Hydrodynamics of Multipole-Conserving Systems

During this talk, we will explore how conserving quantities influence the long-timedynamics of generally strongly interacting closed systems. Typically, interactingquantum systems achieve thermalization via their own unitary dynamics, leading tothe emergence of statistical mechanics. However, the route to equilibrium can differdue to the existence of conserved quantities.

Often, conserved charges spread diffusively across the system. However, mobilityconstraints can impede or even halt their dynamics. The initial part of the talk isdevoted to the non-equilibrium dynamics of fractonic systems, especially those withmultiple conservation laws, such as dipole conservation. In these systems, charges areunable to move independently.

Their limited dynamics are described by a generalizeddiffusion equation that exhibits sub-diffusion [1]. In the second half of the talk, inspired by recent experiments on trapped-ion platformsthat intrinsically display power-law decaying interactions [2], we will delve into theinterplay between long-range interactions that promote thermalization and the dipolemobility constraints that obstruct it [3].