Anomalous Transport in the Fermi-Pasta-Ulam-Tsingou Model: A Review and Open Problems

Abstract

This review provides an up-to-date account of energy transport in Fermi-Pasta-Ulam-Tsingou (FPUT) chains, a key testbed for nonequilibrium statistical physics. We discuss the transition from the historical puzzle of thermalization to the discovery of anomalous heat transport, where the effective thermal conductivity \(\kappa \) diverges with system size L as \(\kappa \propto L^\delta \). The article clarifies the distinction between two universality classes: the FPUT-\(\alpha \beta \) model, characterized by \(\delta = 1/3\) and linked to Kardar-Parisi-Zhang (KPZ) physics, and the symmetric FPUT-\(\beta \) model, where numerical and theoretical evidence support \(\delta = 2/5\). We investigate how finite-size effects—unavoidably induced by the thermostatting protocols— can disguise the asymptotic scaling. Additionally, we analyze the role of conservative noise in preserving hydrodynamic properties and examine how proximity to integrable limits leads to long-lived quasi-particles and, thereby, to diffusive regimes over intermediate spatial scales.