Necessity of ensemble averaging for holography in SYK

Determine whether holographic duality for the q=4 Sachdev–Ye–Kitaev (SYK) model requires averaging over the ensemble of Hamiltonians, or whether it extends to individual Hamiltonian samples without ensemble averaging.

Background

The dual gravitational description (JT gravity) is well established for the ensemble-averaged SYK model, where universal spectral features (e.g., ramp and plateau in SFF) align with semiclassical gravitational computations. Individual SYK samples (without time-averaging) exhibit large SFF oscillations, complicating direct gravitational interpretation.

The authors explicitly state they do not know whether ensemble averaging is necessary for holography. Resolving this would clarify the operational meaning of holographic duality for realizations of SYK in experiments and simulations that necessarily access single Hamiltonian instances.