Long-time preservation of local correlations in the undressed metastable state

Establish whether local correlation functions remain nearly preserved for nonperturbatively long times in the original, undressed metastable state |ψ₀⟩ under unitary evolution by the Hamiltonian H, rather than only in the dressed state |\widetilde{ψ₀}⟩ produced by a quasi-local unitary. Specifically, determine if the rigorous lifetime bounds proved for |\widetilde{ψ₀}⟩ also hold for |ψ₀⟩ in complete generality and quantify any transient dynamics that may occur at short times.

Background

The paper proves nonperturbatively long lifetimes for local correlation functions in a dressed version of a metastable state, |\widetilde{ψ₀}⟩, constructed via a quasi-local unitary. This construction underpins the main prethermalization results, ensuring local observables remain near their initial values up to times exponentially large in the metastability parameters.

The authors expect analogous behavior for the original undressed state |ψ₀⟩, but note potential short-time transients. They explicitly state that a complete general proof for |ψ₀⟩ is lacking, marking this as an unresolved question central to connecting rigorous bounds with experimentally prepared initial states.