arXiv:2606.03272

How long can a non-spherical quantum object remain standing ? - a fundamental quantum question -

Takaharu Otsuka, Yusuke Tsunoda

Published Jun 2, 2026• 0 citations

Abstract

An isolated quantum system generally exhibits rotational symmetry, i.e., conserved spin (angular momentum) in its eigenstates. Non-spherical quantum objects such as many of molecules and atomic nuclei are not exceptions. However, these objects are not rotationally invariant by definition. Such an object therefore restores, as a consequence of the action of Hamiltonian, the rotational symmetry by superposing states of the same object orienting in different directions, where each component represents one direction. We show the time evolution of an individual component of this superposition: this component remains almost unchanged for finite time, called standing time. This implies that if the object is found to be in this component, it basically remains so for the standing time. This feature is shown to be relevant in a variety of cases, such as atomic nuclei, polymers (proteins), and electron drops in atoms. The shapes of many nuclei are ellipsoids with variations. The "viewing" of the ellipsoidal shape is not straightforward, because this ellipsoid is not at rest. A "snapshot" of a nucleus is highly desired as a direct information. Recent experimental approaches with Relativistic Heavy-ion Collision (RHC) are promising for taking such a snapshot. The present work depicts that the standing time, some 10^{-23} sec for typical ellipsoidal nuclei, is much longer than the time scale of RHC, some 10^{-25} sec. This implies that an ellipsoidal nucleus remains practically unchanged for this critical period. As the standing time will be intimately related, through a relation like the energy-time uncertainty relation, to the energy scales involved, we can also explore this concept and its applications in a variety of physical cases such as fusion (tunneling process), fission, alpha-decay/emission, polymers and electron drop in atom.

DOI: 10.48550/arxiv.2606.03272

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