On the generalized hydrodynamics of integrable quantum field theories with irrelevant deformations

The purpose of this Master Thesis is to study the Generalized Hydrodynamics (GHD) of Integrable Quantum Field Theories perturbed by the famous TTbar deformation and its generalizations. These deformations are irrelevant, and therefore alter dramatically the UV structure of the theory and are not renormalizable, but are still considered consistent and interesting theories since they preserve the integrable structure of the underlying model. The specific focus of the work is to find the average densities and currents related to conserved charges of generic spin, which describe the flow of energy, momentum, and higher charges, between two semi-infinite slabs prepared in two different states and placed in contact in the origin, in the setup known as partitioning protocol. From a theoretical point of view this is the most important protocol in out of equilibrium physics, since it is simple enough to have an analytical description and in some situations to have an analytical solution, but at the same time it is complex enough to gain practical knowledge on the effect of inhomogeneities on integrable systems. In particular, through a convenient way of rewriting the Thermodynamic Bethe Ansatz (TBA) equations, I found exact expressions for the currents and densities in the conformal limit, generalizing previously known results in several directions, with excellent numerical validation. I have also performed an in-depth study of possible extensions of the results out of the conformal point in the simplest possible theory, the free fermion, obtaining interesting expressions for the lowest order corrections in terms of special functions. Finally, I have performed numerical simulations which give a perfect confirmation of the analytical results, and allow to gain insight on some interesting aspects of the models which are not accessible analytically.