We consider the non-equilibrium dynamics in quantum field theories (QFTs). After being prepared in a density matrix that is not an eigenstate of the Hamiltonian, such systems are expected to relax locally to a stationary state. In presence of local conservation laws, these stationary states are believed to be described by appropriate generalized Gibbs ensembles. Here we demonstrate that in order to obtain a correct description of the stationary state, it is necessary to take into account conservation laws that are not (ultra-)local in the usual sense of QFT, but fulfil a significantly weaker form of locality. We discuss implications of our results for integrable QFTs in one spatial dimension. PACS numbers:Introduction. The last decade has witnessed dramatic progress in realizing and analyzing isolated many-particle quantum systems out of equilibrium [1][2][3][4][5][6]. Key questions that emerged from these experiments is why and how observables relax towards time independent values, and what principles underlie a possible statistical description of the latter . It was demonstrated early on that non-equilibrium dynamics is strongly affected by dimensionality, and that conservation laws play an important role. In particular, the experiments of [2] on trapped 87 Rb atoms established that three-dimensional condensates rapidly relax to a stationary state characterized by an effective temperature, whereas constraining the motion of atoms to one dimension greatly reduces the relaxation rate and dramatically changes the nature of the stationary state. The suggestion that this unusual steady state is a consequence of (approximate) conservation laws motivated a host of theoretical studies investigation the role played by conservation laws. We may summarize the results of these works as follows: given an initial state |Ψ and a translationally invariant system with Hamiltonian H ≡ I 0 and conservation laws I n such that [I n , I m ] = 0, the stationary behaviour of n-point functions of local operators O a (x) in the thermodynamic limit is described by a generalized Gibbs ensemble, as proposed by Rigol et al in a seminal paper [9]

Interactions are known to have dramatic effects on bosonic gases in one dimension (1D). Not only does the ground state transform from a condensate like state to an effective Fermi sea, but new fundamental excitations, which do not have any higher-dimensional equivalents, are predicted to appear. In this work, we trace these elusive excitations via their effects on the dynamical structure factor of 1D strongly interacting Bose gases at low temperature. An array of 1D Bose gases is obtained by loading a 87 Rb condensate in a two-dimensional lattice potential. The dynamical structure factor of the system is probed by energy deposition through low-momentum Bragg excitations. The experimental signals are compared to recent theoretical predictions for the dynamical structure factor of the Lieb-Liniger model at T > 0. Our results demonstrate that the main contribution to the spectral widths stems from the dynamics of the interaction-induced excitations in the gas, which cannot be described by the Luttinger liquid theory.