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Modular Criticality Without Correlation Length: A Testable Prediction for Open Quantum Systems
2026-04-09

We report the discovery of a new class of critical phenomena in open quantum systems that is not governed by divergence of correlation length. In contrast to the standard paradigm, where criticality is identified by ξ → ∞, we demonstrate the existence of regimes characterized by: Δ → 0, Γ > 0, ξ = O(1), where Δ is the partition gap and Γ is the switching rate of optimal decompositions. We show that such systems exhibit a universal modular scaling law: ν(λ) ∼ 1 log λ, derived from the spectral structure of the modular generator K = −log ρ. This scaling defines a new diagnostic observable independent of spatial correlations. We formulate a hard, experimentally testable prediction: Ξ(λ) = ν(λ) · log λ → 1, which provides a falsifiable signature of modular criticality accessible in quantum simulators. The results establish a new notion of criticality rooted in spectral redistribution, commutator dynamics, and information geometry, rather than correlation length. This reveals a previously unrecognized universality class applicable to open quantum systems, non-equilibrium dynamics, and information-theoretic regimes.

Ссылка для цитирования:

Nesen O. I. 2026. Modular Criticality Without Correlation Length: A Testable Prediction for Open Quantum Systems. PREPRINTS.RU. https://doi.org/10.24108/preprints-3114873