The focus of my research is the theory of hydrodynamics. The two main applications I am interested in are condensed matter phenomenology and holography.

Hydrodynamics is a low-enegy many-body effective theory of universal transport that describes systems near thermal equilibrium in the long-timescale, long-wavelength regime. The relevant degrees of freedom that survive in this regime are the (almost-)conserved charges, usually energy, momentum and internal-symmetry charges (e.g., a U(1) electric current). Hydrodynamic applies when the scattering time between the microscopic constituent of the fluid (e.g., electrons in condensed matters) is the shortest timescale of the system (electron-impurity scatterings are rare), therefore strongly-coupled phases have an enchanced hydrodynamic regime.

One interesting application is the fluid/gravity duality, grounded in holography. It allows us to study strongly-coupled quantum systems using a theory of classical gravity, in particular a Black Hole solution in the bulk of AdS space is dual to a thermal CFT that lives on the boundary. It is then possible to study the transport properties of the quantum system using the duality, which gives a relationship between the gravitational and hydrodynamic descriptions.

In hydrodynamics charges are exactly conserved. However, in real materials this is rarely true, since electrons can lose momentum and energy to impurities and phonons. Therefore the theory of hydrodynamics must be expanded to what is known as quasihydrodynamics, a theory in which charges are not exactly conserved, but are allowed to slowly relax to equilibrium.

On this regard, the research questions I am working on are: is it possible to develop a formally well-defined theory of quasihydrodynamics? How are the equations modified with respect to standard fluid dynamics? Are there constraints coming from symmetries and entropy production? And how should we interpret these physically?

It is a comon lore that static external electric fields should have almost no effect on bulk metallic superconductors. This is because standard BCS superconductors contain many free charges that reorganize to screen the electric field, as it happens in normal metals.

Recently, however, it has been reported that a static electric field can be used to control the value of the supercurrent in thin superconductive films. In particular, for a large enough electric field, a transition to the normal metallic phase has been observed. This effect is called Superconductive Field Effect (SFE). In these films the screening length is much smaller then the thickness of the film, which is about the same size as the coherence length, therefore the external electric field should have no effect on the bulk. Furthermore, it was observed that increasing the thickness of the sample completely suppresses the SFE and no transition to the metal phase occurs.

Part of my research deals with trying to understand this effect. Given the universality of the SFE, my advisor's group and I proposed a modified Ginzburg-Landau model that should capture the EFT of the systems below the critical temperature and managed to reproduce the main features of the SFE observed in experiments, but we still have to obtain a derivation from first principles.