Space-time dualities for general quantum quenches

Characterising the universal aspects of non-equilibrium quantum many-body dynamics is one of
the key goals of contemporary physics research. The progress in this direction is however complicated
by the lack of general methods to study the dynamics of interacting quantum systems. In the talk I will discuss the recently introduced framework of space-time duality (SD), which allows obtain analytical insight by mapping a general out-of equilibrium system to a dual equilibrium theory; this has allowed to derive asymptotic predictions for several quantities of interest in homogeneous quenches.
While this framework was initially affected by some ambiguities which made its application to interacting systems subtle, I will discuss how these ambiguities can be solved from first principles leading to a solution which can be applied in "any" scenario. This allows then to extend the SD approach to general inhomogeneous quenches in integrable systems through the mixture of SD and GHD ingredients.