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A dynamical method for inelastic transport simulations in nanostructures iscompared with a steady-state method based on non-equilibrium Green's functions.A simplified form of the dynamical method produces, in the steady state in theweak-coupling limit, effective self-energies analogous to those in the BornApproximation due to electron-phonon coupling. The two methods are thencompared numerically on a resonant system consisting of a linear trimer weaklyembedded between metal electrodes. This system exhibits enhanced heating athigh biases and long phonon equilibration times. Despite the differences intheir formulation, the static and dynamical methods capture localcurrent-induced heating and inelastic corrections to the current with goodagreement over a wide range of conditions, except in the limit of very highvibrational excitations, where differences begin to emerge.

Inelastic quantum transport: the self-consistent Born approximation and correlated electron-ion dynamics