A stochastic controlled Schroedinger equation: convergence and robust stability for numerical solutions

Q3 Physics and Astronomy

Cybernetics and Physics Pub Date : 2021-11-30 DOI:10.35470/2226-4116-2021-10-3-178-184

C. Romero-Meléndez, D. Castillo-Fernández

引用次数: 0

Abstract

In this paper we study the stochastic stability of numerical solutions of a stochastic controlled Schr¨odinger equation. We investigate the boundedness in second moment, the convergence and the stability of the zero solution for this equation, using two new definitions of almost sure exponential robust stability and asymptotic stability, for the Euler-Maruyama numerical scheme. Considering that the diffusion term is controlled, by using the method of Lyapunov functions and the corresponding diffusion operator associated, we apply techniques of X. Mao and A. Tsoi for achieve our task. Finally, we illustrate this method with a problem in Nuclear Magnetic Resonance (NMR).

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随机控制Schroedinger方程：数值解的收敛性和鲁棒稳定性

本文研究了一类随机控制Schr¨odinger方程数值解的随机稳定性。利用Euler Maruyama数值格式的几乎肯定指数鲁棒稳定性和渐近稳定性两个新定义，研究了该方程零解的二阶矩有界性、收敛性和稳定性。考虑到扩散项是受控的，通过使用李雅普诺夫函数和相应的扩散算子的方法，我们应用X.Mao和A.Tsoi的技术来实现我们的任务。最后，我们用核磁共振（NMR）中的一个问题来说明这种方法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Cybernetics and Physics Chemical Engineering-Fluid Flow and Transfer Processes

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

10 weeks

期刊介绍： The scope of the journal includes: -Nonlinear dynamics and control -Complexity and self-organization -Control of oscillations -Control of chaos and bifurcations -Control in thermodynamics -Control of flows and turbulence -Information Physics -Cyber-physical systems -Modeling and identification of physical systems -Quantum information and control -Analysis and control of complex networks -Synchronization of systems and networks -Control of mechanical and micromechanical systems -Dynamics and control of plasma, beams, lasers, nanostructures -Applications of cybernetic methods in chemistry, biology, other natural sciences The papers in cybernetics with physical flavor as well as the papers in physics with cybernetic flavor are welcome. Cybernetics is assumed to include, in addition to control, such areas as estimation, filtering, optimization, identification, information theory, pattern recognition and other related areas.