论文标题
CONNES $ 2D $谐波振荡器在量子相空间中
Connes distance of $2D$ harmonic oscillators in quantum phase space
论文作者
论文摘要
我们研究相空间中$ 2D $谐波振荡器的量子状态的距离。使用Hilbert-Schmidt操作配方，我们构建了一个玻色子空间和量子Hilbert空间，并获得了与$ 4D $ Quantum Quantum相位空间相对应的DIRAC操作员和光谱三重。根据球条件，我们获得了有关最佳元素的一些约束关系。我们构建相应最佳元素的显式表达式，然后得出两个任意Fock状态之间的距离为$ 2D $ Quantum谐波振荡器。我们证明，这些二维距离满足了毕达哥拉斯定理。
We study the Connes distance of quantum states of $2D$ harmonic oscillators in phase space. Using the Hilbert-Schmidt operatorial formulation, we construct a boson Fock space and a quantum Hilbert space, and obtain the Dirac operator and a spectral triple corresponding to a $4D$ quantum phase space. Based on the ball condition, we obtain some constraint relations about the optimal elements. We construct the explicit expressions of the corresponding optimal elements and then derive the Connes distance between two arbitrary Fock states of $2D$ quantum harmonic oscillators. We prove that these two-dimensional distances satisfy the Pythagoras theorem.
