The assumption of local relaxation in inhomogeneous quantum quenches allows to compute asymptotically the expectation value of local observables via a theory known as generalized hydrodynamics (GHD). I will address formally the question of when an observable is “local enough » to be described by GHD in the playground of partitioning protocols and non-interacting time evolution. I will formulate a phase-space description of any state evolving under a quadratic Hamiltonian, i.e. I will provide a set of decoupled dynamical (classical) fields to fully describe time evolution. By studying the contribution to a connected spin correlation of each of those fields independently, one can determine the nature of the leading order with respect to the locality of the observable. That shows both the regime of validity of standard applications of GHD and the locality conditions necessary for Gaussianification to occur.

Contact : Jérôme Dubail