Crossover from ballistic to normal heat transport in the ${\varphi }^4$ lattice: If nonconservation of momentum is the reason, what is the mechanism?

Abstract

Anomalous (non-Fourier's) heat transport is no longer just a theoretical issue since it has been observed experimentally in a number of low-dimensional nanomaterials, such as SiGe nanowires, carbon nanotubes, and others. To understand these anomalous behaviors, exploring the microscopic origin of normal (Fourier's) heat transport is a fascinating theoretical topic. However, this issue has not yet been fully understood even for one-dimensional (1D) model chains, in spite of a great amount of thorough studies done to date. From those studies it has been widely accepted that the conservation of momentum is a key ingredient to induce anomalous heat transport, while momentum-nonconserving systems usually support normal heat transport where Fourier's law is valid. But if the nonconservation of momentum is the reason, what is the underlying microscopic mechanism for the observed normal heat transport? Here we carefully revisit a typical 1D momentum-nonconserving ${\varphi }^4$ model and present evidence that the mobile discrete breathers or, in other words, the moving intrinsic localized modes with frequency components above the linear phonon band can be responsible for that.

arXiv comment11 pages, 10 figures

References in corpus (42)

• Thermal conduction in classical low-dimensional lattices
• Discrete Breathers
• Solitons in nonlinear lattices
• Heat Transport in low-dimensional systems
• Lévy walks
• Anomalous heat conduction in one dimensional momentum-conserving systems
• Nonlinear fluctuating hydrodynamics for anharmonic chains
• Heat conduction in one dimensional chains
• Finite thermal conductivity in 1d lattices
• Size-dependent thermal conductivity of nanoscale semiconducting systems
• Heat conduction in one dimensional nonintegrable systems
• A new regime of nanoscale thermal transport: collective diffusion counteracts dissipation inefficiency
• Suppression of thermal conductivity in graphene nanoribbons with rough edges
• Heat conduction in the diatomic Toda lattice revisited
• Heat transport in low dimensions: introduction and phenomenology
• Momentum conservation implies anomalous energy transport in 1d classical lattices
• Numerical test of hydrodynamic fluctuation theory in the Fermi-Pasta-Ulam chain
• Superdiffusive heat conduction in semiconductor alloys -- I. Theoretical foundations
• Normal heat conduction in one dimensional momentum conserving lattices with asymmetric interactions
• Heat conduction in the α-β-Fermi-Pasta-Ulam chain
• From kinetic to collective behavior in thermal transport on semiconductors and semiconductor nanostructures
• Fourier law in the alternate mass hard-core potential chain
• Superdiffusive heat conduction in semiconductor alloys -- II. Truncated Lévy formalism for experimental analysis
• Validity of Fourier's law in one-dimensional momentum-conserving lattices with asymmetric interparticle interactions
• Non-integrability and the Fourier heat conduction law
• Perturbation spreading in many-particle systems: a random walk approach
• First principles Kinetic-Collective thermal conductivity of semiconductors
• Diffusion of heat, energy, momentum, and mass in one-dimensional systems
• The effect of discrete breathers on heat conduction in nonlinear chains
• 1D momentum-conserving systems: the conundrum of anomalous versus normal heat transport
• Non-diffusive Lattice Thermal Transport in Si-Ge Alloy Nanowires
• Crossover from Fermi-Pasta-Ulam to normal diffusive behaviour in heat conduction through open anharmonic lattices
• Fourier law in a momentum-conserving chain
• Key role of asymmetric interactions in low-dimensional heat transport
• Thermal conductivity of group-IV Semiconductors from a Kinetic-Collective Model
• Crossover between different universality classes: Scaling for thermal transport in one dimension
• High-frequency thermal processes in harmonic crystals
• Pressure-induced recovery of Fourier's law in one dimensional momentum-conserving systems
• Underlying mechanisms for normal heat transport in one-dimensional anharmonic oscillator systems with a double-well interparticle interaction
• Modulating heat conduction by stretching or compressing
• Using Hilbert transform and classical chains to simulate quantum walks
• Anomalous temperature-dependent heat transport in one-dimensional momentum-conserving systems with soft-type interparticle interaction

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• Anomalous energy diffusion in two-dimensional nonlinear lattices
• Interaction of phonons with discrete breather in strained graphene
• One-dimensional Superdiffusive Heat Propagation Induced by Optical Phonon-Phonon Interactions
• Geometry induced local thermal current from cold to hot in a classical harmonic system
• Universal scaling for recovery of Fourier's law in low-dimensional solids under momentum conservation
• Thermal Conduction in one dimensional ${\Phi }^4$ chains with colliding particles
• Enhanced mobility of high-frequency discrete breathers in a monatomic chain with odd anharmonicity
• Unusual slow energy relaxation induced by mobile discrete breathers in one-dimensional lattices with next-nearest-neighbor coupling
• Subdiffusive Energy Transport and Antipersistent Correlations Due to the Scattering of Phonons and Discrete Breathers
• Weighted average temperature as the effective temperature of a system in contact with two thermal baths