Hydrodynamics can be thought of as an effective long-distance description of a many-body system at non-zero temperature. It is the correct effective field theory to use in order to describe strongly coupled systems near equilibrium, where there are no more well defined particles and the only long-lived modes are the (almost)-conserved currents. Recently, hydrodynamics has been used successfully to study strongly coupled systems, such as quark-gluon plasma or high-temperature superconductors.
The thesis consists in the study of hydrodynamic effective field theories in which different spontaneously broken phases coexist. The results obtained will be applied to the study of strongly coupled quantum critical condensed matter systems, such as High Temperature Superconductors. (Collaborations with the experimental condensed matter group are possible)