The statistical Jacobi approach to quantum dynamics

The push to build controllable and programmable quantum hardware has opened a new intermediate-scale time regime in strongly out-of-equilibrium systems. This regime can neither be treated by early-time techniques like perturbation theory, nor by late-time hydrodynamics/Boltzmann theories that assume local equilibration. Nevertheless, there are interesting qualitative phenomena in this time window. Energy may coherently oscillate, the system may be glassy, or be relaxing towards local equilibrium. 

I propose that the "statistical Jacobi approximation" (SJA) provides a predictive description of the intermediate time regime, and give two examples. The setting for the first is glassy, nearly many-body localized systems with strong spatial inhomogeneity. The SJA reveals that effective two-level systems resonate and cause dynamics, and predicts stretched exponential decay of local observables in the intermediate time regime. The second example is in strongly interacting and well-thermalizing systems, where the SJA reconstructs spectral functions and predicts relaxation rates beyond Fermi's golden rule. I will conclude with thoughts on applications in driven and open systems, and to localization transitions.

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