论文标题
非交互性罗伯逊·史克鲁丁德的不确定性原则
The Non-commutative Robertson-Schrödinger Uncertainty Principle
论文作者
论文摘要
我们研究了协方差矩阵在非共同量子力学框架中的协方差矩阵的性质，用于熟悉的Heisenberg-Weyl代数与其特定扩展之间的单参数转换家族。作为对罗伯逊 - 雪人的不确定性原理的量度，我们确定其相应的界限。建立了非共同相位空间的能力之间的不平等。我们还基于一个简单的模型提供了一个建设性的示例，以证明我们的理论预测是合理的。
We investigate properties of the covariance matrix in the framework of non-commutative quantum mechanics for an one-parameter family of transformations between the familiar Heisenberg-Weyl algebra and a particular extension of it. Employing as a measure of the Robertson-Schrödinger uncertainty principle the linear symplectic capacity of the Weyl ellipsoid (and its dual), we determine its corresponding bounds. Inequalities between the capacities for non-commutative phase-spaces are established. We also present a constructive example based on a simple model to justify our theoretical predictions.
