Abstract
Physical phenomena in reduced spatial dimension (D=1,2) are
often qualitatively different from their three-dimensional
counterparts due to the overwhelming role of statistical
fluctuations.
An important example is the anomalous heat conduction in 1D
many-particle systems. More specifically, anomalous behaviour
manifests as (i) a divergence of the finite-size thermal
conductivity as a power of the system length; (ii) a nonintegrable
long-time tail of the energy current correlator
(the Green-Kubo integrand); (iii) the anomalous diffusion of
energy flucuations (Levy walks). Simulations and theoretical
arguments indicate that anomalies should occur generically
in D=1 whenever momentum is conserved. Universal aspects
are discussed in the framework of mode-coupling theory describing
nonlinear interactions among long-wavelength fluctuations.
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