Thermal transport in the Fermi-Pasta-Ulam model with long-range interactions

Abstract

We study the thermal transport properties of the one dimensional Fermi-Pasta-Ulam model ($\beta$-type) with long-range interactions. The strength of the long-range interaction decreases with the (shortest) distance between the lattice sites as ${distance}^{-\delta }$, where $\delta \ge 0$.Two Langevin heat baths at unequal temperatures are connected to the ends of the one dimensional lattice via short-range harmonic interactions that drive the system away from thermal equilibrium. In the nonequilibrium steady state the heat current, thermal conductivity and temperature profiles are computed by solving the equations of motion numerically. It is found that the conductivity $\kappa$ has an interesting non-monotonic dependence with $\delta$ with a maximum at $\delta =2.0$ for this model. Moreover, at $\delta =2.0$, $\kappa$ diverges almost linearly with system size $N$ and the temperature profile has a negligible slope, as one expects in ballistic transport for an integrable system. We demonstrate that the non-monotonic behavior of the conductivity and the nearly ballistic thermal transport at $\delta =2.0$ obtained under nonequilibrium conditions can be explained consistently by studying the variation of largest Lyapunov exponent ${\lambda }_{max}$ with $\delta$, and excess energy diffusion in the equilibrium microcanonical system.

arXiv comment8 pages, 9 figures

References in corpus (34)

• Thermal conduction in classical low-dimensional lattices
• Phononics: Manipulating heat flow with electronic analogs and beyond
• Discrete Breathers
• Thermal diode: Rectification of heat flux
• Statistical mechanics and dynamics of solvable models with long-range interactions
• Engineered 2D Ising interactions on a trapped-ion quantum simulator with hundreds of spins
• Heat Transport in low-dimensional systems
• Artificial "spin ice" in a geometrically frustrated lattice of nanoscale ferromagnetic islands
• Controlling the energy flow in nonlinear lattices: a model for a thermal rectifier
• The Fermi-Pasta-Ulam problem: 50 years of progress
• Spread of correlations in long-range interacting quantum systems
• Spin Correlations in Ho${}_2$Ti${}_2$O${}_7$: a Dipolar Spin Ice System
• Anomalous heat conduction and anomalous diffusion in one dimensional systems
• Asymmetric Properties of Heat Conduction in a One-Dimensional Frenkel-Kontorova Model
• Long Range Order at Low Temperature in Dipolar Spin Ice
• Finite thermal conductivity in 1d lattices
• Nonequilibrium Statistical Mechanics of Systems with Long-Range Interactions: Ubiquity of Core-Halo Distributions
• Thermodynamics and dynamics of systems with long-range interactions
• Long-range interacting rotators: connection with the mean--field approximation
• Dynamical heat channels
• Heat conduction in the α-β-Fermi-Pasta-Ulam chain
• Breathers on lattices with long range interaction
• Fermi-Pasta-Ulam model with long-range interactions: Dynamics and thermostatistics
• Studies of thermal conductivity in Fermi-Pasta-Ulam like lattices
• Validity of Fourier's law in one-dimensional momentum-conserving lattices with asymmetric interparticle interactions
• Diffusion of heat, energy, momentum, and mass in one-dimensional systems
• Increasing thermal rectification: Effects of long range interactions
• Universal threshold for the dynamical behavior of lattice systems with long-range interactions
• Long-range interacting classical systems: universality in mixing weakening
• 1D momentum-conserving systems: the conundrum of anomalous versus normal heat transport
• Role of the range of the interactions in thermal conduction
• Sensitivity to initial conditions of a $d$-dimensional long-range-interacting quartic Fermi-Pasta-Ulam model: Universal scaling
• Ingredients for an efficient thermal diode
• Chaos suppression in the large size limit for long-range systems

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• Hydrodynamics and transport in the long-range-interacting ${\phi }^4$ chain
• Conformal order and Poincar$\acute{\mathrm{e}}$-Klein mapping underlying electrostatics-driven inhomogeneity in tethered membranes
• Heat perturbations spreading in the Fermi-Pasta-Ulam-$\beta$ system with next-nearest-neighbor coupling: Competition between phonon dispersion and nonlinearity
• Non-equilibrium steady states of long-range coupled harmonic chains
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• Heat transport and cooling performance in a nanomechanical system with local and non local interactions
• Thermal resonance in harmonically driven segmented Frenkel-Kontorova lattices with next-nearest-neighbor interactions
• A family of fractional diffusion equations derived from stochastic harmonic chains with long-range interactions
• Quantum thermal rectification via state-dependent two-photon dissipation
• Subdiffusive Energy Transport and Antipersistent Correlations Due to the Scattering of Phonons and Discrete Breathers
• Recent progress on thermal transport in one-dimensional long-range interacting Fermi-Pasta-Ulam-Tsingou lattice systems
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