Spontaneous spherical symmetry breaking in atomic confinement

TL;DR

This paper demonstrates that an H-like atom confined in a spherical box can spontaneously break spherical symmetry due to boundary conditions, leading to atomic displacement and Goldstone modes that restore symmetry.

Contribution

It reveals a novel spontaneous symmetry breaking phenomenon in atomic confinement caused by boundary conditions, with implications for quantum systems in bounded geometries.

Findings

Symmetry breaking occurs for atoms in spherical confinement under Robin boundary conditions.

Atomic displacement from the center is driven by boundary-induced wavefunction behavior.

Goldstone modes restore symmetry by rotating the atom around the box center.

Abstract

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.