弯曲空间中Schroedinger方程无R项的实验检验

二维弯曲电场和磁场系统的量子力学

Quantum mechanics on curved 2D systems with electric and magnetic fields

本文导出了无自旋带电粒子在外加电场和磁场作用下被约束在曲面上的薛定谔方程。粒子被限制在表面上使用薄层程序，从而产生了众所周知的几何势。电场和磁场通过四维势包含在内。我们发现，有没有场和表面曲率之间的耦合，并与一个适当的选择规范，表面和横向动力学是完全可分离的。最后，解析地导出了圆柱、球面和环面的哈密顿量。

Quantum information of the Aharanov-Bohm ring with Yukawa interaction in the presence of disclination

We investigate the quantum information by a theoretical measurement approach of an Aharanov-Bohm (AB) ring with Yukawa interaction in curved space with disclination. It obtained the so-called Shannon entropy, through the eigenfunctions of the system. The quantum states considered come from a Schroedinger theory with the AB field in the background of curved space. With this entropy, it can explore the quantum information at the position space and reciprocal space. Furthermore, we discussed how the magnetic field, the AB flux, and the topological defect influence the quantum states and the infor…

非常曲率空间上的量子力学：振子问题和超可积性

Quantum mechanics on spaces of nonconstant curvature: the oscillator problem and superintegrability

严格求出了N维非常曲率空间上非线性振子的量子态的全谱和本征函数，由于其下的曲率空间产生了依赖于位置的动能，在量子化后必须保持系统的最大超可积性的条件下，给出了三种不同的量子化公式.通过适当的相似变换，详细描述了这三个薛定谔问题之间的关系。这三种方法被用来说明N维弯曲空间的量子化问题的不同特点，或者，位置相关的质量量子哈密顿。据我们所知，这个量子振子是在具有非常数曲率的N维空间上的最大超可积量子系统的第一个例子。

玻色子 Kitaev 模型中隐藏的弯曲空间

Hidden curved spaces in Bosonic Kitaev model

研究发现玻色子 Kitaev 模型在无物理形变时内含两个双曲面，可支持手性输运等现象，并通过有限化学势耦合实现灵敏度随系统尺寸指数增长的量子传感器。

Quantum phase-space representation for curved configuration spaces

We extend the Wigner-Weyl-Moyal phase-space formulation of quantum mechanics to general curved configuration spaces. The underlying phase space is based on the chosen coordinates of the manifold and their canonically conjugate momenta. The resulting Wigner function displays the axioms of a quasiprobability distribution, and any Weyl-ordered operator gets associated with the corresponding phase-space function, even in the absence of continuous symmetries. The corresponding quantum Liouville equation reduces to the classical curved space Liouville equation in the semiclassical limit. We demonstr…

无自旋量子力学中的挠率驱动非线性

Torsion-Driven Nonlinearity in Spinless Quantum Mechanics

本文研究带挠率空间中无自旋非相对论粒子的量子动力学，提出适配一般坐标系的随机变分方法，推导得挠率大小上界，揭示挠率影响量子系统的新机制。