Efficient implementation of Keldysh field theory for ohmically damped bosons

The presence of widely separate scales of interest is a well-known obstacle to efficient numerical simulations of physical systems. A separation of scales ansatz and the renormalization of slow modes is an established route to treat such problems. The nonequilibrium Greens function formalism of the damped quantum harmonic oscillator suffers from exactly this issue, due to the competition between a slow system- and a fast environment-scale. We present a new approach, falling in the separation of scales paradigm, which allows for solving the Kadanoff-Baym equations using a time discretization on the slow scale without introducing artifacts. Given the cubic time complexity of most time-stepping algorithms, this results in an enormous reduction of computational costs. 

As an example for the application of our method to more complicated systems, we present the simulation of nonequilibrium anharmonic phonon dynamics following an optical pump of multi-layer graphene. We can include effective damping and decoherence due to interactions of the optical phonons with electrons and acoustic phonons without needing to adjust the discretization scale of the numerics.