Modeling the Dynamics of Massless Charge Carries is Two-Dimensional System

Abstract

The paper presents the results obtained in the process of developing a system for simulating the generation of massless charge carriers with a photon-like spectrum by an external electric field for two-dimensional media. The basis of the system is a physical model of the process, built in the formalism of a kinetic equation for an adequate quantum-field theory. It does not use simplifying assumptions, including expansions in some small parameters (perturbation theory). In this sense, the model used is accurate. It is designed as a first-order ODE system for which the Cauchy problem is formulated. The main problem is the computational complexity of determining the observed values from the characteristics of the model. Directly solving the ODE system provides information only about the probability of a certain specific final state being occupied on a two-dimensional continuum of potentially admissible impulse states. The region of localization of the occupied states, the smoothness of their distribution in the momentum space, and, consequently, the size and density of the required mesh, are not known in advance. These parameters depend on the characteristics of the external field and are themselves a matter of definition in the modeling process. The computational complexity of the actual solution of the model system of equations for a given point in the momentum space is also an open problem. In the present case, such a problem is always solved on a single computational core. But the time required for this depends both on the characteristics of the calculator and on the type, type and implementation of the integration method. Their optimal choice, as demonstrated below, has a very significant effect on the resources needed to solve the entire problem. At the same time, due to the large variation in the nature of the behavior of the equations system when the physical parameters of the model change, the choice optimization of the integration methods is not global. This question has to be returned with each significant change in the parameters of the model under study.

Keywords

• numerical modeling
• high-performance computing
• kinetic equation
• graphene