Momentum Distribution of a Fermi Gas with Coulomb Interaction in the Random Phase Approximation
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| Format: | Preprint |
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2025
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| _version_ | 1866912688988225536 |
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| author | Benedikter, Niels Lill, Sascha Naidu, Diwakar |
| author_facet | Benedikter, Niels Lill, Sascha Naidu, Diwakar |
| contents | We analyse the momentum distribution of a three-dimensional Fermi gas in the mean-field scaling regime in a trial state that was recently proven to reproduce the Gell-Mann-Brueckner correlation energy for Coulomb potentials. For a class of potentials including the Coulomb potential we show that the momentum distribution is given by a step profile corrected by a random phase approximation contribution as predicted by Daniel and Vosko. Moreover, for potentials with summable Fourier transform we provide optimal error bounds for the deviation from the random phase approximation. This refines a recent analysis by two of the authors to the physically most relevant potentials and to momenta closer to the Fermi surface. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_03654 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Momentum Distribution of a Fermi Gas with Coulomb Interaction in the Random Phase Approximation Benedikter, Niels Lill, Sascha Naidu, Diwakar Mathematical Physics Quantum Gases 81V74, 82D20, 81Q05 We analyse the momentum distribution of a three-dimensional Fermi gas in the mean-field scaling regime in a trial state that was recently proven to reproduce the Gell-Mann-Brueckner correlation energy for Coulomb potentials. For a class of potentials including the Coulomb potential we show that the momentum distribution is given by a step profile corrected by a random phase approximation contribution as predicted by Daniel and Vosko. Moreover, for potentials with summable Fourier transform we provide optimal error bounds for the deviation from the random phase approximation. This refines a recent analysis by two of the authors to the physically most relevant potentials and to momenta closer to the Fermi surface. |
| title | Momentum Distribution of a Fermi Gas with Coulomb Interaction in the Random Phase Approximation |
| topic | Mathematical Physics Quantum Gases 81V74, 82D20, 81Q05 |
| url | https://arxiv.org/abs/2511.03654 |