Suppression of Quasiperiodicity in Circle Maps with Quenched Disorder

David Müller-Bender, Johann Luca Kastner, Günter Radons

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Category: Not specified
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper’s claims (self-averaging of vω and λω as L→∞, suppression of quasiperiodicity for τmin>l, and a Gaussian tail for P(λω>λcutoff)) are presented with plausible—but heuristic—arguments that rely on approximating the quenched system by an annealed random dynamics and on literature results without fully checking their hypotheses for the concrete model. The model’s solution offers a different, more probabilistic route (subadditivity, mixing SLLN/CLT), but key steps (existence/uniqueness of the stationary law for “environment seen from the particle,” exponential mixing, and especially the Jensen-based strict negativity argument) are not justified. Hence both are incomplete as proofs, though they agree on the main phenomena.

Referee report (LaTeX)

\textbf{Recommendation:} major revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The Letter identifies and convincingly illustrates a striking phenomenon: for quenched, short-range-disordered monotone circle maps, quasiperiodicity is suppressed in the thermodynamic limit and both drift and Lyapunov exponent self-average. The numerical evidence is strong, figures are clear, and the message is timely for disordered dynamical systems. However, the present theoretical arguments are heuristic: key reductions (quenched to annealed), assumptions (no common invariant measure), and limit theorems (CLT for the quenched dynamics) are cited or sketched but not verified for the specific model. Strengthening these points is feasible and would substantially improve the paper’s correctness and impact.