Anomalous transport in non-integrable classical field theories

Matija Koterle; Tomaz Prosen; Tianci Zhou

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arXiv · 2601.19894

Anomalous transport in non-integrable classical field theories

Matija Koterle·Tomaz Prosen·Tianci Zhou

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Abstract

Anomalous KPZ spin transport is well established in integrable non-Abelian lattice models but has not been investigated in continuum field theories as discretization in numerics generally break the continuum theory's integrability. We show that finite temperature acts as a regulator that can restore anomalous transport over a broad time window. In a family of spin field theories labeled by integer $n$, the $n = 1$ case is the Landau-Lifshitz model, whose numerical data shows spin superdiffusion with Kardar-Parisi-Zhang (KPZ) scaling and, at lower temperature ballistic energy transport, whereas both observables are diffusive at high temperature. The non-integrable $n = 2$ case shows the same crossover. While Lyapunov analysis confirms the model's non-integrability, the structure of spin-density space-time profiles suggests that long-lived soliton-like trajectories exist at low temperature.

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Matija Koterle, Tomaz Prosen, Tianci Zhou. 2026-01-27. Anomalous transport in non-integrable classical field theories. https://arxiv.org/abs/2601.19894

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