Numerical Solver for the out-of-equilibrium Boltzmann Collision operator: 2D second-order momentum discretisation

Quantum Boltzmann equation (QBE) is a viable option to study strongly out-of-equilibrium thermalization dynamics which are becoming increasingly critical for many novel physical applications like Ultrafast thermalization, Terahertz radiation etc. However its applicability is greatly limited by the impractical scaling of the solution to the collision integral in QBE. In our previous work[1] we had proposed a numerical solver for the solution of the collision integral in QBE and then improved on it[2] to include second degree momentum discretisation and adaptive time stepping, thus making it fully compatible to the standard numerical solvers for the transport part of QBE. The improved solver is numerically efficient and extremely robust against inherent numerical instabilities.Here we showcase the applications of this improved solver to a simple 2D system,doped graphene, and analyse thermalizations of the introduced out-of-equilibrium populations.