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We consider the out-of-equilibrium dynamics of an interacting integrable system in the presence of an external dephasing noise. In the limit of large spatial correlation of the noise, we develop an exact description of the dynamics of the system based on a hydrodynamic formulation. This results in an additional term to the standard generalized hydrodynamics theory describing diffusive dynamics in the momentum space of the quasiparticles of the system, with a time- and momentum-dependent diffusion constant. Our analytical predictions are then benchmarked in the classical limit by comparison with a microscopic simulation of the non-linear Schrodinger equation, showing perfect agreement. In the quantum case, our predictions agree with state-of-the-art numerical simulations of the anisotropic Heisenberg spin in the accessible regime of times and with bosonization predictions in the limit of small dephasing times and temperatures., 7+7 pages, 2 figures

We identify a class of one-dimensional spin and fermionic lattice models which display diverging spin and charge diffusion constants, including several paradigmatic models of exactly solvable strongly correlated many-body dynamics such as the isotropic Heisenberg spin chains, the Fermi-Hubbard model, and the t-J model at the integrable point. Using the hydrodynamic transport theory, we derive an analytic lower bound on the spin and charge diffusion constants by calculating the curvature of the corresponding Drude weights at half filling, and demonstrate that for certain lattice models with isotropic interactions some of the Noether charges exhibit super-diffusive transport at finite temperature and half filling., Comment: 4 pages + appendices, v2 as published

Understanding possible universal properties for systems far from equilibrium is much less developed than for their equilibrium counterparts and poses a major challenge to present day statistical physics. The study of aging properties, and how the memory of the past is conserved by the time evolution in presence of noise is a crucial facet of the problem. Recently, very robust universal properties were shown to arise in one-dimensional growth processes with local stochastic rules,leading to the Kardar-Parisi-Zhang universality class. Yet it has remained essentially unknown how fluctuations in these systems correlate at different times. Here we derive quantitative predictions for the universal form of the two-time aging dynamics of growing interfaces, which, moreover, turns out to exhibit a surprising breaking of ergodicity. We provide corroborating experimental observations on a turbulent liquid crystal system, which demonstrates universality. This may give insight into memory effects in a broader class of far-from-equilibrium systems., 6 pages + supplemental material (5 pages). 9 figures

We study a quench protocol where the ground state of a free many-particle bosonic theory in one dimension is let unitarily evolve in time under the integrable Lieb-Liniger Hamiltonian of $\delta$-interacting repulsive bosons. By using a recently-proposed variational method, we here obtain the exact non-thermal steady-state of the system in the thermodynamic limit, and discuss some of its main physical properties. Besides being a rare case of a thermodynamically exact solution to a truly interacting quench situation, this interestingly represents an example where a naive implementation of the generalized Gibbs ensemble fails., Comment: 10 pages, 3 figures