Bulk Properties of Anharmonic Chains in Strong Thermal Gradients: Non-Equilibrium ${\varphi }^4$ Theory

Abstract

We study nonequilibrium properties of a one-dimensional lattice Hamiltonian with quartic interactions in strong thermal gradients. Nonequilibrium temperature profiles, T(x), are found to develop significant curvature and boundary jumps. From the determination of the bulk thermal conductivity, we develop a quantitative description of T(x) including the jumps.

14pp, 5 figs

Cited by in corpus (59)

• Heat Transport in low-dimensional systems
• Anomalous heat conduction and anomalous diffusion in one dimensional systems
• Size-dependent thermal conductivity of nanoscale semiconducting systems
• Anomalous Heat Conduction and Anomalous Diffusion in Low Dimensional Nanoscale Systems
• FPU $\beta$ model: Boundary Jumps, Fourier's Law and Scaling
• Anomalous heat conduction and anomalous diffusion in nonlinear lattices, single walled nanotubes, and billiard gas channels
• Nonequilibrium Green's function method for phonon-phonon interaction and ballistic-diffusive thermal transport
• Finite thermal conductivity in 1D models having zero Lyapunov exponents
• Effect of phonon-phonon interactions on localization
• Heat conduction in 1D lattices with on-site potential
• Energy Transport in Weakly Anharmonic Chains
• Studies of thermal conductivity in Fermi-Pasta-Ulam like lattices
• Sufficient conditions for thermal rectification in graded materials
• Effective phonons in anharmonic lattices: anomalous vs normal heat conduction
• Anomalous heat transport in classical many-body systems: overview and perspectives
• Diffusion of heat, energy, momentum, and mass in one-dimensional systems
• Non-Fourier heat transport in nanosystems
• Thermal Rectification in Graded Materials
• 1D momentum-conserving systems: the conundrum of anomalous versus normal heat transport
• Non-equilibrium quantum chains under multi-site Lindblad baths
• Role of the range of the interactions in thermal conduction
• Non-Equilibrium Statistical Mechanics of Classical Lattice ${\varphi }^4$ Field Theory
• Nonlinear Fluctuating Hydrodynamics for the Classical XXZ Spin Chain
• Heat conduction in simple networks: The effect of inter-chain coupling
• Heat Conduction in One-Dimensional chain of Hard Discs with Substrate Potential
• Triggering waves in nonlinear lattices: Quest for anharmonic phonons and corresponding mean free paths
• Normal heat conductivity in chains capable of dissociation
• Thermal conductivities of one-dimensional anharmonic/nonlinear lattices: renormalized phonons and effective phonon theory
• 2D and 3D Dense-Fluid Shear Flows via Nonequilibrium Molecular Dynamics. Comparison of Time-and-Space-Averaged Tensor Temperature and Normal Stresses from Doll's, Sllod, and Boundary-Driven Shear Algorithms
• Heat transfer in a one-dimensional harmonic crystal in a viscous environment subjected to an external heat supply
• Temperature dependence of thermal conductivities of coupled rotator lattice and the momentum diffusion in standard map
• Remarks on NonHamiltonian Statistical Mechanics: Lyapunov Exponents and Phase-Space Dimensionality Loss
• A simulation study of energy transport in the Hamiltonian XY-model
• Anomalous energy diffusion in two-dimensional nonlinear lattices
• Heat wave propagation in a nonlinear chain
• Heat transport in an open transverse-field Ising chain
• Classical physics and blackbody radiation
• Ising chain: Thermal conductivity and first-principle validation of Fourier law
• Numerical examination of steady-state thermodynamics from the entropy connected to the excess heat
• Heat conduction and energy diffusion in momentum-conserving 1D full lattice ding-a-ling model
• Temperature-dependent thermal conductivities of one-dimensional nonlinear Klein-Gordon lattices with soft on-site potential
• Heat transport in nonlinear lattices free from the Umklapp process
• Stretch diffusion and heat conduction in 1D nonlinear lattices
• Stable and unstable periodic orbits in the one dimensional lattice ${\varphi }^4$ theory
• Thermal conductivity of one-dimensional lattices with self-consistent heat baths: a heuristic derivation
• Variational approach to renormalized phonon in momentum-nonconserving nonlinear lattices
• Hydrodynamics and transport in the long-range-interacting ${\phi }^4$ chain
• Nonequilibrium phenomena in nonlinear lattices: from slow relaxation to anomalous transport
• Thermal Conduction in one dimensional ${\Phi }^4$ chains with colliding particles
• Heat pump without particle transport or external work on the medium achieved by differential thermostatting of the phase space
• Projective-truncation-approximation study of the one-dimensional ${\varphi }^4$ lattice model
• Heat flow in anharmonic crystals with internal and external stochastic baths: A convergent polymer expansion for a model with discrete time and long range interparticle interaction
• First-Principle Validation of Fourier's Law: One-Dimensional Classical Inertial Heisenberg Model
• Order and Chaos in the One-Dimensional ${\varphi }^4$ Model : N-Dependence and the Second Law of Thermodynamics
• Nonlinearity-induced transition in heat conduction through a topological metamaterial of rotors
• Mechanical control of heat conductivity in microscopic models of dielectrics
• Computing Nonequilibrium Transport from Short-Time Transients: From Lorentz Gas to Heat Conduction in One Dimensional Chains
• Heat conductivity in the beta-FPU lattice. Solitons and breathers as energy carriers
• Thermal transport characteristics of Fermi-Pasta-Ulam chains undergoing soft-sphere type collisions