Numerical solver for the time-dependent far-from-equilibrium Boltzmann equation

The study of strongly out-of-equilibrium states and their time evolution towards thermalization is critical to the understanding an ever widening range physical processes. We present a numerical method that for first allows solution most difficult part time-dependent Boltzmann equation: full scattering term. Any number bands (and quasiparticles) with arbitrary dispersion, any high order channels (we show here four legs scatterings: electron-electron scattering) can be treated far from equilibrium. No assumptions are done on population all Pauli-blocking factors included in phase-space term scattering. straightforwardly interfaced deterministic solver transport. Finally critically, conserves machine precision particle number, momentum energy resolution, making computation till complete possible. apply this approach two examples, metal semiconductor, undergoing laser excitation. These cases, which literature hitherto under approximations, addressed free those approximations within same method.