Holographic systems far from equilibrium: a review

Abstract

In this paper we give an overview of some recent progress in using holography to study various far-from-equilibrium condensed matter systems. Non-equilibrium problems are notoriously difficult to deal with, not to mention at strong coupling and including quantum effects. Remarkably, using holographic duality one can describe and follow the real time evolution of a far-from-equilibrium systems, including those which are spatially inhomogeneous and anisotropic, by solving partial differential gravity equations (PDEs). We sample developments on two broad classes of questions which are of much recent interest in the condensed matter community: non-equilibrium steady states (NESS), and quantum systems undergoing a global quench. Our discussion focuses on the main physical insights obtained from the gravity approache, rather than comprehensive treatments of each topic or detailed descriptions of gravity calculations. The paper also includes an overview of current numerical techniques, as well as the holographic Schwinger-Keldysh approach to real-time correlation functions.