Chaos and residual correlations in pinned disordered systems.

We study, using functional renormalization, two copies of an elastic system pinned by mutually correlated random potentials. Short scale decorrelation depends on a nontrivial boundary layer regime with (possibly multiple) chaos exponents. Large scale mutual displacement correlations behave as x - x', mu proportional to the difference between Flory (or mean field) and exact roughness exponents zeta. For short range disorder mu>0 and small; e.g., for random bond interfaces mu=5zeta-epsilon, epsilon=4-d, and mu=epsilon{[(2pi)(2)/36]-1} for the one component Bragg glass. Random field (i.e., long range) disorder exhibits finite residual correlations (no chaos mu=0) described by new functional renormalization fixed points. Temperature and dynamic chaos (depinning) are discussed.