量子力学中的零能流和涡旋图样
Zero-Energy Flows and Vortex Patterns in Quantum Mechanics
摘要：
我们表明，零能流出现在许多粒子系统中，在二维单粒子的情况下相同。由零能流构成的涡旋斑图可以用共轭空间中的本征态来研究。稳定的图案由零能量本征态的叠加写入。另一方面，涡的产生和湮灭是由具有复能量本征值的不稳定本征态插入稳定模式来描述的。在二维抛物势垒的情况下，一些具体的例子。%，即，$-m γ^2 (x^2+y^2)/2$。我们指出了零能流的三个有趣的性质：（i）能量消耗的绝对经济性，（ii）涡旋模式的无限多样性，以及（iii）涡旋模式的绝对稳定性。
英文摘要：
We show that zero-energy flows appear in many particle systems as same as in single particle cases in 2-dimensions. Vortex patterns constructed from the zero-energy flows can be investigated in terms of the eigenstates in conjugate spaces of Gel'fand triplets. Stable patterns are written by the superposition of zero-energy eigenstates. On the other hand vortex creations and annihilations are described by the insertions of unstable eigenstates with complex-energy eigenvalues into the stable patterns. Some concrete examples are presented in the 2-dimensional parabolic potential barrier case. %, i.e., $-m γ^2 (x^2+y^2)/2$. We point out three interesting properties of the zero-energy flows; (i) the absolute economy as for the energy consumption, (ii) the infinite variety of the vortex patterns, and (iii) the absolute stability of the vortex patterns .
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。
