Ruelle-Pollicott resonances of diffusive U(1)-invariant qubit circuits

We study Ruelle-Pollicott resonances of translationally invariant magnetization-conserving qubit circuits via the spectrum of the quasi-momentum-resolved truncated propagator of extensive observables. Diffusive transport of the conserved magnetization is reflected in the Gaussian quasi-momentum k k dependence of the leading eigenvalue (Ruelle-Pollicott resonance) of the truncated propagator for small k k . This, in particular, allows us to extract the diffusion constant. For large k k , the leading Ruelle-Pollicott resonance is not related to transport and governs the exponential decay of correlation functions. Additionally, we conjecture the existence of a continuum of eigenvalues below the leading diffusive resonance, which governs non-exponential decay, for instance, power-law hydrodynamic tails. We expect our conclusions to hold for generic systems with exactly one U(1) conserved quantity.