Dissipative hydrodynamics of systems with broken symmetries
Joël Mabillard (ULB Bruxelles)
In phases of condensed matter with broken continuous symmetries, as well as in fluids, transport processes generate irreversibility at the macroscale. To be complete, the hydrodynamic equations must include these dissipative effects. A fundamental question is to deduce all of them from the microscopic Hamiltonian dynamics of the particles with the methods of non-equilibrium statistical mechanics. In this presentation, a first-principle derivation based on a local-equilibrium approach is introduced. As an example of application, the crystalline solid is considered. The breaking of the three-dimensional continuous group of spatial translations implies the existence of three slow modes in addition to the five slow modes arising from the fundamental conservation laws of mass, energy, and linear momentum. Finally, based on the results of the local-equilibrium approach, the equilibrium and nonequilibrium properties relevant to the hydrodynamics of the perfect hard-sphere crystal are obtained with molecular dynamics simulations.