Controllability of schrödinger equations

薛定谔方程的可控性

• 批准号: 261883-2007
• 负责人: Teismann, Holger
• 金额: $ 1.02万
• 依托单位: Acadia University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2012
• 资助国家: 加拿大
• 起止时间: 2012-01-01 至 2013-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=503725
• 关键词: Controllability; schr; dinger; equations

In the last few decades, developments in physics, chemistry, and engineering, such as the ever-increasing miniaturization of devices, the emergence of the quantum-computation paradigm, or the desire to influence molecular reactions and to manipulate condensates of ultra-cold atoms (Bose-Einstein condensates), have triggered a growing interest in controlling systems at the quantum scale; i.e., systems that are critically influenced by quantum effects. This research project is aimed at contributing to the theory of the emerging field of "quantum engineering'' by investigating the control properties of the fundamental equation of quantum theory, the Schrödinger equation (and its nonlinear variants). The basic question is whether a given control objective (such as the preparation of an excited or superposition state, the transfer of a Bose-Einstein condensate, or the increase in the yield of a molecular reaction) can be realized by applying suitably designed control fields (usually laser fields) to the system. Although the mathematical control theory for partial differential equations is well developed and many equations arising in physics and engineering have been studied in great detail, the theory for Schrödinger's equation is less complete. This research project is aimed at closing this gap. The results of this research may potentially have implications for areas such as semiconductor technology, nanoscience, or quantum computing.

在过去的几十年里，物理学、化学和工程学的发展，例如设备的不断小型化，量子计算范例的出现，或者对影响分子反应和操纵超冷原子凝聚体(玻色-爱因斯坦凝聚体)的渴望，引发了人们对在量子尺度上控制系统的日益增长的兴趣，即受到量子效应严重影响的系统。这个研究项目的目的是通过研究量子理论的基本方程-薛定谔方程(及其非线性变体)的控制性质，为新兴的量子工程领域的理论做出贡献。基本问题是，是否可以通过对系统施加适当设计的控制场(通常是激光场)来实现给定的控制目标(例如制备激发态或叠加态、转移玻色-爱因斯坦凝聚体或增加分子反应的产率)。虽然偏微分方程组的数学控制理论已经很发达，物理和工程中出现的许多方程也得到了很详细的研究，但薛定谔方程的理论还不够完整。本研究项目旨在缩小这一差距。这项研究的结果可能会对半导体技术、纳米科学或量子计算等领域产生潜在的影响。