Anomalous heat conduction and anomalous diffusion in nonlinear lattices, single walled nanotubes, and billiard gas channels

Abstract

We study anomalous heat conduction and anomalous diffusion in low dimensional systems ranging from nonlinear lattices, single walled carbon nanotubes, to billiard gas channels. We find that in all discussed systems, the anomalous heat conductivity can be connected with the anomalous diffusion, namely, if energy diffusion is ${\sigma }^2(t)\equiv <\Delta x^2>=2D{t}^{\alpha }(0<\alpha \le 2)$, then the thermal conductivity can be expressed in terms of the system size $L$ as $\kappa =c{L}^{\beta }$ with $\beta =2-2/\alpha$. This result predicts that a normal diffusion ($\alpha =1$) implies a normal heat conduction obeying the Fourier law ($\beta =0$), a superdiffusion ($\alpha >1$) implies an anomalous heat conduction with a divergent thermal conductivity ($\beta >0$), and more interestingly, a subdiffusion ($\alpha <1$) implies an anomalous heat conduction with a convergent thermal conductivity ($\beta <0$), consequently, the system is a thermal insulator in the thermodynamic limit. Existing numerical data support our theoretical prediction.

15 Revtex pages, 16 figures. Invited article for CHAOS focus issue commemorating the 50th anniversary of the Fermi-Pasta-Ulam (FPU) model

References in corpus (32)

• Thermal transport measurements of individual multiwalled nanotubes
• Unusually High Thermal Conductivity of Carbon Nanotubes
• Thermal conduction in classical low-dimensional lattices
• Thermal diode: Rectification of heat flux
• Controlling the energy flow in nonlinear lattices: a model for a thermal rectifier
• Anomalous heat conduction in one dimensional momentum-conserving systems
• Heat conduction in one dimensional chains
• Finite thermal conductivity in 1d lattices
• Heat conduction in one dimensional nonintegrable systems
• Granular Avalanches in Fluids
• Steady-State Electrical Conduction in the Periodic Lorentz Gas
• Momentum conservation implies anomalous energy transport in 1d classical lattices
• Heat Conduction and Entropy Production in a One-Dimensional Hard-Particle Gas
• Heat conduction in a one-dimensional gas of elastically colliding particles of unequal masses
• Intriguing Heat Conduction of a Polymer Chain
• Bulk Properties of Anharmonic Chains in Strong Thermal Gradients: Non-Equilibrium ${\varphi }^4$ Theory
• Fermi-Pasta-Ulam $\beta$ lattice: Peierls equation and anomalous heat conductivity
• FPU $\beta$ model: Boundary Jumps, Fourier's Law and Scaling
• Relaxation of classical many-body hamiltonians in one dimension
• Anomalous Heat Conduction in a Di-atomic One-Dimensional Ideal Gas
• Finite thermal conductivity in 1D models having zero Lyapunov exponents
• Dynamical heat channels
• Can disorder induce a finite thermal conductivity in 1D lattices?
• Anomalous diffusion and the first passage time problem
• Heat conduction in 1D lattices with on-site potential
• Fourier law in the alternate mass hard-core potential chain
• Heat conductivity in linear mixing systems
• Energy transport and correlation between two attractors connected by Fermi-Pasta-Ulam chain
• Mode-coupling theory and molecular dynamics simulation for heat conduction in a chain with transverse motions
• Microscopic chaos from Brownian motion?
• Absence of local thermal equilibrium in two models of heat conduction
• Wave scattering by discrete breathers

Cited by in corpus (38)

• Phononics: Manipulating heat flow with electronic analogs and beyond
• Nanoscale Heat Transfer: from Computation to Experiment
• Thermal rectification in carbon nanotube intramolecular junctions: Molecular dynamics calculations
• Nonequilibrium Green's function approach to mesoscopic thermal transport
• Size-dependent thermal conductivity of nanoscale semiconducting systems
• Thermal transport in nanostructures
• Computation and data driven discovery of topological phononic materials
• Heat flow in nonlinear molecular junctions
• Nonequilibrium Green's function method for thermal transport in junctions
• Coupled electron and phonon transport in one-dimensional atomic junctions
• Energy carriers in the Fermi-Pasta-Ulam $\beta$ lattice: Solitons or Phonons?
• Validity of Fourier's law in one-dimensional momentum-conserving lattices with asymmetric interparticle interactions
• Magnetically Induced Thermal Rectification
• Thermal rectifier from deformed carbon nanohorns
• 1D momentum-conserving systems: the conundrum of anomalous versus normal heat transport
• Heat conduction in simple networks: The effect of inter-chain coupling
• Graphene Helicoid: The Distinct Properties Promote Application of Graphene Related Materials in Thermal Management
• Thermal conductivities of one-dimensional anharmonic/nonlinear lattices: renormalized phonons and effective phonon theory
• Displacement Autocorrelation Functions for Strong Anomalous Diffusion: A Scaling Form, Universal Behavior, and Corrections to Scaling
• Localization of low-frequency oscillations in single-walled carbon nanotubes
• A simple non-chaotic map generating subdiffusive, diffusive and superdiffusive dynamics
• Thermal rectification of a single-wall carbon nanotube: a molecular dynamics study
• Temperature dependence of thermal conductivities of coupled rotator lattice and the momentum diffusion in standard map
• Recurrence for quenched random Lorentz tubes
• Non-Gaussian normal diffusion induced by delocalization
• Heat conduction and energy diffusion in momentum-conserving 1D full lattice ding-a-ling model
• Energy spread and current-current correlation in quantum systems
• Temperature-dependent thermal conductivities of one-dimensional nonlinear Klein-Gordon lattices with soft on-site potential
• The Role of Chaos in One-Dimensional Heat Conductivity
• Solitons as candidates for energy carriers in Fermi-Pasta-Ulam lattices
• Stretch diffusion and heat conduction in 1D nonlinear lattices
• Equivalence of position-position auto-correlations in the Slicer Map and the Lévy-Lorentz gas
• Temperature dependent divergence of thermal conductivity in momentum conserving 1D lattice with asymmetric potential
• Heat conduction and diffusion of hard disks in a narrow channel
• Effect of external potential on the energy transport in harmonically driven segmented Frenkel-Kontorova lattices
• Thermal resonance in harmonically driven segmented Frenkel-Kontorova lattices with next-nearest-neighbor interactions
• Generalized autocorrelation function in the family of deterministic and stochastic anomalous diffusion processes
• Strong overlap of deterministic and stochastic dynamics in a super-diffusive regime