Derivation of fluctuating hydrodynamics and crossover from diffusive to anomalous transport in a hard-particle gas

Abstract

A recently developed non-linear fluctuating hydrodynamics theory has been quite successful in describing various features of anomalous energy transport. However the diffusion and the noise terms present in this theory are not derived from microscopic descriptions but rather added phenomenologically. We here derive these hydrodynamic equations with explicit calculation of the diffusion and noise terms in a one-dimensional model. We show that in this model the energy current scales anomalously with system size $L$ as $\sim L^{-2/3}$ in the leading order with a diffusive correction of order $\sim L^{-1}$. The crossover length ${\ell }_c$ from diffusive to anomalous transport is expressed in terms of microscopic parameters. Our theoretical predictions are verified numerically.

arXiv comment12 pages, 3 figures

References in corpus (20)

• Thermal conduction in classical low-dimensional lattices
• Heat Transport in low-dimensional systems
• Anomalous heat conduction in one dimensional momentum-conserving systems
• Nonlinear fluctuating hydrodynamics for anharmonic chains
• On the anomalous thermal conductivity of one-dimensional lattices
• Exact results for anomalous transport in one dimensional Hamiltonian systems
• A momentum conserving model with anomalous thermal conductivity in low dimension
• Heat transport in low dimensions: introduction and phenomenology
• Local Temperature and Universal Heat Conduction in FPU chains
• Intriguing Heat Conduction of a Polymer Chain
• On the universality of anomalous one-dimensional heat conductivity
• Constraint driven condensation in large fluctuations of linear statistics
• A stochastic model of anomalous heat transport: analytical solution of the steady state
• Current fluctuations for anharmonic chains in thermal equilibrium
• Density Profiles in Open Superdiffusive Systems
• Coarsening dynamics in a simplified DNLS model
• Nonequilibrium dynamics of a stochastic model of anomalous heat transport: numerical analysis
• The Fourier heat conduction as a strong kinetic effect
• Temperature profile and boundary conditions in an anomalous heat transport model
• Long range correlations in stochastic transport with energy and momentum conservation

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• Microscopic theory of the fluctuating hydrodynamics in nonlinear lattices
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• L{é}vy walks on finite intervals: A step beyond asymptotics
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• Origin of universality in the onset of superdiffusion in Lévy walks
• Nonanomalous heat transport in a one-dimensional composite chain
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• A Novel Mechanism of Ordering in a Coupled Driven System: Vacancy Induced Phase Separation
• Infinite-temperature thermostats by energy localization in a nonequilibrium setup