What does "instant thermalization" in large- q SYK models mean?

Motivated by the Planckian thermalization rate Γ about T observed in the two-body interacting SYK model, we study thermalization in the q/2-body case. Previous studies of such systems have established the notion of instantaneous thermalization to leading order in 1/q. It was conjectured that the thermalization may still be Planckian but with a divergent rate Γ about T q, explaining the ``instantaneous'' part. For an analytically and numerically tractable system, we calculate the effective temperatures after a quench at time t = 0 and indeed find a Planckian rate, albeit with the unexpected decaying behavior Γ about T q-1. This is contrasted with the behavior of the causal Green's function G(t 1, t 2), which instantly acquires a thermal form in the two-time plane block t 1, t 2 > 0. The resulting picture is that instant thermalization is a meaningful concept only for this block, while the off-diagonal blocks t 1 times t 2 < 0 are inherently non-thermal at any q. Since the effective temperature is obtained from correlations spanning all blocks, it inherits a finite rate set by the off-diagonal. We illustrate this directly by studying the non-thermal correlations' time dependence.