Abstract: | I will discuss a set of results on the classical mechanics of fractons - being defined as particles whose dynamics obeys a consistent set of multipole conservation laws. I will show that the nonlinear, Machian, dynamics of the fractons is characterized by late-time attractors in position-velocity space, despite the absence of attractors in phase space dictated by Liouville's theorem. These attractors violate ergodicity and lead to non-equilibrium steady states, which always break translational symmetry, even in spatial dimensions where the Hohenberg-Mermin-Wagner-Coleman theorem for equilibrium systems forbids such breaking. While a full understanding of the many-body nonlinear problem is a formidable and incomplete task, I will discuss progress towards a conceptual understanding of these results. Altogether, these fracton systems host a new paradigm for Hamiltonian dynamics and non-equilibrium many-body physics.
Joint work with Abhishodh Prakash, Alain Goriely and Ylias Sadki:
[2308.07372] Classical Non-Relativistic Fractons (arxiv.org)
[2312.02271] Machian fractons, Hamiltonian attractors and non-equilibrium steady states (arxiv.org) |