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

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.

References in corpus (14)

• Thermal conduction in classical low-dimensional lattices
• Fractional Langevin equation
• Anomalous heat conduction in one dimensional momentum-conserving systems
• From anomalous energy diffusion to Levy walks and heat conductivity in one-dimensional systems
• Intriguing Heat Conduction of a Polymer Chain
• Fermi-Pasta-Ulam $\beta$ lattice: Peierls equation and anomalous heat conductivity
• Dynamical heat channels
• On the universality of anomalous one-dimensional heat conductivity
• Self-Consistent Mode-Coupling Approach to 1D Heat Transport
• Studies of thermal conductivity in Fermi-Pasta-Ulam like lattices
• Mode-coupling theory and molecular dynamics simulation for heat conduction in a chain with transverse motions
• Long-Time Tails, Weak Localization, and Classical and Quantum Critical Behavior
• The one-dimensional Lennard-Jones system: collective fluctuations and breakdown of hydrodynamics
• A simulation study of energy transport in the Hamiltonian XY-model

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• From Near-Integrable to Far-from-Integrable: A Unified Picture of Thermalization and Heat Transport