Cite this article as:

Levenets S. A., Verevin T. T., Makhankov A. V., Panferov A. D., Pirogov S. O. Modeling the Dynamics of Massless Charge Carries is Two-Dimensional System. Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2020, vol. 20, iss. 1, pp. 127-137. DOI: https://doi.org/10.18500/1816-9791-2020-20-1-127-137


Published online: 
02.03.2020
Language: 
Russian
Heading: 
UDC: 
501.1

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.

References
  1. Novoselov K. S., Fal’ko V. I., Colombo L., Gellert P. R., Schwab M. G., Kim K. A roadmap for graphene // Nature. 2012. Vol. 490. P. 192–200. DOI: https://doi.org/10.1038/nature11458
  2. Lee C., Wei X., Kysar J. W. Hone J. Measurement of the elastic properties and intrinsic strength of monolayer graphene // Science. 2008. Vol. 321, iss. 5887. P. 385–388. DOI: https://doi.org/10.1126/science.1157996
  3. Ang Y. S., Chen Q., Zhang C. Nonlinear optical response of graphene in terahertz and near-infrared frequency regime // Front. Optoelectron. 2015. Vol. 8, iss. 1. P. 3–26. DOI : https://doi.org/10.1007/s12200-014-0428-0
  4. Vandecasteele N., Barreiro A., Lazzeri M., Bachtold A., Mauri F. Current-voltage characteristics of graphene devices: Interplay between Zener – Klein tunneling and defects // Phys. Rev. B. 2010. Vol. 82, iss. 4. P. 045416. DOI: https://doi.org/10.1103/PhysRevB.82.045416
  5. Kane G., Lazzeri M., Mauri F. J. High-field transport in graphene: The impact of Zener tunneling // Journal of Physics : Condensed Matter. 2015. Vol. 27, № 16. P. 164205. DOI: https://doi.org/10.1088/0953-8984/27/16/164205
  6. Dora B., Moessner R. Nonlinear electric transport in graphene: Quantum quench dynamics and the Schwinger mechanism // Phys. Rev. B. 2010. Vol. 81, iss. 16. P. 165431. DOI: https://doi.org/10.1103/PhysRevB.81.165431
  7. Smolyansky S. A., Churochkin D. V., Dmitriev V. V., Panferov A. D., Kampfer B. ¨ Residual currents generated from vacuum by an electric field pulse in 2+1 dimensional QED models // EPJ Web Conf. 2017. Vol. 138. XXIII International Baldin Seminar on High Energy Physics Problems Relativistic Nuclear Physics and Quantum Chromodynamics (Baldin ISHEPP XXIII). Art. 06004. DOI: https://doi.org/10.1051/epjconf/201713806004
  8. Wallace P. R. The Band Theory of Graphite // Phys. Rev. 1947. Vol. 71, iss. 9. P. 622–634. DOI: https://doi.org/10.1103/PhysRev.71.622
  9. Wolfram Mathematica : [сайт]. URL: http://www.wolfram.com/mathematica/ (дата обращения: 18.04.2018).
  10. MPI Forum. URL: https://www.mpi-forum.org/ (дата обращения: 18.04.2018).
  11. MPICH. URL: https://www.mpich.org/about/overview/ (дата обращения: 18.04.2018).
  12. GSL — GNU Scientific Library. URL: https://www.gnu.org/software/gsl/ (дата обращения: 18.04.2018).
  13. Browne S., Dongarra J., Trefethen A. Numerical Libraries and Tools for Scalable Parallel Cluster Computing. URL: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1. 438.4231&rep=rep1&type=pdf (дата обращения: 18.04.2018).
  14. Narozhnyi N. B., Nikishov A. I. Simplest processes in the pair-creating electric field // Yad. Fiz. 1970. Vol. 11. P. 1072. [Sov. J. Nucl. Phys. 1970. Vol. 11, pp. 596].
  15. Hebenstreit F., Alkofer R., Dunne G. V., Gies H. Momentum signatures for Schwinger pair production in short laser pulses with sub-cycle structure // Phys. Rev. Lett. 2009. Vol. 102, iss. 15. P. 150404. DOI: https://doi.org/10.1103/PhysRevLett.102.150404
  16. Blaschke D., Juchnowski L., Panferov A., Smolyansky S. Dynamical Schwinger effect: Properties of the e −e + plasma created from vacuum in strong laser fields // Phys. Part. Nuclei. 2015. Vol. 46, iss. 5. P. 797–800. DOI: https://doi.org/10.1134/S106377961505010X
  17. Колеконов С. В., Панферов А. Д., Смолянский С. А. Исследование тонкой структуры функции распределения электрон-позитронных пар при динамическом эффекте Швингера // Компьютерные науки и информационные технологии : материалы междунар. науч. конф. Саратов : Изд-во Сарат. ун-та, 2014. С. 157–160. 
Full text: