Developments in quasihydrodynamics - Theory and applications

At its core, hydrodynamics is a many-body low-energy effective theory for the long-wavelength, long-timescale dynamics of conserved charges in systems close to thermodynamic equilibrium. It has a wide range of applications, that span from nuclear physics, astrophysics, cosmology, and more recently strongly-interacting electronic phases of matter. In condensed matter, however, symmetries are often only approximate, and softly broken by the presence of the lattice, impurities and defects, or because the symmetry is accidental. Therefore, the hydrodynamic regime must be expanded to include weak non-conservation effects, which lead to a theory known as quasihydrodynamics. In this thesis we make progress in understanding the theory of (quasi) hydrodynamics, with a specific focus on applications to condensed matter systems and their holographic description. First, we consider an electron fluid in a strong magnetic field for which translations are broken by the presence of Charge Density Waves. Therefore, the low-energy theory contains Goldstone modes associated with the broken symmetries, which modify the spectrum and transport properties. We focus on a new regime at non-zero lattice pressure and compare with holographic models, finding perfect agreement between the two descriptions. Next we consider a simple system that mimics the weakly-coupled Drude model from a hydrodynamic perspective. Specifically, a charged fluid in an external electric field in the presence of impurities that relax momentum and energy. We look for steady states, and we find that stationarity constraints should be modified to include relaxations, which consequently give novel predictions for the thermoelectric transport. Finally, we study the effect of the axial anomaly on the transport properties of Weyl semimetals in the hydrodynamic regime. We suggest a better approach to deal with the derivative counting of the magnetic field, correcting mistakes in the literature. Subsequently, we discuss the DC values of the conductivities and look for models that obey fundamental and phenomenological considerations. We find that generalized relaxations, which we study in depth using variational methods and kinetic-theory approaches, are a necessary ingredient to have finite DC conductivity, conserve electric charge, and have the correlators obey Onsager relations. Moreover, our model provides qualitatively new predictions for the thermoelectric transport, which could be used to probe the hydrodynamic regime in such materials.