Mermin's dielectric function and the f-sum rule
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866911484280307712 |
|---|---|
| author | Chuna, Thomas Vorberger, Jan Gawne, Thomas Dornheim, Tobias Murillo, Michael S. |
| author_facet | Chuna, Thomas Vorberger, Jan Gawne, Thomas Dornheim, Tobias Murillo, Michael S. |
| contents | Mermin's dielectric function [N.D. Mermin, Phys. Rev. B 1, 2362 (1970)] is widely assumed to satisfy the f-sum rule because he constrains his ansatz with the continuity equation. However, we identify a moment-closure problem in Mermin's use of the continuity equation. Further, we show that the Mermin's model can be derived without invoking continuity. We describe how other approaches such as the ``completed Mermin'' model of Chuna and Murillo [Phys. Rev. E 111, 035206 (2025)] remedy this closure issue. We then inspect the f-sum rule for both the original and completed Mermin models and find for the Mermin ansatz that collision frequencies scaling as $ω$ must violate the f-sum rule, whereas constant, real, positive collision frequencies will satisfy it, with the caveat that, in practice, convergence with respect to the upper integration limit $ω_{\max}$ is sufficiently slow that finite-domain numerical evaluations exhibit apparent violations, regardless of wavenumber $q$. We also find that collision frequencies with constant imaginary components cause f-sum rule violations. We conclude that if Mermin's model is fit to data via optimizing its collision frequency, then the f-sum rule is not inherently satisfied; constraints, though broad, are needed in order to assume the f-sum rule is satisfied. Further, if the f-sum rule is theoretically satisfied, but violations still appear, then these deviations ought to be included in the error estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_04054 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Mermin's dielectric function and the f-sum rule Chuna, Thomas Vorberger, Jan Gawne, Thomas Dornheim, Tobias Murillo, Michael S. Statistical Mechanics Mermin's dielectric function [N.D. Mermin, Phys. Rev. B 1, 2362 (1970)] is widely assumed to satisfy the f-sum rule because he constrains his ansatz with the continuity equation. However, we identify a moment-closure problem in Mermin's use of the continuity equation. Further, we show that the Mermin's model can be derived without invoking continuity. We describe how other approaches such as the ``completed Mermin'' model of Chuna and Murillo [Phys. Rev. E 111, 035206 (2025)] remedy this closure issue. We then inspect the f-sum rule for both the original and completed Mermin models and find for the Mermin ansatz that collision frequencies scaling as $ω$ must violate the f-sum rule, whereas constant, real, positive collision frequencies will satisfy it, with the caveat that, in practice, convergence with respect to the upper integration limit $ω_{\max}$ is sufficiently slow that finite-domain numerical evaluations exhibit apparent violations, regardless of wavenumber $q$. We also find that collision frequencies with constant imaginary components cause f-sum rule violations. We conclude that if Mermin's model is fit to data via optimizing its collision frequency, then the f-sum rule is not inherently satisfied; constraints, though broad, are needed in order to assume the f-sum rule is satisfied. Further, if the f-sum rule is theoretically satisfied, but violations still appear, then these deviations ought to be included in the error estimates. |
| title | Mermin's dielectric function and the f-sum rule |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2603.04054 |