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arXiv 1907.09397quant-ph
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旋量态的时间最优量子控制

Time Optimal Quantum Control of Spinor States

Peter G. Morrison

摘要:

分析了相对论电子在四维线性约束下的运动。有趣的结果表明,电子的状态下的时间最佳量子态控制的形式下,很好地定义。我们建立了实现时间依赖幺正演化的紧凑机制,并提出了时间有序指数算子的新计算方法。一个强大的修改的brachistochrone技术,允许通过矩阵分解的哈密顿一类问题的解决方案。这些技术使我们能够为量子系统找到一系列解决方案,这些解决方案具有易于访问的物理实现。我们对比的理论输出时,约束到相对论性的时空,其他物理系统的低维。对超复数及其在量子力学中的应用作了一些评述。

英文摘要:

An analysis of the motion of a relativistic electron under a linear constraint in four dimensions is presented. Interesting results are given that show that the state of the electron is well defined under the formalism of time optimal quantum state control. We establish compact mechanisms for achieving time dependent unitary evolution, and present new calculation methods for time-ordered exponential operators. A powerful modification of the brachistochrone technique is presented that allows solution of a class of problems via matrix decomposition of the Hamiltonian. These techniques allow us to arrive at a series of solutions for quantum systems that have readily accessible physical realisations. We contrast the output of the theory when constrained to a relativistic space-time to that of other physical systems of lower dimensionality. Some comment is given regarding hypercomplex numbers and their application in quantum mechanics.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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