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Seven Etudes on dynamical Keldysh Model
by D. V. Efremov, M. N. Kiselev
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Mikhail Kiselev |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2206.06609v2 (pdf) |
| Date accepted: | 2022-10-07 |
| Date submitted: | 2022-06-30 07:26 |
| Submitted by: | Kiselev, Mikhail |
| Submitted to: | SciPost Physics Lecture Notes |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
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.
Published as SciPost Phys. Lect. Notes 65 (2022)
Reports on this Submission
Report 1 by Michael Sadovski on 2022-9-14 (Invited Report)
- Cite as: Michael Sadovski, Report on arXiv:2206.06609v2, delivered 2022-09-14, doi: 10.21468/SciPost.Report.5692
Strengths
1. Pedagogical style
2. Clear presentation
3. Important contribution to this field
Weaknesses
None that should be mentioned
Report
This paper presents an interesting and elegant discussion of a simplified dynamic field - theory models (dynamical generalization of the so called Keldysh model in the theory of disordered systems), which belongs to rather limited class of models where ALL Feynman diagrams (of perturbation series) can be summed exactly. Actually, the authors deal with a particle in a multicomponent dynamic, non-Markovian Gaussian random field. They present exact results for single-particle Green's functions, self-energies and vertex parts. Their results are based mainly on a closed form solution of the Dyson equation combined with the Ward identity. Asymptotically exact equations for the number of skeleton diagrams in the limit of large N are derived. Some examples of exact perturbation series summation are also presented. In this respect they analyze the combinatorics of the Feynman diagrams for the Green's function and the skeleton diagrams for the self-energy and vertex, using (and generalizing) the recurrence relations between Taylor expansion coefficients of self-energy, derived in earlier works by Kuchinskii, Sadovskii and Suslov. Possible physical realizations of a their multicomponent Gaussian random model in quantum transport via complex quantum dot experiments are also discussed in detail.
Requested changes
None