Abstract
A deformable body can rotate even with no angular momentum simply by changing its shape. Here the first all-atom level molecular dynamics example of this phenomenon is presented. For this the thermal vibrations of individual atoms in an isolated cyclopropane molecule are simulated in vacuum and at ultra-low internal temperature values. When the molecule is observed stroboscopically, at discrete equidistant time steps, the random thermal vibrations of the individual atoms become self-organized into a collective oscillatory motion of the entire molecule. The period of oscillation is emergent and intrinsic to the molecule so that this self-organization bears resemblance to a driven time crystal. The oscillation period increases in a self-similar manner when the length of the stroboscopic time step is increased. In the limit of very long stroboscopic time steps the entire molecule can then rotate in an apparent uniform fashion, but with no angular momentum. It is proposed that the observed behavior is universal in the case of triangular molecules. Moreover, it is shown that the emergent uniform rotation without any angular momentum, can be described in an effective theory approach as an autonomous Hamiltonian time crystal. The emergent oscillatory motion appears to be highly sensitive to temperature. This proposes that potential applications could be found from the development of molecular level detector to sensor and control technologies.
Highlights
Additional examples of simple triangular molecules that can be analyzed and where effective theory timecrystalline dynamics can be expected to appear, include aziridine, oxirane and 1,2-dimethylcyclopropane [25]
The initial configurations for the production runs that evaluate this angle, are described in the methods section: they are a set of 50 ‘random’ initial configurations each with a different internal temperature value T < 1.0 K with temperature determined by the equipartition theorem
The present results demonstrate that cyclopropane can realize emergent discrete timecrystalline dynamics, with different periodicity at different stroboscopic time scales
Summary
Additional examples of simple triangular molecules that can be analyzed and where effective theory timecrystalline dynamics can be expected to appear, include aziridine, oxirane and 1,2-dimethylcyclopropane [25]. It is shown how, in the case of a deformable body with three identical point-like particles, the effective rotation angle relates to a Dirac monopole connection in the space of shapes; the Dirac monopole connection describes nontrivial holonomy which is the cause of rotation by shape deformation. It presents all the simulations results, in the case of a cyclopropane molecule. The supplementary material (https://stacks.iop.org/NJP/23/073024/mmedia) includes three movies that show how the cyclopropane rotates, at different internal temperature values
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