Does a single atom vibrate? Thermal vibration looks impossible, but does a single atom in vacuum vibrate due to the electrons' or subatomic particles' actions? If yes, how much is that vibration and is there a way to stop it?
 A: 
Vibration is a mechanical phenomenon whereby oscillations occur about an equilibrium point. The word comes from Latin vibrationem ("shaking, brandishing"). The oscillations may be periodic, such as the motion of a pendulum—or random, such as the movement of a tire on a gravel road.

Vibration is a classical mechanics phenomenon. Atoms may be considered classical mechanics points when in bulk and a model with mechanical vibrations used, but a single atom can only be described quantum mechanically about its center of mass.
The quantum mechanical wavefunction has electrons in orbitals and nuclei within  the nucleus  in energy levels depending on the quantum mechanical model used. All the periodic functions describing the atom have to do with the probability of measurement, which means many atoms must be measured in order to see the phase space of the possible positions, and any periodic function has to do with the frequencies displayed in the probability distributions, not space distributions for one atom.
Within the envelope of the Heisenberg uncertainty, one cannot know exactly the position of the single atom, because then the uncertainty in its momentum would be very large, but that does not mean it vibrates, it just means that the probability of its location and momentum are correlated.
