Pole skipping away from maximal chaos

A bstract Pole skipping is a recently discovered subtle effect in the thermal energy density retarded two point function at special complex ( ω, p ) planes. We propose that pole determined by stress tensor contribution to many-body chaos, and p.s. = $$ i{\lambda}^{(T)}\left(1,1/{u}_B^{(T)}\right) i λ T 1 / u B , where λ T 2 π/β {u}_B^{(T)} are contributions Lyapunov exponent butterfly velocity respectively. While this proposal consistent with previous studies conducted for maximally chaotic theories, dominates it clarifies one cannot use extract of theory, which obeys ≤ . On other hand, large class strongly coupled but non-maximally theories true we conjecture u B universal bound. remains challenge explain general framework, provide stringent test our large- q limit SYK chain, determine λ, closed form all values coupling, interpolating between free limits. Since such an explicit expression correlator kind, take opportunity analyze many its properties: coupling dependence diffusion constant, dispersion relations poles, convergence properties order hydrodynamics.