Anomalous transport in the Fermi-Pasta-Ulam-Tsingou model: a review and open problems

TL;DR

This review discusses energy transport in FPUT chains, highlighting anomalous heat conduction, universality classes, finite-size effects, and the impact of noise and integrability on transport behavior.

Contribution

It clarifies the universality classes of anomalous transport in FPUT models and analyzes finite-size effects, noise, and integrability influences on energy transport.

Findings

FPUT-$eta$ model exhibits $oldsymbol{ ext{exponent } oldsymbol{rac{2}{5}}}$ for thermal conductivity divergence.

FPUT-$eta$ model's universality class is supported by numerical and theoretical evidence.

Finite-size effects can mask true asymptotic scaling behaviors.

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.