Classical non-relativistic fractons

I will discuss some results on the classical mechanics of non-relativistic fractons in its simplest setting - that of identical one dimensional particles with local Hamiltonians characterized by a conserved dipole moment in addition to the usual symmetries of space and time translation invariance. Locality leads to a "Machian" dynamics in which a given particle exhibits finite inertia only if within a specified distance of at least another one. For well separated particles this leads to immobility, much as for quantum models of fractons discussed before. For two or more particles within inertial reach of each other at the start of motion we get an interesting interplay of inertia and interactions. Interestingly, Machian clusters exhibit physical attractors and limit cycles in a Hamiltonian system even though mathematical limit cycles are forbidden by Liouville's theorem. 

(work with Abhishodh Prakash, Alain Goriely and Ylias Sadki)