  A Hamiltonian time crystal can emerge when a Noether symmetry is subject to a
condition that prevents the energy minimum from being a critical point of the
Hamiltonian. A somewhat trivial example is the Schr\"odinger equation of a
harmonic oscillator. The Noether charge for its particle number coincides with
the square norm of the wave function, and the energy eigenvalue is a Lagrange
multiplier for the condition that the wave function is properly normalized. A
more elaborate example is the Gross-Pitaevskii equation that models vortices in
a cold atom Bose-Einstein condensate. In an oblate, essentially two dimensional
harmonic trap the energy minimum is a topologically protected timecrystalline
vortex that rotates around the trap center. Additional examples are constructed
using coarse grained Hamiltonian models of closed molecular chains. When
knotted, the topology of a chain can support a time crystal. As a physical
example, high precision all-atom molecular dynamics is used to analyze an
isolated cyclopropane molecule. The simulation reveals that the molecular
D$_{3h}$ symmetry becomes spontaneously broken. When the molecule is observed
with sufficiently long stroboscopic time steps it appears to rotate like a
simple Hamiltonian time crystal. When the length of the stroboscopic time step
is decreased the rotational motion becomes increasingly ratcheting and
eventually it resembles the back-and-forth oscillations of Sisyphus dynamics.
The stroboscopic rotation is entirely due to atomic level oscillatory shape
changes, so that cyclopropane is an example of a molecule that can rotate
without angular momentum. Finally, the article is concluded with a personal
recollection how Frank's and Betsy's Stockholm journey started.

Other Condensed Matter;Statistical Mechanics