Spectral Theory of the Fermi Polaron
arXiv:1805.07229 · doi:10.1007/s00023-019-00796-1
Abstract
The Fermi polaron refers to a system of free fermions interacting with an impurity particle by means of two-body contact forces. Motivated by the physicists' approach to this system, the present article develops a general mathematical framework for defining many-body Hamiltonians with two-body contact interactions by means of a renormalization procedure. In the case of the Fermi polaron the well-known TMS Hamiltonians are shown to emerge. For the Fermi polaron in a two-dimensional box a novel variational principle, established within the general framework, links the low-lying eigenvalues of the system to the zero-modes of a Birman-Schwinger type operator. It allows us to show, e.g., that the \emph{polaron}- and \emph{molecule} energies, computed in the physical literature, are indeed upper bounds to the ground state energy of the system.
arXiv comment37 pages, updated introduction with reference to singular perturbation theory and new publications, several clarifying remarks. Accepted by AHP
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Cited by in corpus (6)
- Three-Body Hamiltonian with Regularized Zero-Range Interactions in Dimension Three
- On the self-adjointness of H+A*+A
- From Short-Range to Contact Interactions in Two-dimensional Many-Body Quantum Systems
- From Short-Range to Contact Interactions in the 1d Bose Gas
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