The weakly coupled two-dimensional Fermi polaron. Archive for Rational Mechanics and Analysis. 249(3), 30. D.J. Mitrouskas, Archive for Rational Mechanics and Analysis 249 (2025). Mitrouskas, David Johannes. “The Weakly Coupled Two-Dimensional Fermi Polaron.” <i>Archive for Rational Mechanics and Analysis</i>, vol. 249, no. 3, 30, Springer Nature, 2025, doi:<a href="https://doi.org/10.1007/s00205-025-02098-9">10.1007/s00205-025-02098-9</a>. 196602025-05-11T22:02:37Z2025-09-30T12:25:19Z