Generalized Beth--Uhlenbeck entropy formula from the $Φ-$derivable approach
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912746567630848 |
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| author | Blaschke, David Röpke, Gerd Baym, Gordon |
| author_facet | Blaschke, David Röpke, Gerd Baym, Gordon |
| contents | We derive a generalized Beth-Uhlenbeck formula for the entropy of a dense fermion system with strong two-particle correlations, including scattering states and bound states. We work within the $Φ-$derivable approach to the thermodynamic potential. The formula takes the form of an energy-momentum integral over a statistical distribution function times a unique spectral density. In the near mass-shell limit, the spectral density reduces, contrary to naïve expectations, not to a Lorentzian but rather to a "squared Lorentzian" shape. The relation of the Beth-Uhlenbeck formula to the $Φ$-derivable approach is exact at the two-loop level for $Φ$. The formalism we develop, which extends the Beth-Uhlenbeck approach beyond the low-density limit, includes Mott dissociation of bound states, in accordance with Levinson's theorem, and the self-consistent back reaction of correlations in the fermion propagation. We discuss applications to further systems, such as quark matter and nuclear matter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_03876 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized Beth--Uhlenbeck entropy formula from the $Φ-$derivable approach Blaschke, David Röpke, Gerd Baym, Gordon Nuclear Theory High Energy Physics - Theory Plasma Physics We derive a generalized Beth-Uhlenbeck formula for the entropy of a dense fermion system with strong two-particle correlations, including scattering states and bound states. We work within the $Φ-$derivable approach to the thermodynamic potential. The formula takes the form of an energy-momentum integral over a statistical distribution function times a unique spectral density. In the near mass-shell limit, the spectral density reduces, contrary to naïve expectations, not to a Lorentzian but rather to a "squared Lorentzian" shape. The relation of the Beth-Uhlenbeck formula to the $Φ$-derivable approach is exact at the two-loop level for $Φ$. The formalism we develop, which extends the Beth-Uhlenbeck approach beyond the low-density limit, includes Mott dissociation of bound states, in accordance with Levinson's theorem, and the self-consistent back reaction of correlations in the fermion propagation. We discuss applications to further systems, such as quark matter and nuclear matter. |
| title | Generalized Beth--Uhlenbeck entropy formula from the $Φ-$derivable approach |
| topic | Nuclear Theory High Energy Physics - Theory Plasma Physics |
| url | https://arxiv.org/abs/2512.03876 |