Super-diffusion and crossover from diffusive to anomalous transport in a one-dimensional system
arXiv:2209.07739 · doi:10.21468/SciPostPhys.15.1.038
Abstract
We study transport in a one-dimensional lattice system with two conserved quantities -- `volume' and energy. Considering a slowly evolving local equilibrium state that is slightly deviated from an underlying global equilibrium, we estimate the correction to the local equilibrium distribution. This correction arises mainly through the space-time correlations of some local currents. In the continuum limit, we show that the local equilibrium distribution along with the correction yields drift-diffusion equation for the `volume' and super-diffusion equation for the energy in the linear response regime as macroscopic hydrodynamics as one would obtain from non-linear fluctuating hydrodynamic theory. We find explicit expression of the super-diffusion equation. Further, we find diffusive correction to the super-diffusive evolution. Such a correction allows us to study a crossover from diffusive to anomalous transport. We demonstrate this crossover numerically through the spreading of an initially localized heat pulse in equilibrium as well as through the system size scaling of the stationary current in non-equilibrium steady state.
arXiv comment24 pages
References in corpus (26)
- Heat Transport in low-dimensional systems
- Thermal conductivity of suspended pristine graphene measured by Raman spectroscopy
- Nonlinear fluctuating hydrodynamics for anharmonic chains
- Heat conduction in a one-dimensional gas of elastically colliding particles of unequal masses
- From anomalous energy diffusion to Levy walks and heat conductivity in one-dimensional systems
- Anomalous Heat Conduction and Anomalous Diffusion in Low Dimensional Nanoscale Systems
- Numerical test of hydrodynamic fluctuation theory in the Fermi-Pasta-Ulam chain
- Anomalous Heat Conduction in a Di-atomic One-Dimensional Ideal Gas
- Heat conduction in the α-β-Fermi-Pasta-Ulam chain
- Nonlinear Fluctuating Hydrodynamics in One Dimension: the Case of Two Conserved Fields
- Validity of Fourier's law in one-dimensional momentum-conserving lattices with asymmetric interparticle interactions
- Exact solution of a Levy walk model for anomalous heat transport
- Too Close to Integrable: Crossover from Normal to Anomalous Heat Diffusion
- Superdiffusion of energy in a chain of harmonic oscillators with noise
- A stochastic model of anomalous heat transport: analytical solution of the steady state
- Current fluctuations for anharmonic chains in thermal equilibrium
- Anomalous heat transport in one dimensional systems: a description using non-local fractional-type diffusion equation
- Energy diffusion in hard-point systems
- Green-Kubo formula for heat conduction in open systems
- Anomalous diffusion for a class of systems with two conserved quantities
- 3/4 Fractional superdiffusion of energy in a system of harmonic oscillators perturbed by a conservative noise
- Microscopic theory of the fluctuating hydrodynamics in nonlinear lattices
- Derivation of fluctuating hydrodynamics and crossover from diffusive to anomalous transport in a hard-particle gas
- Fractional diffusion equation description of an open anomalous heat conduction set-up
- Temperature profile and boundary conditions in an anomalous heat transport model
- Anomalous heat equation in a system connected to thermal reservoirs