Autonomous topological time crystals and knotty molecular motors

Abstract

We show that topology is a very effective tool, to construct classical Hamiltonian time crystals. For this we numerically analyze a general class of time crystalline Hamiltonians that are designed to model the dynamics of molecular closed strings. We demonstrate how the time crystalline qualities of a closed string are greatly enhanced when the string becomes knotted. The Hamiltonians that we investigate include a generalized Kratky–Porod wormlike chain model in combination with long range Coulomb and Lennard–Jones interactions. Such energy functions are commonplace in coarse grained molecular modeling. Thus we expect that physical realizations of Hamiltonian time crystals can be constructed in terms of knotted ring molecules.