Seven Études on dynamical Keldysh model
We present a comprehensive pedagogical discussion of a family of models describing the propagation of a single particle in a multicomponent non-Markovian Gaussian random field. We report some exact results for single-particle Green's functions, self-energy, vertex part and T-matrix. These resu...
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| Format: | Article |
| Language: | English |
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SciPost
2022-12-01
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| Series: | SciPost Physics Lecture Notes |
| Online Access: | https://scipost.org/SciPostPhysLectNotes.65 |
| _version_ | 1811179231966658560 |
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| author | Dmitri V. Efremov, Mikhail N. Kiselev |
| author_facet | Dmitri V. Efremov, Mikhail N. Kiselev |
| author_sort | Dmitri V. Efremov, Mikhail N. Kiselev |
| collection | DOAJ |
| description | We present a comprehensive pedagogical discussion of a family of models describing the propagation of a single particle in a multicomponent non-Markovian Gaussian random field. We report some exact results for single-particle Green's functions, self-energy, vertex part and T-matrix. These results are based on a closed form solution of the Dyson equation combined with the Ward identity. Analytical properties of the solution are discussed. Further we describe the combinatorics of the Feynman diagrams for the Green's function and the skeleton diagrams for the self-energy and vertex, using recurrence relations between the Taylor expansion coefficients of the self-energy. Asymptotically exact equations for the number of skeleton diagrams in the limit of large $N$ are derived. Finally, we consider possible realizations of a multicomponent Gaussian random potential in quantum transport via complex quantum dot experiments. |
| first_indexed | 2024-04-11T06:31:24Z |
| format | Article |
| id | doaj.art-214de8051e724827ae988c6bac65cedf |
| institution | Directory Open Access Journal |
| issn | 2590-1990 |
| language | English |
| last_indexed | 2024-04-11T06:31:24Z |
| publishDate | 2022-12-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics Lecture Notes |
| spelling | doaj.art-214de8051e724827ae988c6bac65cedf2022-12-22T04:40:01ZengSciPostSciPost Physics Lecture Notes2590-19902022-12-016510.21468/SciPostPhysLectNotes.65Seven Études on dynamical Keldysh modelDmitri V. Efremov, Mikhail N. KiselevWe present a comprehensive pedagogical discussion of a family of models describing the propagation of a single particle in a multicomponent non-Markovian Gaussian random field. We report some exact results for single-particle Green's functions, self-energy, vertex part and T-matrix. These results are based on a closed form solution of the Dyson equation combined with the Ward identity. Analytical properties of the solution are discussed. Further we describe the combinatorics of the Feynman diagrams for the Green's function and the skeleton diagrams for the self-energy and vertex, using recurrence relations between the Taylor expansion coefficients of the self-energy. Asymptotically exact equations for the number of skeleton diagrams in the limit of large $N$ are derived. Finally, we consider possible realizations of a multicomponent Gaussian random potential in quantum transport via complex quantum dot experiments.https://scipost.org/SciPostPhysLectNotes.65 |
| spellingShingle | Dmitri V. Efremov, Mikhail N. Kiselev Seven Études on dynamical Keldysh model SciPost Physics Lecture Notes |
| title | Seven Études on dynamical Keldysh model |
| title_full | Seven Études on dynamical Keldysh model |
| title_fullStr | Seven Études on dynamical Keldysh model |
| title_full_unstemmed | Seven Études on dynamical Keldysh model |
| title_short | Seven Études on dynamical Keldysh model |
| title_sort | seven etudes on dynamical keldysh model |
| url | https://scipost.org/SciPostPhysLectNotes.65 |
| work_keys_str_mv | AT dmitrivefremovmikhailnkiselev sevenetudesondynamicalkeldyshmodel |