Small distance behavior of one-particle Green's functions in electronic structure theory
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910875870298112 |
|---|---|
| author | Flad, Heinz-Juergen Griebel, Michael |
| author_facet | Flad, Heinz-Juergen Griebel, Michael |
| contents | Within the framework of many-particle perturbation theory, we develop an analytical approach that allows us to determine the small distance behavior of Green's functions and related quantities in electronic structure theory. As a case study, we consider the one-particle Green's function up to 2nd order in the perturbation approach. We derive explicit expressions for the leading order terms of the asymptotic small distance behavior. In particular, we demonstrate the appearance of a logarithmic term in the corresponding 2nd order Feynman diagrams. Our asymptotic analysis leads to an improved classification scheme for the diagrams, which takes into account not only the perturbation order, but also the asymptotic smoothness properties near their diagonals. Such a classification may be useful in the design of numerical algorithms and helps to improve their efficiency. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_11354 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Small distance behavior of one-particle Green's functions in electronic structure theory Flad, Heinz-Juergen Griebel, Michael Mathematical Physics 35A21, 35B40, 35J08, 35Sxx Within the framework of many-particle perturbation theory, we develop an analytical approach that allows us to determine the small distance behavior of Green's functions and related quantities in electronic structure theory. As a case study, we consider the one-particle Green's function up to 2nd order in the perturbation approach. We derive explicit expressions for the leading order terms of the asymptotic small distance behavior. In particular, we demonstrate the appearance of a logarithmic term in the corresponding 2nd order Feynman diagrams. Our asymptotic analysis leads to an improved classification scheme for the diagrams, which takes into account not only the perturbation order, but also the asymptotic smoothness properties near their diagonals. Such a classification may be useful in the design of numerical algorithms and helps to improve their efficiency. |
| title | Small distance behavior of one-particle Green's functions in electronic structure theory |
| topic | Mathematical Physics 35A21, 35B40, 35J08, 35Sxx |
| url | https://arxiv.org/abs/2503.11354 |