论移动壁对盒中量子粒子的全局近似可控性

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS SIAM Journal on Control and Optimization Pub Date : 2024-03-04 DOI:10.1137/22m1518980

Aitor Balmaseda, Davide Lonigro, Juan Manuel Pérez-Pardo

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引用次数: 0

摘要

SIAM 控制与优化期刊》第 62 卷第 2 期第 826-852 页，2024 年 4 月。摘要我们研究了一个由被困在箱体内的自由量子粒子组成的系统，箱壁可以改变其位置。我们证明了该系统的全局近似可控性：任何初始纯态都可以被任意驱动到接近自由粒子的希尔伯特空间中的任何目标纯态，而盒子的最终位置是预先确定的。为此，我们考虑了薛定谔方程的弱解，并使用了与时间相关的薛定谔方程的稳定性定理。

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On Global Approximate Controllability of a Quantum Particle in a Box by Moving Walls

SIAM Journal on Control and Optimization, Volume 62, Issue 2, Page 826-852, April 2024.
Abstract. We study a system composed of a free quantum particle trapped in a box whose walls can change their position. We prove the global approximate controllability of the system: any initial pure state can be driven arbitrarily close to any target pure state in the Hilbert space of the free particle with a predetermined final position of the box. To this purpose we consider weak solutions of the Schrödinger equation and use a stability theorem for the time-dependent Schrödinger equation.

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来源期刊

SIAM Journal on Control and Optimization 数学-应用数学

CiteScore

4.00

自引率

4.50%

发文量

143

审稿时长

12 months

期刊介绍： SIAM Journal on Control and Optimization (SICON) publishes original research articles on the mathematics and applications of control theory and certain parts of optimization theory. Papers considered for publication must be significant at both the mathematical level and the level of applications or potential applications. Papers containing mostly routine mathematics or those with no discernible connection to control and systems theory or optimization will not be considered for publication. From time to time, the journal will also publish authoritative surveys of important subject areas in control theory and optimization whose level of maturity permits a clear and unified exposition. The broad areas mentioned above are intended to encompass a wide range of mathematical techniques and scientific, engineering, economic, and industrial applications. These include stochastic and deterministic methods in control, estimation, and identification of systems; modeling and realization of complex control systems; the numerical analysis and related computational methodology of control processes and allied issues; and the development of mathematical theories and techniques that give new insights into old problems or provide the basis for further progress in control theory and optimization. Within the field of optimization, the journal focuses on the parts that are relevant to dynamic and control systems. Contributions to numerical methodology are also welcome in accordance with these aims, especially as related to large-scale problems and decomposition as well as to fundamental questions of convergence and approximation.