Time-retarded electronic friction and enhanced mass of classical nuclei innonadiabatic molecular dynamics due to self-consistent coupling to electronictime-dependent nonequilibrium Green function

The most conventional way to calculate current induced force (including steady state and friction force) on classical degree of freedom due to fast electron dynamics is to use Wigner representation of Keldysh Green function that assumes slow variation of central time and fast variation of relative time leading to an expression for Born-Oppenheimer force in adiabatic limit and friction as the first order adiabatic correction. Here we present a new scheme of ab-initio MD that self-consistently couples molecular dynamics (MD) to quantum description of electrondynamics where current induced force is calculated including all higher order terms using time-dependent nonequilibrium Green function (TDNEGF) which leads to memory effect and show that the effect of highly nonadiabatic inertia term which has not been considered in previous studies. We took example of single electronic energy level of Hydrogen like atom which is coupled to a classical degree of freedom and showed that our formalism, unlike the conventional approach, captures the effect of inertia term included in current induced force leading to a highly nontrivial change in damping dynamics in a classial-quantum system.