Anomalous Correlators, Negative Frequencies, and Non-Phase-Invariant Hamiltonians in Random Waves

Villois, A., Dematteis, G., Lvov, Y. V., Onorato, M. and Shatah, J. (2025) Anomalous Correlators, Negative Frequencies, and Non-Phase-Invariant Hamiltonians in Random Waves. Physical Review Letters, 135 (16). ISSN 0031-9007

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Abstract

We investigate a generic non-phase-invariant Hamiltonian model that governs the dynamics of nonlinear dispersive waves. We give evidence that initial data characterized by random phases naturally evolve into phase correlations between positive and negative wave numbers, leading to the emergence of nonzero anomalous correlators and negative frequencies. Using analytical techniques, we show that anomalous correlators develop on a timescale of O(1/ϵ), earlier than the kinetic timescale. Our theoretical predictions are validated through direct numerical simulations of the deterministic system.

Item Type:	Article
Additional Information:	Publisher Copyright: © 2025 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
Uncontrolled Keywords:	physics and astronomy(all) ,/dk/atira/pure/subjectarea/asjc/3100
Faculty \ School:	Faculty of Science > School of Engineering, Mathematics and Physics
Related URLs:	http://www.scopus.com/inward/record.url?...
Depositing User:	LivePure Connector
Date Deposited:	10 Feb 2026 10:37
Last Modified:	15 Feb 2026 07:30
URI:	https://ueaeprints.uea.ac.uk/id/eprint/101884
DOI:	10.1103/3brq-j34x

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