原子约束中的自发球对称破缺
Spontaneous spherical symmetry breaking in atomic confinement
摘要：
当处于基态的类H原子被限制在一个球盒中，在一般的边界条件下（即第三类边界条件或Robin边界条件），当系统参数在一个物理上合理的范围内时，初始SO（3）对称性的自发破缺效应是可能的.原因是这样的边界条件可以在盒子边界的某些扇区产生很大的电子波函数，这反过来又促进了原子从盒子中心向边界的这一部分的位移，因此潜在的SO（3）对称性自发地破缺。出现的戈德斯通模式，与围绕盒子中心的旋转相吻合，通过将原子分散在离盒子中心一定距离的球壳上来恢复对称性。腔体内的原子限制动态地进行-由于边界条件，边界附近的电子波函数的变形起弹簧的作用，使原子核返回盒体积。
英文摘要：
The effect of spontaneous breaking of initial SO(3) symmetry is shown to be possible for an H-like atom in the ground state, when it is confined in a spherical box under general boundary conditions of "not going out" through the box surface (i.e. third kind or Robin's ones), for a wide range of physically reasonable values of system parameters. The reason is that such boundary conditions could yield a large magnitude of electronic wavefunction in some sector of the box boundary, what in turn promotes atomic displacement from the box center towards this part of the boundary, and so the underlying SO(3) symmetry spontaneously breaks. The emerging Goldstone modes, coinciding with rotations around the box center, restore the symmetry by spreading the atom over a spherical shell localized at some distances from the box center. Atomic confinement inside the cavity proceeds dynamically -- due to the boundary condition the deformation of electronic wavefunction near the boundary works as a spring, that returns the atomic nuclei back into the box volume.
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