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Open AccessArticle
Estimation of the Attraction Domain for the Quantum Systems Based on the Schrödinger Equation
by
Hongli Yang
Hongli Yang 1,2,†
,
Guohui Yu
Guohui Yu 2,† and
Ivan Ganchev Ivanov
Ivan Ganchev Ivanov 3,*
1
College of Big Data, Qingdao Huanghai University, Qingdao 266427, China
2
College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
3
Faculty of Economics and Business Administration, St. Kl.Ohridski Sofia University, 1113 Sofia, Bulgaria
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Axioms 2024, 13(8), 542; https://doi.org/10.3390/axioms13080542 (registering DOI)
Submission received: 22 June 2024
/
Revised: 30 July 2024
/
Accepted: 8 August 2024
/
Published: 9 August 2024
Abstract
This paper investigates a quantum system described by the Schrödinger equation, utilizing the concept of the quantum Lyapunov function. The Lyapunov function is chosen based on the mean value of a virtual mechanical quantity, where different values of P, the mean value of the virtual mechanical quantity in the Lyapunov function, have an impact on the attractive domain of the quantum system. The selected primary optimization algorithms approximating matrix P are the particle swarm optimization (PSO) algorithm and the simulated annealing (SA) algorithm. This study examines the characteristics of the system’s attraction domain under these two distinct algorithms and establishes stability conditions for the nonlinear quantum system. We introduce a method to estimate the size of the attractive domain using the Lyapunov function approach, converting the attractive domain issue into an optimization challenge. Numerical simulations are conducted in various two-dimensional test systems and spin 1/2 particle systems.
Share and Cite
MDPI and ACS Style
Yang, H.; Yu, G.; Ivanov, I.G.
Estimation of the Attraction Domain for the Quantum Systems Based on the Schrödinger Equation. Axioms 2024, 13, 542.
https://doi.org/10.3390/axioms13080542
AMA Style
Yang H, Yu G, Ivanov IG.
Estimation of the Attraction Domain for the Quantum Systems Based on the Schrödinger Equation. Axioms. 2024; 13(8):542.
https://doi.org/10.3390/axioms13080542
Chicago/Turabian Style
Yang, Hongli, Guohui Yu, and Ivan Ganchev Ivanov.
2024. "Estimation of the Attraction Domain for the Quantum Systems Based on the Schrödinger Equation" Axioms 13, no. 8: 542.
https://doi.org/10.3390/axioms13080542
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