Improved transport equations including correlations for electron-phonon systems. Comparison with exact solutions in one dimension

TL;DR

This paper develops improved transport equations for quantum electron-phonon systems that incorporate correlations, demonstrating significant accuracy improvements over traditional models by comparing with exact solutions in one-dimensional models.

Contribution

The paper introduces correlation-inclusive transport equations for electron-phonon systems and validates them against exact solutions in one-dimensional models, showing enhanced accuracy.

Findings

Significant improvement over non-Markovian equations in Born approximation.

Equations account for renormalization of propagation by self-energies.

Validated against exact solutions in 1D models.

Abstract

We study transport equations for quantum many-particle systems in terms of correlations by applying the general formalism developed in an earlier paper to exactly soluble electron-phonon models. The one-dimensional models considered are the polaron model with a linear energy dispersion for the electrons and a finite number of electrons and the same model including a Fermi sea (Tomonaga-Luttinger model). The inclusion of two-particle correlations shows a significant and systematic improvement in comparison with the usual non-Markovian equations in Born approximation. For example, the improved equations take into account the renormalization of the propagation by the self-energies to second order in the coupling.