Abstract
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.
Highlights
Modeling the response processes of graphene to the action of an external electric field makes it possible to evaluate the characteristics of promising solutions based on this material for a wide range of frequencies, intensities, and pulse durations [1–4]
A similar problem appears in modeling the processes of production of electron-positron pairs in quantum electrodynamics (QED), [10–12]
1.012780 × 109 0.967066 × 109 1.002584 × 109 1.013377 × 109 1.014233 × 109 1.014268 × 109 1.014269 × 109 this case, the construction of an adaptive mesh is possible by a similar algorithm in the octree format
Summary
Modeling the response processes of graphene to the action of an external electric field makes it possible to evaluate the characteristics of promising solutions based on this material for a wide range of frequencies, intensities, and pulse durations [1–4]. The inclusion of an external field starts the process of the creation of free carriers and their subsequent evolution. Their momentum determines the properties of carriers. The process model used determines the procedure for calculating f (p1, p2, t) for the selected point of the momentum space −π ≤ p1 ≤ π, −π ≤ p2 ≤ π (first Brillouin zone) [5–7]. The procedure implements a numerical solution of the quantum kinetic equation formulated as a system of ordinary differential equations. It is universal for any point in the momentum space and parameters of the external field.. We consider only the final state of the distribution function when, after switching off the external field, the evolution in the system became frozen, and the distribution function ceases to depend on time
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
