Simulation the Behavior of a Two-Level Quantum System Using Scalable Regular Grids

Natalia V. Posnova; Anatolii D. Panferov; Anastasia A. Ulyanova

Program Systems:
Theory and Applications

ISSN 2079-3316

12+

Bilingual electronic scientific Electronic scientific journal of the Ailamazyan Program System Institute of the Ailamazyan PSI of PSI of Russian Academy of Science of RAS

Volume 14 (2023) . Issue 2 (57) . Paper No. 2 (428)

Computational science

Research Article

DOI

10.25209/2079-3316-2023-14-2-27-47

Simulation the Behavior of a Two-Level Quantum System Using Scalable Regular Grids

Anatolii Dmitrievich Panferov, Natalia Vladimirovna Posnova, Anastasia Alekseevna Ulyanova

Saratov State University, Saratov, Russia

Anatolii Dmitrievich Panferov — Correspondent author

panferovad@sgu.ru

Abstract. The paper demonstrates a method for constructing a grid with a changing scale for modeling the behavior of a two-level quantum system. The method was proposed and implemented in relation to the problem of reproducing the behavior of graphene in external electric fields using the quantum kinetic equation. A direct numerical solution of the kinetic equation makes it possible to accurately and completely reproduce the behavior of models of this type. But a large amount of computation is required for a good quality reproduction of the observed parameters. The complexity of the problem is directly proportional to the number of grid nodes in the two-dimensional space of states, in each of which a system of ordinary differential equations is solved to reproduce the evolution of the population of the upper energy level. The study of the behavior of the model made it possible to develop and implement an economical procedure for constructing a computational grid, which ensures the localization of the region of formation of excited states and exact reproduction of the observed process parameters. (In Russian).

Keywords: numerical simulation, graphene, charge carrier distribution function, optimal choice of computational grid

MSC-2020

65M50; 81T10, 81T40

MSC-2020 65-XX: Numerical analysis
MSC-2020 65Mxx: Numerical methods for partial differential equations, initial value and timedependent initial-boundary value problems
MSC-2020 65M50: Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initialboundary value problems involving PDEs
MSC-2020 81-XX: Quantum theory
MSC-2020 81Txx: Quantum field theory; related classical field theories
MSC-2020 81T10,: Model quantum field theories
MSC-2020 81T40: Two-dimensional field theories, conformal field theories, etc. in quantum mechanics

Acknowledgments: The study was supported by a grant from the Russian Science Foundation No. 23-21-00047

For citation: Anatolii D. Panferov, Natalia V. Posnova, Anastasia A. Ulyanova. Simulation the Behavior of a Two-Level Quantum System Using Scalable Regular Grids. Program Systems: Theory and Applications, 2023, 14:2, pp. 27–47. (In Russ.). https://psta.psiras.ru/2023/2_27-47.

Full text of article (PDF): https://psta.psiras.ru/read/psta2023_2_27-47.pdf.

The article was submitted 20.02.2023; approved after reviewing 12.05.2023; accepted for publication 04.06.2023; published online 07.07.2023.

2023

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