Seven Etudes on dynamical Keldysh Model

TL;DR

This paper provides a detailed analysis of a family of models describing particle propagation in non-Markovian Gaussian fields, offering exact solutions, diagrammatic combinatorics, and potential quantum transport applications.

Contribution

It introduces exact analytical results for Green's functions and diagrammatics in multicomponent non-Markovian models, with implications for quantum transport.

Findings

Exact solutions for Green's functions and self-energy

Recurrence relations for Feynman diagram combinatorics

Asymptotic analysis of skeleton diagrams for large N

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.