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arXiv · 2510.16979

Fractatomic Physics: An Invitation with Atomic Stability and Rydberg States in Fractal Spaces

Nhat A. Nghiem·Trung V. Phan
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Abstract

We explore the physical quantum properties of atoms in fractal spaces, both as a theoretical generalization of normal integer-dimensional Euclidean spaces and as an experimentally realizable setting. We identify the threshold of fractality at which Ehrenfest atomic instability emerges, where the Schr\"{o}dinger equation describing the wave-function of a single electron orbiting around an atom becomes scale-free, and discuss the potential of observing this phenomena in laboratory settings. We then study the Rydberg states of stable atoms using the Wentzel-Kramers-Brillouin approximation, along with a proposed extension for the Langer modification, in general fractal dimensionalities. We show that fractal space atoms near instability explode in size even at low-number excited state, making them highly suitable to induce strong entanglements and foster long-range many-body interactions. We argue that atomic physics in fractal spaces -- ``fractatomic physics'' -- is a rich research avenue deserving of further theoretical and experimental investigations.

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Nhat A. Nghiem, Trung V. Phan. 2025-10-19. Fractatomic Physics: An Invitation with Atomic Stability and Rydberg States in Fractal Spaces. https://doi.org/10.3390/atoms14010002

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