Microscopic theory of the fluctuating hydrodynamics in nonlinear lattices

Abstract

The theory of fluctuating hydrodynamics has been an important tool for analyzing macroscopic behavior in nonlinear lattices. However, despite its practical success, its microscopic derivation is still incomplete. In this work, we provide the microscopic derivation of fluctuating hydrodynamics, using the coarse-graining and projection technique; the equivalence of ensembles turns out to be critical. The Green-Kubo (GK) like formula for the bare transport coefficients is presented in a numerically computable form. Our numerical simulations show that the bare transport coefficients exist for a sufficiently large but finite coarse-graining length in the infinite lattice within the framework of the GK like formula. This demonstrates that the bare transport coefficients uniquely exist for each physical system.

arXiv comment6+13 pages, 6 figures

References in corpus (26)

• Thermal conduction in classical low-dimensional lattices
• Heat Transport in low-dimensional systems
• Emergent hydrodynamics in integrable quantum systems out of equilibrium
• Anomalous heat conduction in one dimensional momentum-conserving systems
• Nonlinear fluctuating hydrodynamics for anharmonic chains
• Generalized HydroDynamics on an Atom Chip
• Hydrodynamic Diffusion in Integrable Systems
• Kardar-Parisi-Zhang physics in the quantum Heisenberg magnet
• Diffusion in generalized hydrodynamics and quasiparticle scattering
• 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
• Quantum Generalized Hydrodynamics
• Numerical test of hydrodynamic fluctuation theory in the Fermi-Pasta-Ulam chain
• Kardar-Parisi-Zhang Scaling for an Integrable Lattice Landau-Lifshitz Spin Chain
• Relativistic hydrodynamics from quantum field theory on the basis of the generalized Gibbs ensemble method
• Too Close to Integrable: Crossover from Normal to Anomalous Heat Diffusion
• Fluctuating hydrodynamics for a discrete Gross-Pitaevskii equation: mapping to Kardar-Parisi-Zhang universality class
• Derivation of Hydrodynamics from the Hamiltonian description of particle systems
• Interacting and noninteracting integrable systems
• High-temperature spin dynamics in the Heisenberg chain: Magnon propagation and emerging KPZ-scaling in the zero-magnetization limit
• Nonlinear Fluctuating Hydrodynamics for the Classical XXZ Spin Chain
• Energy current correlation in solvable long-range interacting systems
• Heat transport via low-dimensional systems with broken time-reversal symmetry
• Derivation of fluctuating hydrodynamics and crossover from diffusive to anomalous transport in a hard-particle gas
• Stochastic order parameter dynamics for phase coexistence in heat conduction

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• Integrable hydrodynamics of Toda chain: case of small systems
• Super-diffusion and crossover from diffusive to anomalous transport in a one-dimensional system
• Dissipation in Hydrodynamics from Micro- to Macroscale: Wisdom from Boltzmann and Stochastic Thermodynamics
• Energy diffusion in the long-range interacting spin systems
• Chapman-Enskog theory and crossover between diffusion and superdiffusion for nearly integrable quantum gases
• Effect of relative timescale on a system of particles sliding on a fluctuating energy landscape: Exact derivation of product measure condition
• Unifying renormalized and bare viscosity in two-dimensional molecular dynamics simulations
• A Novel Mechanism of Ordering in a Coupled Driven System: Vacancy Induced Phase Separation
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