Eur. Phys. J. Special Topics 151, 85-93 (2007)
https://doi.org/10.1140/epjst/e2007-00364-7

Anomalous transport and relaxation in classical one-dimensional models

¹ Dipartimento di Matematica, Università di Firenze, viale Morgagni 67a, 50134 Firenze, Italy
² Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, via Madonna del Piano 10, 50019 Sesto Fiorentino, Italy
³ Dipartimento di Fisica, via G. Sansone 1, 50019 Sesto Fiorentino, Italy
⁴ Ceremade, UMR-CNRS 7534, Université de Paris Dauphine, 75775 Paris Cedex 16, France

Corresponding author: stefano.lepri@isc.cnr.it

Abstract

After reviewing the main features of anomalous energy transport in 1D systems, we report simulations performed with chains of noisy anharmonic oscillators. The stochastic terms are added in such a way to conserve total energy and momentum, thus keeping the basic hydrodynamic features of these models. The addition of this “conservative noise" allows to obtain a more efficient estimate of the power-law divergence of heat conductivity κ(L) ∼L^α in the limit of small noise and large system size L. By comparing the numerical results with rigorous predictions obtained for the harmonic chain, we show how finite-size and time effects can be effectively controlled. For low noise amplitudes, the α values are close to 1/3 for asymmetric potentials and to 0.4 for symmetric ones. These results support the previously conjectured two-universality-classes scenario.