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

Ruelle-Pollicott resonances are intrinsic properties of chaotic systems governing exponential decay of correlation functions of observables. In the talk, I will focus on their (numerical) extraction via the quasi-momentum-resolved truncated propagator of extensive observables and their relation to diffusive transport in magnetization-conserving qubit circuits. The diffusive transport of the conserved magnetization is reflected in the Gaussian quasi-momentum k dependence of the leading eigenvalue (Ruelle-Pollicott resonance) of the truncated propagator for small k. This, in particular, allows for the extraction of the diffusion constant. For large k, the leading Ruelle-Pollicott resonance is not related to transport and merely governs the exponential decay of correlation functions. Additionally, I will discuss the conjectured existence of a continuum of eigenvalues below the leading diffusive resonance, which governs non-exponential decay, for instance, power-law hydrodynamic tails. The conclusions are expected to hold for generic systems with exactly one U(1) conserved quantity. Based on arXiv:2506.24097, in collaboration with Marko Žnidarič.