Rotation by shape change, autonomous molecular motors and effective timecrystalline dynamics

Abstract: A deformable body can rotate even with no angular momentum, simply by changing its shape. A good example is a falling cat, how it maneuvers in air to land on its feet. Here a first principles molecular level example of the phenomenon is presented. For this the thermal vibrations of individual atoms in an isolated cyclopropane molecule are simulated in vacuum and at ultralow internal temperature values, and the ensuing molecular motion is followed stroboscopically. It is observed that in the limit of long stroboscopic time steps the vibrations combine into an apparent uniform rotation of the entire molecule even in the absence of angular momentum. This large time scale rotational motion is then modeled in an effective theory approach, in terms of timecrystalline Hamiltonian dynamics. The phenomenon is a temperature sensitive measurable. As such it has potential applications that range from models of autonomous molecular motors to development of molecular level detector, sensor and control technologies.