A violation of universality in anomalous Fourier's law

Abstract

Since 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 renormalization-group arguments and mode-coupling approximations within fluctuating hydrodynamics, is that the anomaly is universal in 1d momentum-conserving systems and belongs in the Levy/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 renormalization-group and mode-coupling universality predictions for anomalous Fourier's law in 1d, offering a new perspective on transport in low dimensions.

10 pages + 6 figs + Supplementary Material (7 pages + 6 figs)

References in corpus (11)

• Length-dependent thermal conductivity in suspended single-layer graphene
• Heat Transport in low-dimensional systems
• Heat transport in low dimensions: introduction and phenomenology
• Fibonacci family of dynamical universality classes
• Numerical test of hydrodynamic fluctuation theory in the Fermi-Pasta-Ulam chain
• Self-Consistent Mode-Coupling Approach to 1D Heat Transport
• Non-integrability and the Fourier heat conduction law
• Current fluctuations for anharmonic chains in thermal equilibrium
• 1D momentum-conserving systems: the conundrum of anomalous versus normal heat transport
• Energy diffusion in hard-point systems
• Role of conserved quantities in normal heat transport in one dimenison

Cited by in corpus (26)

• Heat transport in low dimensions: introduction and phenomenology
• Too Close to Integrable: Crossover from Normal to Anomalous Heat Diffusion
• Anomalous heat transport in classical many-body systems: overview and perspectives
• Non-Fourier heat transport in nanosystems
• Blast in a One-Dimensional Cold Gas: From Newtonian Dynamics to Hydrodynamics
• The Fourier heat conduction as a strong kinetic effect
• The Taylor-von Neumann-Sedov blast-wave solution: comparisons with microscopic simulations of a one-dimensional gas
• Crossover between different universality classes: Scaling for thermal transport in one dimension
• A large deviation theory perspective on nanoscale transport phenomena
• Temperature profile and boundary conditions in an anomalous heat transport model
• Heat current fluctuations and anomalous transport in low dimensional carbon lattices
• Observing Golden Mean Universality Class in the Scaling of Thermal Transport
• Thermal conductance of one dimensional disordered harmonic chains
• QCD phase diagram and critical exponents within the nonextensive Polyakov-Nambu-Jona-Lasinio model
• Anomalous temperature-dependent heat transport in one-dimensional momentum-conserving systems with soft-type interparticle interaction
• A splash in a one-dimensional cold gas
• Heat conduction in a three-dimensional momentum-conserving fluid
• Anomalous diffusion and Noether's second theorem
• A lattice gas model for generic one-dimensional Hamiltonian Systems
• KPZ modes in $d$-dimensional directed polymers
• Heat flux direction controlled by power-law oscillators under non-Gaussian fluctuations
• First-Principle Validation of Fourier's Law: One-Dimensional Classical Inertial Heisenberg Model
• Infinite family of universal profiles for heat current statistics in Fourier's law
• Molecular hints of two-step transition to convective flow via streamline percolation
• Non-equilibrium stationary properties of the boundary driven zero-range process with long jumps
• Dynamical correlations of conserved quantities in the one-dimensional equal mass hard particle gas