Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

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. Sarat. Univ. Math. Mech. Inform., 2020, vol. 20, iss. 1, pp. 127-137. DOI: 10.18500/1816-9791-2020-20-1-127-137

Published online: 
02.03.2020
Full text:
(downloads: 50)
Language: 
Russian
Heading: 
Article type: 
Article
UDC: 
501.1
DOI: 
10.18500/1816-9791-2020-20-1-127-137

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

Autors: 
Levenets Sergey Alekseevich, Saratov State University
Verevin Timofey Timofeevich, Saratov State University
Makhankov Aleksey Vladimirovich, Saratov State University
Panferov Anatolii Dmitrievich, Saratov State University
Pirogov Stanislav Olegovich, Saratov State University
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, pp. 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, pp. 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, pp. 3–26. DOI: https://doi.org/10.1007/s12200-014-0428-0
  4. Vandecasteele N., Barreiro A., Lazzeri M., Bachtold A., Mauri F. Currentvoltage characteristics of graphene devices: Interplay between Zener – Klein tunneling and defects. Phys. Rev. B, 2010, vol. 82, iss. 4, pp. 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, no. 16, pp. 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, pp. 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, pp. 622–634. DOI: https://doi.org/10.1103/PhysRev.71.622
  9. Wolfram Mathematica. Site. Available at: http://www.wolfram.com/mathematica/ (accessed 18 April 2018).
  10. MPI Forum. Available at: https://www.mpi-forum.org/ (accessed 18 April 2018).
  11. MPICH. Available at: https://www.mpich.org/about/overview/ (accessed 18 April 2018).
  12. GSL — GNU Scientific Library. Available at: https://www.gnu.org/software/gsl/ (accessed 18 April 2018).
  13. Browne S., Dongarra J., Trefethen A. Numerical Libraries and Tools for Scalable Parallel Cluster Computing. Available at: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.438.4231&rep=re... (accessed 18 April 2018).
  14. Narozhnyi N. B., Nikishov A. I. Simplest processes in the pair-creating electric field. Yad. Fiz., 1970, vol. 11, pp. 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, pp. 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, pp. 797–800. DOI: https://doi.org/10.1134/S106377961505010X
  17. Kolekonov S. V., Panferov A. D., Smolyansky S. A. Investigation of the fine structure of the distribution function of electron-positron pairs with the dynamic Schwinger effect. In: Komp’iuternye nauki i informatsionnye tekhnologii [Computer Science and Information Technologies. Int. Sci. Conf. Materials]. Saratov, Izdatel’stvo Saratovskogo universiteta, 2014, pp. 157–160 (in Russian).
Received: 
04.12.2018