Abstract

Let an infinite, homogeneous, many-body quantum system be unitarily evolved for a long time from a state where two halves are independently thermalized. If there are nonzero steady currents in the central region then we say that a non-equilibrium steady state emerges; their presence is a signature of ballistic transport. I will discuss some recent results for such non-equilibrium steady states in any dimensionality, obtained with my collaborators Denis Bernard and Marianne Hoogeveen, and Joe Bhaseen, Andrew Lucas and Koenraad Schalm. I will first discuss a simple and general bound on the average current and on the noise, which occur, under certain conditions, from the Lieb-Robinson bound. This suggests to define a natural velocity parameter bounded by the Lieb-Robinson velocity: it is a ``nonlinear sound velocities’’, specializing to the sound velocity near equilibrium in non-integrable models and to a ``generalized sound velocities’’ encoding generalized Gibbs thermalization in integrable models. Then, I will discuss explicit results concentrating on conformal field theories. I will explain how to obtain the exact current in one dimension using chiral factorization, and how this generalizes in two separate ways to higher dimensions: for interacting models using fluid dynamics and AdS/CFT ideas, and for non-interacting models where independent mode thermalization occurs. Interestingly, the general bound is saturated at one-dimensional criticality, and in interacting models, the nonlinear sound velocity has an explicit physical realization as the velocity of (almost-)shock waves emanating form the contact hypersurface. If time permits, I will explain how ``extended fluctuation relations’’ hold in all cases, leading an exact description of the large-time fluctuations (interpreted as independent Poisson processes).