Ground state energy of the dilute spin-polarized Fermi gas: upper bound via cluster expansion. (English) Zbl 07807073
Summary: We prove an upper bound on the ground state energy of the dilute spin-polarized Fermi gas capturing the leading correction to the kinetic energy resulting from repulsive interactions. One of the main ingredients in the proof is a rigorous implementation of the fermionic cluster expansion of M. Gaudin et al. [Nucl. Phys., A 176, No. 2, 237–260 (1971; doi:10.1016/0375-9474(71)90267-3)].
MSC:
| 81V74 | Fermionic systems in quantum theory |
| 13F60 | Cluster algebras |
| 35P10 | Completeness of eigenfunctions and eigenfunction expansions in context of PDEs |
| 35B38 | Critical points of functionals in context of PDEs (e.g., energy functionals) |
| 78A35 | Motion of charged particles |
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