Electron-phonon thermalization in a scalable method for real-time quantum dynamics

We present a quantum simulation method that follows the dynamics of out-of-equilibrium many-body systems of electrons and oscillators in real time. Its cost is linear in the number of oscillators and it can probe timescales from attoseconds to hundreds of picoseconds. Contrary to Ehrenfest dynamics, it can thermalize starting from a variety of initial conditions, including electronic population inversion. While an electronic temperature can be defined in terms of a non-equilibrium entropy, a Fermi-Dirac distribution in general emerges only after thermalization. The time evolution of the populations is rationalized in terms of a kinetic model.