Solvable relaxation in discrete unitary systems: Ruelle-Pollicott resonances and CMV matrices

What the math gives to ML

The paper provides a concrete mechanism for relaxation in globally unitary dynamics: correlations decay because an initially local observable spreads into directions that are discarded by a finite observation subspace. The relevant decay rates are Ruelle–Pollicott resonances, which are poles of an analytically continued resolvent and need not equal the eigenvalues of a naively truncated propagator, especially in the backflow phase where truncation eigenvalues become ill-conditioned. This suggests a resonance-aware recurrent architecture or regularizer that estimates poles from hidden-state Krylov correlations rather than trusting the spectrum of a projected recurrent matrix. The central falsifiable prediction is that long-horizon memory is governed by the largest nontrivial resonance modulus, while projected-matrix eigenvalues can become misleading near a detectable conditioning transition.