Density Matrix Dynamics for Electron-Phonon Interactions

The time evolution of the electron density matrix in the presence of electron-phonon (e-ph) interactions gives access to nonequilibrium electronic populations and coherences. Here, we derive the dynamics of the density matrix of a coupled electron-phonon system using both the Heisenberg and Lindblad equations. Rather than using the Lindblad equation with the Redfield procedure [1], we focus on solving the equations of motion for the density matrix in the Heisenberg picture, which allows us to explicitly compute the damping factor that appears in the Lindblad equation, as well as derive higher-order e-ph terms. We discuss the implementation of a simple multi-band model as a prototype toward the full first-principles implementation in the PERTURBO code developed by our group.

[1] R. Rosati, F. Dolcini, and F. Rossi, Electron-phonon coupling in metallic carbon nanotubes: Dispersionless electron propagation despite dissipation. Phys. Rev. B 92 (2015)