Category Archives: anomalous transport

Violation of universality in anomalous Fourier’s law

Pablo I. Hurtado, Pedro L. Garrido

fig3Since the discovery of long-time tails, it has been clear that Fourier’s law in low dimensions is typically anomalous, with a size-dependent heat conductivity, though the nature of the anomaly remains puzzling. The conventional wisdom, supported by recent results from nonlinear fluctuating hydrodynamics, is that the anomaly is universal in 1d momentum-conserving systems and belongs in the Kardar-Parisi-Zhang universality class. Here we challenge this picture by using a novel scaling method to show unambiguously that universality breaks down in the paradigmatic 1d diatomic hard-point fluid. Hydrodynamic profiles for a broad set of gradients, densities and sizes all collapse onto an universal master curve, showing that (anomalous) Fourier’s law holds even deep into the nonlinear regime. This allows to solve the macroscopic transport problem for this model, a solution which compares flawlessly with data and, interestingly, implies the existence of a bound on the heat current in terms of pressure. These results question the use of standard fluctuating hydrodynamics to understand anomalous Fourier’s law in 1d, offering a new perspective on transport and its anomalies in low dimensions.

Nature Sci. Rep. 6, 38823 (2016)arXiv:1506.03234

Scaling laws and bulk-boundary decoupling in heat flow

J.J. del Pozo, P.L. Garrido, P.I. Hurtado

When driven out of equilibrium by a temperature gradient, fluids respond by developing a nontrivial, inhomogeneous structure according to the governing macroscopic laws. Here we show that such structure obeys strikingly simple scaling laws arbitrarily far from equilibrium, provided that both macroscopic local equilibrium and Fourier’s law hold. Extensive simulations of hard disk fluids confirm the scaling laws even under strong temperature gradients, implying that Fourier’s law remains valid in this highly nonlinear regime, with putative corrections absorbed into a nonlinear conductivity functional. In addition, our results show that the scaling laws are robust in the presence of strong finite-size effects, hinting at a subtle bulk-boundary decoupling mechanism which enforces the macroscopic laws on the bulk of the finite-sized fluid. This allows to measure for the first time the marginal anomaly of the heat conductivity predicted for hard disks.

Additional material: video demonstrating the scaling procedure (credit: J. del Pozo 2014)

Phys. Rev. E 91, 032116 (2015)arXiv:1401.5244