The use of an adaptive mesh based on a quadtree for modeling the final state of a quantum field system under pulsed external action

The success of using mathematical models that determine the behavior of quantum field systems in parametric spaces critically depends on the level of optimization of the procedure of finding the solution. The paper considers the problem of calculating the density of carriers arising in graphene as a result of the action of a pulsed electric field. The basis of the model is a system of kinetic equations that provide the calculation of the residual distribution function. Its integration over momentum space gives the desired carrier density.
The problem lies in the high computational complexity of covering the momentum space with a uniform mesh, which provides an accurate calculation of the density for various parameters of the field momentum. Moreover, the model does not contain criteria for determining satisfactory mesh parameters. The article proposes and implements a procedure for constructing an adaptive mesh in the form of a quadtree having a variable size of covering squares. The procedure is iterative and combined with the process of calculating the values of the distribution function.