Higher-order effects in non-Markovian theory of electronic relaxation in interacting electron-phonon systems

Abstract

A finite coupling generalised master equation theory of the electronic relaxation among electronic eigen-states is presented. When converted into a closed time-convolution form (TCGME) for just diagonal elements of the density matrix, the theory is appreciably non-Markovian with the memory kernel summed partially up to the infinite order in the electron-phonon coupling. On soluble examples, it is shown that: (a), higher-order effects may influence even the lowest-order relaxation rates; (b), weakness of the finite coupling is not sufficient for reducing the theory to the standard lowest-order form; (c), the Markov approximation to the TCGME is in general misleading; (d), the initial condition term may appreciably influence the long-time development of the relaxation; (e), the theory is able to yield quasi-coherent effects (quantum beats) due to the electron coupling to the bath; (f), very effective tunnelling through barriers between equivalent sites appears with non-zero tunnelling currents starting from the second order in the electron-phonon coupling. Limitations from above (below) for the time (frequency) are found for the theory to reduce to the standard lowest-order form.