Anomalous kinetics and transport from 1D self--consistent mode--coupling theory

TL;DR

This paper analyzes the anomalous transport properties in 1D many-particle systems using self-consistent mode-coupling theory, revealing how nonlinear interactions influence the decay of correlations and divergence of transport coefficients.

Contribution

It provides an analytical and numerical study of the nonlinear integro-differential equations governing 1D fluctuations, establishing the impact of nonlinear order on universality classes and transport anomalies.

Findings

Memory functions decay with power-law and oscillations

Viscosity diverges in cubic nonlinear systems

Finite viscosity in quartic systems with faster decay

Abstract

We study the dynamics of long-wavelength fluctuations in one-dimensional (1D) many-particle systems as described by self-consistent mode-coupling theory. The corresponding nonlinear integro-differential equations for the relevant correlators are solved analytically and checked numerically. In particular, we find that the memory functions exhibit a power-law decay accompanied by relatively fast oscillations. Furthermore, the scaling behaviour and, correspondingly, the universality class depends on the order of the leading nonlinear term. In the cubic case, both viscosity and thermal conductivity diverge in the thermodynamic limit. In the quartic case, a faster decay of the memory functions leads to a finite viscosity, while thermal conductivity exhibits an even faster divergence. Finally, our analysis puts on a more firm basis the previously conjectured connection between anomalous heat conductivity and anomalous diffusion.